Laser Cannon

There is a great summary of the various issues of directed-energy weapons. Luke Campbell has an in depth analysis of laser weapons for science fiction on his website, don't miss the on-line calculator for laser weapon pulse parameters. Eric Rozier has another on-line calculator for laser weapons. Rick Robinson's analysis Space Warfare V: Laser Weapons is also quite good. You also might want to look over this 1979 NASA report on using nuclear reactions to directly power a laser beam. (Thanks to Andrew for suggesting this link.)

Before we get to all the boring equations, lets have some juicy details. Say that the habitat module of your combat starship gets penetrated by an enemy laser beam. What happens? Luke Campbell and Anthony Jackson have the straight dope:

That depends on the parameters of the beam.

A single pulse with a total energy of 100 MJ would have the effect of the detonation of 25 kg of TNT. Everyone in the compartment who is not shredded by the shrapnel will have their lungs pulverized by the blast.

That same 100 MJ delivered as 1,000,000 pulses of 100 J each could very well drill a hole. The crew see a dazzling flash and flying sparks. Some may be blinded by the beam-flash. Anyone in the path of the beam has a hole through them (and the shock from the drilling of that personal hole could scatter the rest of them around the crew compartment). Everyone else would still be alive and would now be worrying about patching the hole.

Although it occurs to me that the jet of supersonic plasma escaping from the hole being drilled could have the combined effect of a blowtorch and grenade on anyone standing too close to the point of incidence, even if they are not directly in the beam. The effect would probably be similar to the arc flash you can get in high power, high voltage electrical systems, where jets of superheated plasma can cause severe burns from contact with the plasma, blast damage from the shock waves, blindness from the intense light produced, and flash burns from the radiated heat.

A continuous beam could have enough scattered and radiant heat to cause flash burns to those near the point of incidence, along with blinding those who are looking at the point of incidence when the beam burns through. If it burns a wide hole, people die quickly when the compartment explosively decompresses, throwing everyone into deep space. If it burns a narrow hole, the survivors who can see can just slap a patch over the hole to prevent the escape of their air.

Luke Campbell

Luke Campbell said: "Although it occurs to me that the jet of supersonic plasma escaping from the hole being drilled could have the combined effect of a blowtorch and grenade..."

Well, it really depends on what you're standing next to, and on how wide the beam is. The energy release at any point along the beam path will be equal to the energy required to drill through the object (so you'll get pulses of heat from each object hit), and it won't really be explosive. Flash burns is the most likely consequence.

Flash burns start at about 5 J/cm2 on exposed skin, and can go above 100 J/cm2 with reasonable protection. At a range of 1 meter, that requires an energy release of 0.63MJ, and once the beam is substantially inside the object, most of the flash will be deposited on the rest of the inside of the object, so it's really only object shells we need to worry about.

If the beam has an area of 50 square centimeters ( AV:T scale) to emit a total of 630 kJ it must be emitting 12.6 kJ/cm2. About the same amount is probably consumed drilling through the object. 1mm of steel requires about 6 kJ/cm2, so anything with a casing of at least 2mm steel, or anything comparable, will cause flash burns within 1 meter.

This is not particularly terrifying, unless of course the beam drills through something like a high pressure steam line, at which point it's suddenly very exciting, though not because of the laser per se.

Anthony Jackson

Anthony Jackson said: "so you'll get pulses of heat from each object hit, and it won't really be explosive"

My thought was that the shocks could coalesce. All shocks are supersonic to the material they have not gone through, and subsonic to the material they have traveled through. As a consequence, a second shock will catch up to a previous shock until they merge into a single, stronger shock. If the beam is pulsed at a high rate (say, a MHz or so) a good number of the individual blasts could coalesce within a short distance to create a more potent blast that might cause significant problems.

The physics of shocks is tricky, and for spherically expanding shocks you get into issues of rarefaction and backflow, which should limit the number of shocks that can coalesce. While I have a highly recommended text on shock physics, I've not had the time to look through it yet, so I don't have a good idea yet on the limits and possibilities of this mechanism.

There's also the issue that iron heated to 10,000 K, for example, will expand in volume about 150,000 times from its solid phase. So burning a 10 cm wide hole through a 1 cm steel bulkhead would produce a cloud of iron vapor with a volume of about a cubic meter if the final temperature was 10,000 K (note that if the iron was converted to a singly ionized plasma, the temperature would be ten times that much, and you would get ten times the volume). Getting caught in that incandescent cloud simply cannot be healthy.

There's also the ozone and nitrogen oxides and reactive chemicals produced as a consequence of incomplete combustion, which will not be healthy to breathe, but I expect that would be secondary.

Luke Campbell

Luke Campbell said: "My thought was that the shocks could coalesce."

They could if the drilling speed is supersonic. Usually it won't be.

Anthony Jackson


Now for the dull equations.

"Laser" is an acronym for light amplification by stimulated emission of radiation. A laser beam can cut through steel while a flashlight cannot due to the fact that laser light is coherent. This means all the photons in the beam are "in step" with each other. By analogy, a unit of army troops marching in step can inadvertently cause a bridge to collapse, while the same number of people using the bridge in a random fashion have no effect. Laser light at amazingly low energies can still cause permanent blindness by destroying the retina.

Maximum range will be a few hundred thousand kilometers, otherwise almost every shot will miss due to light-speed lag. This is explained in more detail here.

Laser beams are not subject to the inverse-square law, but they are subject to diffraction. The radius of the beam will spread as the distance from the laser cannon increases.

RT = 0.305 * D * L / RL


  • RT = beam radius at target (m)
  • D = distance from laser emitter to target (m)
  • L = wavelength of laser beam (m, see table below)
  • RL = radius of laser lens or reflector (m)
BandWavelength (m)
Far Infrared1e-3 to 5e-5 m (1,000,000 to 50,000 nanometers)
Mid Infrared5e-5 to 2.5e-6 m (50,000 to 2,500 nanometers)
Near Infrared2.5e-6 to 7.5e-7 m (2,500 to 750 nanometers)
Red7.5e-7 to 6.2e-7 m (750 to 620 nanometers)
Orange6.2e-7 to 5.9e-7 m (620 to 590 nanometers)
Yellow5.9e-7 to 5.7e-7 m (590 to 570 nanometers)
Green5.7e-7 to 4.95e-7 m (570 to 495 nanometers)
Blue4.95e-7 to 4.5e-7 m (495 to 450 nanometers)
Indigo4.5e-7 to 4.2e-7 m (450 to 420 nanometers)
Violet4.2e-7 to 3.8e-7 m (420 to 380 nanometers)
Ultraviolet A4e-7 to 3.15e-7 m (400 to 315 nanometers)
Ultraviolet B3.15e-7 to 2.8e-7 m (315 to 280 nanometers)
Start of
Vacuum Frequencies
2.e-7 m (200 nanometers)
Ultraviolet C2.8e-7 to 1e-7 m (280 to 100 nanometers)
Extreme Ultraviolet1e-7 to 1e-8 m (100 to 10 nanometers)
Start of
Ionizing Radiation
1e-8 m (10 nanometers)
Soft X-Ray1e-8 to 2e-10 m (10 to 2e-1 nanometers)
Hard X-Ray2e-10 to 2e-11 m (2e-1 to 2e-2 nanometers)
Gamma-Ray2e-11 to 1e-13 m (2e-2 to 1e-4 nanometer)
Cosmic-Ray1e-13 to 1e-17 m (1e-4 to 1e-8 nanometers)

Use horizontal scroll bar to pan the spectrum right and left.

Note that wavelengths shorter than 200 nanometers are absorbed by Terra's atmosphere (so they are sometimes called "Vacuum frequencies") and anything shorter than 10 nanometers is considered "ionizing radiation" (i.e., what the an average person on the street calls "atomic radiation"). Vacuum frequencies will be worthless for a laser in orbit attempting to shoot at ground targets protected by the atmosphere.

Sometimes wavelengths are expressed in Ångström units, 1.0 Ångström = 0.1 nanometer.

More to the point is the intensity of the beam at the target. First we calculate the beam divergence angle θ

θ = 0.61 L/RL


  • θ = beam divergence angle (radians)
  • L = wavelength of laser beam (m, see table above)
  • RL = radius of laser lens or reflector (m)

Note that this is the theoretical minimum size of the divergence angle, it will be larger with inferior lasers.

Next we decide upon the beam power BP, then calculate the beam intensity at the target (the beam "brightness"):

BPT = BP/(π * (D * tan(θ/2))2)


  • BPT = Beam intensity at target (megawatts per square meter)
  • BP = Beam Power at laser aperture (megawatts)
  • D = range to target (meters)
  • θ = Theta = Beam divergence angle (radians or degrees depending on your Tan() function)
  • π = Pi = 3.14159...

Kerr notes that if you already know the beam radius at target RT, the above equation simplifies to:

BPT = BP/(π * RT2)

There are a few notes on laser firing rates and power requirements here.

In the US military, the minimum threshold for a tactical weapons-grade laser is 100 kilowatts.

In the US military, the minimum threshold for a strategic weapons-grade laser is 1 megawatt.

When figuring the tangent, remember that θ from the beam divergence angle equation is in radians, not degrees (Divide radians by 0.0174532925 to get degrees).

What this means is if you are calculating the Beam Intensity equation with a pocket calculator or the Windows calculator program, the calculator is generally set to degrees and it expects you to punch in the angle in degrees before you hit the TAN key. If you punch in the angle in radians you will get the wrong answer.

If instead you are calculating the Beam Intensity equation with a computer spreadsheet or with a computer program you are writing from scratch, the TAN() function wants the input angle to be in radians.

For comparison purposes, the average beam intensity of sunlight on your skin is about 0.0014 MW/m2.

Please note that the amount of beam power deposited on the target is still BP, the intensity just measures how tightly it is focused. It's like using sunlight through a magnifying glass to burn a hole in a piece of paper (or to incinerate ants if you were one of those evil children). The amount of beam power hitting the paper does not change, it is always BP. But if the magnifying glass is so close that the spot size is large, the paper will just get warm. If you move the glass so the spot focuses down to a tiny dot, the intensity increases and the paper spot starts to burn.

Also note that a laser cannon might have lens/mirror which is larger than strictly required for the desired spot size, due to the fact that otherwise the mirror would melt. The larger the mirror, the more surface area to dilute the beam across, and the less the thermal stress on the mirror.


The good ship Collateral Damage becomes aware of an incoming hostile missile. Collateral Damage has a laser cannon with a ten meter diameter mirror operating on a mid-infrared wavelength of 2700 nanometers (0.0000027 meters). The divergence angle is (1.22 * 0.0000027) / 10 = 0.00000033 radians or 0.000019 degrees.

The laser cannon has an aperture power of 20 megawatts, and the missile is at a range of four megameters (4,000,000 meters). The beam brightness at the missile is 20 / (π * (4,000,000 * tan(0.000019/2))2) = 15 MW/m2 or 1.5 kW/cm2.

If the missile has a "hardness" of 10 kilojoules/cm2, the laser will have to dwell on the same spot on the missile for 10/1.5 = 6.6 seconds in order to kill it.

Figured another way, at four megameters the laser will have a spot size of 0.66 meters in radius, which has an area of 1.36 square meters. The missile's skin has a hardness of 10 kilojoules/cm2 so 13,600 kilojoules will be required to burn a hole of 0.66 meters radius. 20 megawatts for 6.9 seconds is 13,600 kilojoules. 6.9 seconds is close enough for government work to 6.6 seconds.

Eric Henry has a spreadsheet that does most of this calculation for you here.

In the game Attack Vector: Tactical, the smallest laser lens is three meters in diameter, the frequency of various models of cannon is from 0.0000024 meters (2400 nanometer) to 0.0000002 meters (200 nanometer) and the efficiency varies from 20% down to 1.5%.


Say you have an ultraviolet (20 nanometer) laser cannon with a 3.2 meter lens. Your hapless target spacecraft is at a range of 12,900 kilometers (12,900,000 meters). The Beam Radius equation says that the beam radius at the target will be about 4 centimeters (0.04 meters), so the beam will be irradiating about 50 cm2 of the target's skin (area of circle with radius of 4 centimeters). If the hapless target spacecraft had a hull of steel armor, the armor has a heat of vaporization of about 60 kiloJoules/cm3. Say the armor is 12.5 cm thick. So for the laser cannon to punch a hole in the armor it will have to remove about 625 cm3 of steel (volume of cylinder with radius of 4 cm and height of 12.5 cm). 625 * 60 = 37,500 kiloJoules. If the laser pulse is one second, this means the beam requires a power level of 37,500 watts or 38 megawatts at the target.

In practice, a series of small pulses might be more efficient, causing a shattering effect and driving chips of armor out of the hole, which of course requires less energy than actually vaporizing the armor.


 Laser weapons are what the general public thinks of when asked to describe space weapons.  They have a number of advantages in the space environment, but also suffer from significant drawbacks.

Lasers are obviously made of light, and this drives their performance.  First off, they obviously propagate at the speed of light.  This makes them almost impossible to dodge at PMF ranges, which will be discussed below.  At the same time, the fact that they are composed of light causes laser to fall off with range, as opposed to kinetics, which do not.  Lasers have a minimum size they can focus their beam spot to that is limited by diffraction.  This is at the point where the beam is focused.  It is described by the equation

where BD is beam diameter (m), R is range (m), L is wavelength (m), and D is mirror diameter (m).  As can be seen, spot size is proportional to range and wavelength, and inversely proportional to the mirror diameter.  Please note that this equation is the minimum possible spot size.  The actual spot size is also affected by the focus of the laser, which may not be set at the correct distance, and the various real-world factors discussed below.

Some people have claimed that lasers do not follow the inverse square law, and, strictly speaking, this is true.  A fixed-focus laser will not follow the inverse square law.  The beam will initially be diffuse at the emitter, then narrow to the minimum spot size at the focal point, then widen again as it passes that point.  A side profile of the beam will look something like an hourglass.  However, a variable-focus laser will effectively obey the inverse-square law.  From the equation above, note that beam diameter scales linearly with R, range to target. Area will be proportional to the square of diameter. Intensity or flux will be inversely proportional to area, which is proportional to the square of distance.

All of the above analysis assumes an ideal, diffraction-limited beam.  This is obviously not the case in reality, and a more realistic equation is

where BD, R, L, and D mean the same as in the equation above, Q is beam quality, a dimensionless measurement of the actual beam diameter to the theoretical beam diameter, and J is jitter in radians.  Typical values for Q for modern lasers are generally less than 3, and likely below 1.5.  Numbers for jitter, which is caused by vibration of the platform, are harder to come by, but on the Airborne Laser Laboratory in the 1980’s, jitter numbers of around 25 microradians (25×10-6radians) were achieved.  It is not unreasonable to assume that a two order of magnitude reduction in this number could be achieved between technological development and the fact that the ALL was mounted on an aircraft in the atmosphere, and it is entirely possible that significant farther reductions are possible.  As a word of caution, this equation only holds true for Continuous-wave (CW) lasers, and the author is unsure of the impact of jitter on pulsed lasers.  It is possible that some or all of the jitter will instead become pointing error for a pulsed laser, significantly increasing the efficiency of such vis à vis CW lasers.

The potential issues caused by vibration are such that it is likely that a laserstar’s designer will pay as much attention to them as the designer of a ballistic missile submarine does to noise.  Current texts on space optical communications systems (Deep Space Optical Communications, JPL) indicate that there is potential for sub-microradian pointing accuracy and active jitter control.  Passive vibration damping can remove the low-frequency components of the vibration, and severely attenuate the high-frequency ones.  However, these are for low-powered communication laser systems with small optics operating in the relatively benign environment of a satellite, not large mirrors and high-power laser systems on a thrusting spacecraft with active cooling systems.  The exact impact of these factors is unknown at the present.

One interesting fact contained in the same book was that modern optical communication jitter compensation relies at least partly on a low-power laser from the target providing a reference for the optics.  This means that an attempt to blind an opponent could actually tend to make their lasers more accurate, although there were no details about the specific requirements of the process.

Beam quality and jitter are helpful to the hard SF author, as they allow him to reduce the potency of lasers.  Jitter is particularly helpful for this purpose, as it affects larger mirrors proportionately more than small ones.  The minimum spot size for a jitter-limited mirror will be BD = 2JR, and the spot size according to the above equation approaches that value as the mirror grows.  In a setting with high jitter, the limit on mirror size might be the diminishing returns of the effect on spot size instead of manufacturing processes or cost.

Space is an environment that is uniquely suited for laser weapons.  The lower the wavelength of the beam, the smaller the spot size of the laser is.  However, it is generally more difficult to generate lower wavelengths, and wavelengths shorter than the visible are strongly absorbed by the atmosphere.  This is obviously not a problem in space, unless the laser must also be capable of planetary bombardment.  Very low wavelengths, in the X-ray region and below, begin to suffer unusual interactions with matter, which prevents the use of optical mirrors.  Grazing mirrors and diffraction gratings must be used instead, which significantly complicates the optical train.  

All of the above looks only at the beam as it emerges from the mirror, and ignores what occurs inside the laser system.  While the only critical facts are output power, input power, wavelength, mass, and efficiency, this area deserves a closer look.  First, the laser beam has to be generated.  The methods available can be divided for our purposes into chemical and solid-state.  Both of these are used here more loosely then is strictly accurate under the technical definition.  Chemical lasers are any lasers that require an expendable fuel for the lasing mechanism.  Almost all modern military lasers fall into this category.  Solid-state lasers use electricity to generate the laser beam.  They have significant logistical advantages over chemical lasers, but are more difficult to build.  Chemical lasers have the advantage of not requiring large power sources, and the fact that the dumping of the reaction products provides built-in heat rejection.  A solid-state laser will have to either store or radiate heat, both from the reactor and the laser mechanism itself.  The power that must be dealt with in the form of heat will almost certainly be several times greater than the power released in the beam.

  Once the beam is generated, it must then be formed and routed to the mirror.  The difficulty of this will depend on how deep in the vessel the laser generator is located.  There is no reason that it could not be mounted deep in the vessel, far away from possible damage.  This will likely require extra mirrors, and raises the possibility of damage to the optics train from shock.  If the laser system is modular, it is obviously necessary to mount the generator close to the hull.  The ultimate extension of this principle is to have exactly one laser generator mounted in the core of the ship, and direct the beam out among the various mirrors on the ship.

Mirrors can obviously be divided into two types, either turreted or fixed.  Turreted mirrors obviously benefit from a much wider field of fire then provided by fixed mirrors. A fixed mirror will still be capable of limited steering due to adaptive optics and the necessity of fine pointing capabilities, but probably no more than a few degrees.  It benefits from a significantly less complex beam path, and is likely to be capable of more accurate pointing.  Thus, fixed mirrors are likely to be used for primary weapons while turreted ones are used for kinetic defense.

At this point, we’ve followed the beam to the target.  Once it gets there, it still has to disable the target.  There are multiple methods by which this could occur.  First, laser damage mechanisms depend on the type of laser, continuous-wave or pulsed.  CW lasers operate at a constant power for long periods, and do damage by heating the target until the surface vaporizes.  Pulsed lasers fire a string of very high powered pulses at the target.  The damage they deal is compounded by mechanical effects from the flash-vaporization of the target material.  Pulsed lasers are generally more energy-efficient for a given level of damage, and would be expected to be used unless technical constraints made them impractical.

In either case, it can begin to do damage far before it can begin to burn through armor.  Delicate systems on the outside of the ship, most notably sensors and thrusters, are vulnerable to far lower levels of laser radiation.  This can be dealt with by proper design and networking.  Armoring schemes will involve a heavy faceplate in the front, and much lighter protection on the sides.  The faceplate systems will be built with the assumption that they will be damaged or destroyed during the course of the battle, and operations planned around that fact.

The other object that will dominate the faceplate of a laserstar is the main laser itself.  This has multiple consequences.  First, the laser in question is vulnerable to being shot at itself.  It has been proposed to use some form of shutter to prevent this from happening, but that raises the issue of time to open and close the shutters, during which the laser is vulnerable and unable to fire.  Some commentators have proposed that battles between laserstars will turn into eyeball-frying contests where the first person to burn out the other’s mirror wins.  The logic runs that the engagement will begin at ranges where the spot size is similar to the mirror size.  When one laser hits another, the target laser’s mirror will focus the beam into the rest of the optics train, destroying it.  Furthermore, the laser is also the ship’s best sensor system.  In between shots, it can also function as a telescope with resolution comparable to spot size provided that the observation is made in a similar wavelength to that which the laser operates at.  It has been claimed that this capability will give the laser the ability to target specific points on a target, particularly the mirrors of the opposing ship.

It has been suggested that turreted lasers would not need shutters, as they could be protected by simply turning them inward and armoring the back side.  This might be a viable suggestion for small turrets with nearly complete rotation arcs, but larger turrets would probably be significantly less massive with a shutter and limited arcs.  

A proposed alternative to conventional shutters is the use of some sort of electrically-activated material which changes from opaque to transparent when a current is applied.  This concept shows promise in reducing shutter time during a laser duel, as the lag time will be negligible, possibly low enough to synchronize with a pulsed laser.  A serious potential problem with this approach is that the material will not be transparent enough to be capable of safely having the laser fired through it.  Another problem is that the material will be itself damaged by kinetic impacts, hindering transmission of the laser and leading to more damage to the material when the laser is fired.  This fact necessitates the use of an additional moving shutter to defend against kinetics.

A very similar, and perhaps more effective, option for a shoot-through anti-laser lens would be a polarized covering.  All lasers are inherently polarized, and the chance of an enemy’s laser having the same polarization is miniscule.  This, however, suffers from the same problems as the previous solution.  The transparency requirements are very demanding, and the lens itself is vulnerable to damage from kinetics and from other lasers. Such lenses are only useful if eyeball-frying contests are the norm, which appears unlikely.

The problem with the eyeball-frying theory is pointing error.  The simple fact is that the laser will probably not be capable of being pointed with angular accuracy comparable to the divergence angle of the beam for any number of reasons.  There are also questions about the vulnerability of lasers to other lasers.  It is quite likely that small portions of the mirror will fail instead of the entire system, and these failures can be compensated for by the control system for the adaptive optics. This would be more likely to produce a slow degradation of the system then a quick kill.

One interesting suggestion from John Lumpkin’s Through Struggle, The Stars is counterbattery lasers.  These are specialized high-speed laser systems designed to shoot back at attacking lasers and disable their mirrors.  The author finds it unlikely that dedicated systems would be implemented for the role, but it is possible that shootback software would be added to the control systems for some or all of a vessel’s lasers.  The effectiveness of said solution depends heavily on the ability to very precisely point the lasers, and the effectiveness of a laser against a mirror.

Another possibility for the use of lasers is sensor blinding.  Even if the intensity is too low to do any permanent damage, the laser would be quite effective at jamming sensors operating in the same wavelength.  The problem with this tactic is twofold.  First, it requires the laser to be matched to the sensors.  This is unlikely to be the case for most vacuum-frequency lasers, as spotting will likely be done in visible or IR spectra.  Second, it requires the use of the laser, which might be more urgently required for other tasks.  The solution to both problems is quite simple.  Dedicated jamming lasers are quite feasible, given that the required mirror is small and the power levels needed are generally modest compared to those necessary to kill other vessels.

Defending against lasers is difficult.  One common suggestion is mirrored armor, but this has significant practical problems.  The first and simplest is that the mirroring only works against the first shot.  Any mirror is not a perfect reflector, and will absorb some of the incident energy.  At long ranges, this might be useful, but as the range closes, even that small amount of energy will be enough to melt the outer layer of the mirror, which in turn will destroy its reflective properties, leaving the vessel exposed to further shots.  A normal mirror might have a reflectivity as high as 99.9%.  A rough calculation suggests that for an aluminum outer skin, the beam intensity would have to be on the order of 40 MW/m2.  Any other materials would require significantly higher intensities.  This suggests that a pulsed beam would be more effective than a CW laser.  The above calculation was based entirely on blackbody radiation, and ignores any number of complications.  The author is unfamiliar with the response of reflective materials to laser radiation, but it does not seem outside the realm of possibility that the reflectivity could be significantly impaired by much lower rises in temperature.  It is also unlikely that 99.9% reflectivity could be maintained on an operational spacecraft.  This number reflects the maximum for conventional mirrors under laboratory conditions.  The outer hull of a warship is far from the lab, and is exposed to things like solar wind and micrometeorites, which would likely limit the practical reflectivity to 99% at most.  While it might be possible to put some form of protective covering on the armor and jettison it before battle, that limits the tactic to once per mission, and would require considerable effort to implement.

However, the author did run across an interesting suggestion for a type of mirrored armor in an Air Force research paper. (The Use of Liquid Film for Spacecraft Survivability to Laser Radiation, DTIC.)  To defend against IR lasers, a graphite sample was coated with a thin layer of tungsten carbide.  When the laser was fired at the sample, the tungsten carbide melted, but remained on the surface, allowing the carbon vapor to pass through it when the carbon was vaporized.  Because the tungsten carbide absorbed only about 25% of the laser’s energy, instead of approximately 80% for the graphite, the amount of energy required to vaporize a unit mass of graphite increased by a factor of 3.  While this is an intriguing idea, there are massive uncertainties in trying to apply it to other wavelength and material combinations.  At a guess, the protected material needs to vaporize instead of melting, limiting choices to carbon-based materials.  Also, the film must melt at a lower temperature than the protected material vaporizes at, and yet have as high a boiling point as possible, to prevent it from being burned off.

One might point out that the laser has to be focused by a mirror, and that the same mirror should be capable of being used as armor.  The problem with this suggestion is that the mirrors used for lasers are not conventional mirrors, but dielectric mirrors.  A dielectric mirror is made of numerous thin sheets of dielectric material, and is optimized for a particular wavelength and direction.  Over that narrow band, reflectivity could be as high as 99.999%, but the mirror is significantly less reflective against any other incoming light sources.  To use this type of mirror as armor, one would have to know the exact wavelength of an opponent’s weapons, and be able to control the direction on an engagement.  Both of these are unlikely in practice, as any power will undoubtedly use slightly different wavelengths on different craft to defeat these tactics, and it is unlikely that one could control the engagement well enough to keep the enemy in the proper zone, certainly not likely enough to be worth the expense of fitting dielectric armor to a spacecraft.

An interesting idea that was raised involved using a laser beam against itself, with the example given of the retroreflectors used on the Apollo missions. This approach suffers from all the problems of mirror armor, and even if said problems could be overcome, there are other significant issues with bouncing the beam back at its source. Quite simply, it is impossible to return sufficient power to the firer to achieve anything of note. In the best-case scenario, that of a flat mirror perpendicular to the beam, the intensity when the beam returns to the firing ship will be only one-fourth the intensity at the target. If the target can maintain an optical surface under the impact of the beam, the firer will have no difficulty doing so. Also, this is a set of ridiculously optimistic assumptions. The reflectors used on Apollo were corner reflectors, which are used on many reflective objects. In theory, they should perform exactly as a flat mirror would, no matter what direction the incident beam comes from.  In reality, they do an excellent job reflecting in the general direction of the incident beam, but it's nowhere near precise enough for what this concept would require. It might somewhat dazzle the shooter at long range, but it is unlikely to do more before the reflectors themselves burn off, particularly given the fact that they cannot employ dielectric mirrors. While corner reflectors have the advantage of reflecting no matter what direction the signal comes from, other methods (such as the aforementioned flat mirror) do not, which means they need pointing capabilities on par with the laser itself, and have to deal with higher energy fluxes than the laser optics. Coupled with the issues described above, it seems vanishingly unlikely that reflecting a laser back to its target will be a practical countermeasure to laser firepower.

Another option is some form of particle screen such as the Traveller sandcasters.  One problem with this proposal is that it is less mass-efficient than conventional armor.  When the particle is struck by the laser, it flashes to plasma, which then begins to disperse.  The plasma initially blocks the laser beam, but as it disperses and the density drops, the laser beam continues on.  If conventional armor is being used, the laser has to bore a hole, and the plasma is generated at the back of the hole.  The hole contains and channels the plasma, keeping it in the path of the beam and preventing it from dispersing.  The only form of particle screen that could prove practical is one made of small crystals such as diamonds.  Instead of absorbing the beam, it refracts it, dispersing it and reducing the intensity on the target.  Small ice crystals have also been suggested for use in this role, but the ice will sublimate even without taking laser fire, and a high-power laser will tend to turn the ice to vapor or plasma even more quickly.

The other issue with particle screens is even simpler.  They are expendable and not attached to the vessel in question.  At best, it is only effective for one battle, and only so long as the vessel does not maneuver.  This ignores issues of particle dispersion.  The screen must be deployed somehow, and that is likely to involve throwing the particles out at significant speed.  This dispersion will not stop when the screen is at the proper density, forcing the deployment of additional screens.  The screen also stops the vessel from returning fire with lasers, and will significantly interfere with any kinetic weapons.  Missiles launched from the vessel would be largely unaffected, except for the holes punched in the cloud. However, any launcher projectiles would likely be severely damaged by it as they passed through, as would any incoming projectiles.  The other issue is targeting of kinetics through the cloud, particularly as the vessel itself would be unable to use its sensors.  The used screen particles would also persist, and would serve as a significant constraint on maneuver.  Even at low velocity, the particles would be potentially damaging to mirrors.  This neglects the fact that the particles might constitute a significant debris hazard after the battle, depending on the deployment situation.

“Smokescreens” have also been suggested, intended to block observation instead of interfering with the laser itself.  The screened area would be significantly larger than the vessel, so the enemy is uncertain as to its location. The need for only optical thickness significantly reduces the mass requirements, but has other issues.  Achieving the required particle density and cloud size on a reasonable timescale will be extremely difficult, and the vessel would have to maneuver to take advantage of the uncertainty.  It would also be possible to burn paths through the cloud without too much difficulty, possibly revealing the position of the vessel.

All of the above refers to the use of particles defensively.  It is, however, at least somewhat more practical to use them offensively against laser-armed targets.  This would involve the use of kinetics filled with particles, referred to here as sand, and a bursting charge, which, when fired, spreads out and threatens to damage the optics of any laser in its path.  The laser operator has three options: accept the damage, try to burn the cloud away, or shutter the laser when the cloud hits.  The sand projectiles would be mixed in with the standard ones, and at some point shortly before impact, the burster fires, spreading the sand out and slightly ahead of the rest of the projectiles.  The various sand shells will stagger their bursts and spread their clouds out along the axis of flight to threaten the enemy for the longest possible time.  The biggest advantage is that the laser is interdicted precisely when it is the most effective (namely, when the incoming projectiles are at short range.)

Note that this is a surface-effect warhead, not simply a projectile throwing out small pieces of shrapnel.  The particle sizes are so small that they are ineffective against anything not requiring a precision surface.

The actual math involved is quite interesting, and suggests that the projectiles could be reasonably effective.  For a given mirror, amount of damage, and particle diameter, the mass per unit area required remains constant no matter what the density.  Smaller particles are more effective per unit mass than large ones, with mass required scaling with diameter^.92.  This suggests that whatever fine powder is available is the most effective.  However, there are two complicating factors.  First, ideally the density of the sand warhead will be the same as the density of a conventional warhead, so the enemy can’t tell it apart before it breaks.  Thus, low-density materials like sawdust might be poor choices.  Second, it is possible to defend against the cloud by burning a hole in it.  The amount of time it takes to burn this hole depends on the diameter and material of the projectile, with carbon-based materials significantly outperforming stone or metal.

The exact optimum material and diameter will depend on the situation, but a representative calculation will show that the masses involved are reasonable. (Based on Micrometeor Damage Estimate to the MOLA II Primary Mirror.) Taking a beryllium mirror, .5mm particles impacting at 30 km/s, and a requirement to damage 10% of the mirror’s surface, the total mass will be 5.1e-3 kg/m2.  Taking as the target a laserstar with a 10-meter, 1 GW laser, the total time to clear the particles will be 1.67 seconds for steel, 8.15 seconds for nanotubes, and 1.32 seconds for granite.  These are theoretical values, based on the laser spreading its power evenly over a circle equal to its mirror diameter and assuming that the particle must be completely burned away.   In reality, the vaporizing particle material will impart thrust to the rest of the particle, which might push it enough to render it harmless.  Larger particles would increase the time required, probably directly in proportion to the mass per unit area.

If we assume that the value above is representative of various sand warheads, we can then look at the total mass requirements.  If the projectile bursts 60 seconds before impact, and the target can dodge at 1 m/s2 (as in the example in Section 8) the total area to cover is 10.18e6 m2.  This corresponds to a warhead mass of 51,911 kg.  Obviously, this is not terribly practical.  However, there were several assumptions made that might change the scenario.  The first is the target’s dodging acceleration.  1 m/s2 may or may not be a plausible dodging acceleration.  At .1 m/s2, the circle has an area of 101.8e3 m2, and the sand mass drops to 519 kg.  Another is that the damage to the mirror is limited to the physical crater itself.  While the author is unfamiliar with the impact of hypervelocity particles on mirrors, intuition suggests that the damage to the optical properties of the mirror might extend well past the physical crater.  On the other hand, intuition is often a poor guide to space warfare.  The fact that the particles are quite easy to clear can be dealt with by sending in multiple projectiles from slightly different angles, so that burning away one set of particles does not affect the others.  Depending on the exact characteristics of the lasers, the few seconds it takes to burn away a set of particles could save several kinetics of equal mass to the launching projectile.

Another method of achieving a similar effect is the use of Jello.  Strange as this may sound, it is used by current BMD systems to discriminate decoys and damage optics.  The jello is released into space and the water flash-boils out, leaving a mass of fine, very hard, sharp granules.  The efficacy of this approach compared to the use of sand as described above is unknown.  The material properties of the particles become less important at higher velocities, and the water that is lost would probably be a significant mass penalty.

Other forms of heavier particle kinetics have been proposed to be used against lightly-armored parts of the spacecraft, most notably the radiators.  These would be more like ball bearings or buckshot, and are intended to puncture the radiator tubes, sending coolant leaking into space.  The efficacy of this sort of attack is unknown at the moment, and the concept requires further study, but it is possible that it would be quite effective.  At some point, however, the projectile will become big enough to be individually targeted, which in turn means that it can be burned out significantly faster than would be possible with a particle.  The author chooses to define particle in this use as a sub-projectile small enough that it is not detected and targeted independently, but must be dealt with by firing at the entire area.

Dodging lasers is possible, but difficult.  The biggest problem is that at any reasonable range, dodging is going to require high acceleration, which in the PMF will involve either chemfuel or nuclear-thermal.  This burns through a very large amount of delta-V very quickly, and limits the amount of time that can be spent dodging.  There are also significant performance penalties in the creation of a ship that is capable of dodging, as it must be capable of high accelerations in all directions.

As an example of the magnitudes involved in the problem, take a 10-meter-diameter cylindrical laserstar at .5 light-seconds.  The laser targeting it is fired instantaneously at the apparent center of the vessel, and is precisely targeted.  To avoid being shot, the laserstar must accelerate at 10 m/s2.  To be able to do this, the vessel would require 4 engines, each capable of 1G, one on each side of the ship.  Alternatively, fewer engines could be used, with the ship rotating to bring them to bear.  This would, however, slow dodging, and make it more predictable.

The above scenario has neglected a number of complications.  These include:

  1. Beam diameter:
    The beam will have nonzero diameter, so in the above scenario, the ship accelerating at 10 m/s2 would still have been hit by about half the beam. This would increase the delta-V required to avoid a hit.
  2. Perfect dodging:
    It has been assumed that the ship began dodging at the instant the enemy would have opened fire (relative to light lag), and was able to hold a course the entire time. Neither of these assumptions bear any resemblance to reality, tremendously complicating dodging. Dodging would require that (if the enemy was aiming at the center of the ship) that no part of the ship was in the same line as the center was 1 second previously, and was not accelerating in a straight line.
  3. Beam inaccuracy:
    This can either help or hinder dodging. If the diameter of the inaccuracy circle was 10 meters, and the hit probability for each area was constant, dodging as described would reduce hit probability to about .333 instead of 1. However, if the circle had a diameter of 20 meters, then dodging at 10 m/s2 would be useless, as the hit probability would remain the same.

On a slightly more theoretical level, this scenario suggests several rules related to dodging. First, the required delta-V will scale inversely with distance, while the acceleration will scale with the square of distance. Second, if the target is able to accelerate faster, it can cut the required delta-V. The theoretical minimum is the circle radius/time. If constant acceleration is used, then the required delta-V is double that of the theoretical minimum.

There is an alternative to the conventional large mirrors in the form of phased arrays.  A phased array is composed of a number of synchronized transmitting elements.  The beam is formed by the interference patterns between the different elements, and can be steered instantaneously by varying the transmission lag between the elements.  It is also possible to split the beam into multiple sections of varying power.  This is a significant advantage for point-defense use.  On the other hand, the phased array is less effective for a given aperture area/overall diameter then a conventional mirror.  However, given sufficiently large numbers of transmitting elements, it is entirely possible that the phased array will be capable of very similar performance to a conventional mirror, and at significantly lower cost.  This suggests that a laserstar might have a single large mirror and a phased array for point defense.  The phased array also has logistical advantages.  Particularly if all of the lasers in the fleet are phased arrays, the transmitters can be modular and mass-produced, not to mention field-replaceable.  It’s also possible that the transmitters will be more damage-resistant then a conventional laser.  At the very least, each transmitter can be individually shuttered, and the small size of the required shutter makes it easier to engineer a high shutter speed.

It might also be possible to use the instantaneous response of the phased array to correct for some of the vibration inherent in a laserstar, above and beyond what is possible with conventional mirrors.  First, each element can probably be isolated individually, making the system smaller and lighter, and quite possibly more effective.  Second, the phased array can be used to compensate for vibration with greater accuracy then adaptive optics, due to the electronic pointing capabilities.  In fact, phased array pointing accuracy angles are often smaller than the spot size for the array.  Phased arrays are also inherently more tolerant of jitter than are conventional mirrors.  A phased array will have the same apparent jitter as a large mirror with individual element jitter that is equal to the square root of the number of elements times the unitary mirror jitter.

It has been suggested that instead of an eyeball-frying contest, a “tumbling pigeon” approach could be used.  The laserstars would be making random attitude changes throughout the approach, which occasionally exposes the mirror for a snap shot.  Except in the case on an extremely lucky hit, neither vessel can scorch the other’s mirror.  The problem with this approach is that it significantly complicates the design of the vessel.  A conventional laserstar has a faceplate designed to receive enemy fire, while a pigeon will receive fire from all around.  Among other things, this renders the use of radiators in battle impossible.

As laser weapons continue to develop, more information about them becomes available to the public.  However, because of the classified status of most developments, the information we do receive is out of date, probably by about 5 years.  Furthermore, most of it is only of limited relevance to space warfare.  For example, the US Navy’s Laser Weapon System, which recently went to sea aboard the USS Ponce, is composed of six solid-state welding lasers fastened together for a total power of 33 kW.  It has a mirror of approximately 1 meter diameter, and is designed to kill aircraft and small boats at short range.  A 1 km, the diffraction-limited beam diameter is only 1.22 mm, and the beam will drill through steel at a rate of approximately 60 cm/s.  At 10 km, however, even a diffraction-limited beam can only drill through steel at around 1.5 cm/s.  Most surface-based lasers get their performance in a similar manner, as the horizon forces them to fight at close range.  A spacecraft, however, does not normally have a horizon to hide behind and much use much larger mirrors and much higher power to deal damage at long range.  This produces a fundamentally difference in character between laser engagements on the surface and in space.  On the surface, laser battles are over almost instantly, as one side or the other gets the first shot in.  In deep space, long lines of sight allow both sides to open fire as soon as they could begin doing damage, slowing the battle down.  If the craft did close to point-blank range, their lasers would become incredibly lethal, but both sides would be aware of this and probably avoid tactical geometries that lead to such situations.

It has also been suggested that a battle between laserstars will be resolved by damage control.  The sensors and mirrors would be replaceable, and whoever can do so fastest would win.  The problem with this theory is the size and expense of the mirrors, along with the precision mounting requirements.  The optimum ratio of lasers to mirrors can be derived to show why this concept is impractical.  

At short ranges (maximum possible crater size exceeds minimum possible spot size):

At long ranges (minimum possible spot size exceeds maximum possible crater size), drill rates will be proportional to:


or to


(and to 1/range^3).

The point where short range turns into long range depends on your laser and mirror, so when comparing two laser setups there will be an intermediate range area where one laser is using the short-range formula and one is using the long-range formula, further complicating the question of which setup is best. The transition point is when

meaning that

Getting through your armor will take an amount of time equal to:

(where armor thickness is measured in units of mass per units of surface area, and drill rate is the values given above).

All this assumes that your goal is to penetrate as deeply as possible, without caring how thick your wound channel is. If thin needler beams are incapable of sufficiently damaging the machinery you're shooting at, that'll make short-range lasers less effective.  Mirror-scorching and sensor-frying would use different formulas entirely.

Using these, we can calculate that if you're optimizing purely for mass, then at short ranges it is optimal to have the laser and the mirror be equally massive, while at long ranges it is optimal to have 9 parts mirror for every 8 parts laser! If you're optimizing for price rather than mass, then you would use the ratios, but they would instead mean you spend about the same amount of money on both laser and mirror, regardless of how much mass that gives you — but you should calculate the price for components including the value of the additional engine and propellant (and radiators, etc.) you need to add to carry this additional mass (which requires you to already know what engine ratio you want). If you're also optimizing for minimizing vulnerability, then at first glance you might think that encourages focusing more on the laser, since it's far less vulnerable than mirrors — but that's wrong. Since mirrors are vulnerable, it's more important to build them larger so it's harder for the enemy to shoot the entire mirror off. (The preceding calculations on laser drill rate and mirror proportions were done by Milo, and posted to the Rocketverse forum. The author has cleaned the formulas up slightly, but otherwise posted them as written. The basis was Luke Campbell’s laser damage calculators.)

The same math makes the idea of mounting a mirror on a spacecraft and relaying a beam from another craft dubious.  The mirror will be too expensive, and the coordination problems are formidable, particularly as the beam must not only hit the relaying spacecraft, but do so in a manner that allows it to be redirected to the target.  

by Byron Coffey (2016)

(ed note: this is a discussion on how laser mechanics are implemented in the ultra-realistic game Children of a Dead Earth)

Comparatively, lasers are far more complex than any of the weapon designs we’ve looked into, with far more components and considerations.

For example, in module design, railguns and the like can be optimized by simple tweaking and trial and error. On the other hand, it is very difficult to do so when designing lasers. The relations between the inputs and outputs are not only nonlinear, they are absolutely not monotonic, so simply using trial and error to find ideal cases is not always possible.

While there was an explosion of different design options and choices for railguns as we saw in Origin Stories, with lasers, it was far worse. First you’ll choose your laser type from amongst a staggering array of types. Then you’ll need a pumping source, which includes a nearly infinite number of pumping and lasing geometries, each with different advantages. And you’ll probably want to add a nonlinear crystal to harness Frequency Switching in order to double, triple, or quadruple your photon frequency.

Then you need to worry about the optics between each and every subsystem, ensuring the photons don’t seriously damage each lens, mirror, or nonlinear crystal at each point. Plus, you need to arbitrarily focus your beam at different distances, either with a Zoom Lens or with a Deformable Mirror (though in practice, zoom lens tend to be impractical for extremely long ranges, meaning you’re usually stuck with using a deformable mirror).

Also, and if you want to pulse your laser, you’ll need to use Mode Locking, Q Switching, or Gain Switching to do so. Finally, while mechanical stress are basically irrelevant for lasers (recoil of lasers is minuscule), thermal stresses are huge. Cooling your laser effectively is one of the most important parts of building a working laser.

Laser construction is not for the faint of heart, but the outputs of lasers are actually fairly simple compared to mass weapons. While mass weapons produce a projectile of varying dimensions and materials at a certain speed, possibly with excess temperature, and possibly carrying a complex payload, lasers just shoot a packet of photons. Even if the laser is continuous, the beam fired can be considered series of discrete packets.

Since laser beams move at the speed of light, it is actually impossible to dodge a laser unless you are always dodging. This is because the speed of light is the speed at which information travels in the universe. Thus, you can never determine where a laser will be until it actually hits you. This would be impossibly overpowered in warfare were it not for diffraction.

A packet of photons is focused on a single point of a certain size, and carries a discrete amount of energy of a single wavelength/frequency. Technically, due to quantum mechanics, particularly the Uncertainty Principle, there will be many different wavelengths, an uncertain size, and an uncertain amount of energy. These quantum effects are glossed over because approximating the entire packet as a discrete bundle is both simpler and still remains very close to reality.

The only quantum effect that significantly affects the output of a laser in terms of warfare is Diffraction.

Diffraction causes a laser beam to diffuse the further it gets from its exit aperture, spreading out the energy of the laser. This is a problem because the energy a beam carries is not what inflicts damage. The energy per unit area, or Fluence, is what causes damage. For continuous beams, it would be the power per unit area, or Irradiance.

A hypothetically perfect laser will suffer from diffraction and is referred to as being Diffraction Limited. But this is not what is actually limits most actual high powered lasers in warfare.

Most high powered lasers will never even come close to being diffraction limited.

Truth is, the Beam Waist, or the minimum diameter the beam will achieve, is a more effective measurement of how damaging a laser is. A perfect laser will have a beam waist limited only by diffraction, but lasers like that don’t exist. And the greater the power of a laser, the further and further away that laser strays from being diffraction limited.

A good way to measure this is with the Beam Quality of the laser, or with the M Squared. M2 is the beam quality factor, which can be considered a multiplier of the beam waist. So, an M2 of 5 means the beam waist is 5 times that of a diffraction limited beam. In terms of area, this means the beam is 25 (52) times the area of a diffraction limited beam, or 25 times as weak. As you can see, having a M2 even in the high single digits will yield beams a far cry from “perfect” diffraction limited beams.

In practice, it is not the pumping efficiency, nor the power supply, nor diffraction, which ultimately limits lasers. It is the beam quality factor. In the end, M2 ends up being the number one limit on laser damage in combat.

In small lasers, M2 close to 1 is easily achieved without issue, but in high power lasers, M2 can easily reach into the millions if not accounted for. This is because generally, M2 scales linearly with laser power.

Each optical component of a laser affects the M2. In particular, using a deformable mirror to focus a laser at arbitrarily long ranges (such as from 1 km to 100 km) is measured at reducing M2 to between 1.5 to 3. Problematic, but not exactly debilitating.

But the main issue is Thermal Lensing (Note that this is different from Thermal Blooming, which only occurs outside the laser in the presence of an atmosphere). The heating of a laser gain medium generates a thermal lens which defocuses the beam, ultimately widening the beam waist, preventing the beam from focusing properly. Also note that thermal lensing actually occurs in every single optical component of the laser, though it is strongest in the lasing medium.

Thermal lensing increases M2 roughly linearly with input power. This means if you have 1 kW laser with a M2 of 1.5 (which is reasonable), this means dumping 1 MW into that same laser will yield a M2 of about 1500 (going the other way does not work, since M2 can’t be less than 1).

One might try to predict the thermal conditions and add in an actual lens reversing the thermal lens. Unfortunately, the thermal lens is not a perfect lens either, and the imperfections of this lens remain the primary cause of beam quality reduction.

Fiber lasers are often touted as a solution to thermal lensing. They are considered immune to thermal lensing except in extreme cases. Unfortunately, dumping hundreds of megawatts through a fiber laser constitutes an extreme case, and fiber lasers suffer thermal lensing nearly as badly as standard solid state lasers.

The largest innovation for combating thermal lensing are negative thermal lenses. Most gain mediums have a positive thermo-optic coefficient, and this is what generates the thermal lens. Certain optical materials have a negative thermo-optic coefficient, which produces a thermal lens inverse of what the gain medium produces. Ideally, this negative thermal lens would perfectly reverse the positive thermal lens, but in practice, the M2 still suffers.

In the end, the primary way to combat thermal lensing is with cooling. And the primary way to cool your laser is to make it bigger.

If the proportions of a laser are kept identical, lasers can be scaled up or down with minimal change to the laser’s efficiency or output power. Indeed, you can pump 100 MW or power into a tiny palm-sized laser just as well as you can into a building-sized laser, and they will produce roughly equal beams in terms of efficiency and M2. The only difference is that the palm-sized laser will melt into slag when you try to fire it.

Laser size is mostly a matter of how much do you need to distribute the heat of the laser pumping. And if you want to combat thermal lensing, you’ll want a really big laser. This means laser size is essentially about cooling, and by extension, having a low M2.

And because size is closely related to mass, and mass is so critical to spacecraft design, the limiting factor of using lasers in space is how poor of an M2 you want to have, given a certain power level. Though the radiator mass needed for the enormous power supplies is the other major consideration.

A final way to combat thermal lensing is to use Beam Combining of many smaller lasers. Combining beams side by side increases the beam waist linearly, which defeats the point, but Filled Aperture Techniques can combine beams without increasing the beam waist. However, this technique produces greater inefficiency to the final beam. The ideal way to combine beams is to simply use multiple separate lasers which all focus on a single point.

In Children of a Dead Earth, either single large lasers or multiple small, separately focused lasers can be used, and both have varying pros and cons.

Of course, designing lasers in Children of a Dead Earth is often far more difficult than designing any other system, so there are plenty of factory-made options for players to use. But the option is always there for those who really want to explore the depths of laser construction!


So, I gather more’n a few laser fans are coming to visit these days, so just to save time, here’s the canonical reason that lasers are the ‘verse’s secondary weapons system, not its primary one:

(It turns out that this is really a recapitulation of points raised in Non-Standard Starship Scuffles, so if you’re already nodding along to that, you can more or less skip the rest. I’ll just hit a few high points.)

Lasers, for the most part, are useful weapons systems under many circumstances. (Obviously they have to be, given their use as point-defense; if you couldn’t get effective results from lasing a k-rod, they wouldn’t be used.) As mentioned elsewhere, you can get an effective result out of a laser weapon, due to collimation, up to around a light-second, which is the entirety of the inner engagement envelope, and as such every military starship mounts a passel of phased-array plasma lasers for point-defense, and larger classes cram in some broadside offensive lasers too.

You can actually collimate reasonably effective beams at rather longer distances than that, as the existence of starwisp tenders demonstrates – although they themselves are of little use for military purposes despite the incidents mentioned in that article, seeing as they shift angular vector and alter their focus with all the grace and speed of apatosauruses mating. One would, however, make a dandy generator for a laser web.

(Yes, they exist in the ‘verse, and have done ever since the Admiralty paid the Spaceflight Initiative to launch Sky-Shield, the homeworld’s first orbital defense grid, back in the day. Orbital defense grids remain their main military use, along with civilian beamed power.)

It’s just that the IN sees no particular point in paying in either cashy money or mass/volume budget for collimation to make them effective beyond the inner engagement envelope, because you aren’t going to hit any actively evading targets at that range anyway, golden BBs and spies having gotten you a copy of their drunkwalk algorithms aside, and kinetics/AKVs work better for the geometry games played in the outer envelope.

Here, though, is the spoiler in the deck where military lasers are concerned:

Thermal Superconductors.

(The laws of physics do permit them, I am assured, and local materials science is more than up to producing them.)

In up-to-date designs, starship armor is woven through with a dense mesh of the stuff, with wicking into big heat-sink tanks of thermal goo. This causes something of a problem for weaponized lasers, because it makes it ridiculously hard to create a hot spot that’ll vaporize – instead, you just add heat to the whole starship. Which is not useless by any means, if you can manage lots of repeated hits or keep a beam on target, because if you can pump enough heat into a starship, either it, the crew, or both, will go into thermal shutdown; but this is what lasers are for in ‘verse starship combat. If you want to blast things apart, you go for kinetics, because you can’t tank (sic) big lumps of baryons.

Of course, this defense has its limitations: a laser grid at short range can hit its target with enough power to overcome the armor and, indeed, to chop its target neatly into a pile of small cubes. But that’s for definitions of short range meaning “inside knife-fight range”, and any Flight Commander who let the range close that much without having his entire propulsion bus shot off first would be summarily cashiered for incompetence.

And that’s why lasers aren’t the primary or only weapons system around these parts.

From ON LASERS by Alistair Young (2018)


Note that laser cannon are notoriously inefficient. This means if your beam power is 5,000 megawatts (five gigawatts), and your cannon has an efficiency of 20%, the cannon is producing 25,000 megawatts, of which 5,000 is laser beam and 20,000 is waste heat! Ken Burnside describes weapon lasers as blast furnaces that produce coherent light as a byproduct. Rick Robinson describes them as an observatory telescope with a jet engine at the eyepiece. Laser cannons are going to need seriously huge heat radiators. And don't forget that heat radiators really cannot be armored.

The messy alternative is to use open-cycle cooling, where the lasing gas is vented to dispose of the waste heat. Not only does this endanger anything in the path of the exhaust, it limits the number of laser shots to the amount of gas carried.

But Troy Winchester Campbell brings to my attention a recent news item. In 2004, a company named Alfalight, Inc. demonstrated a 970 nm diode laser with a total power conversion efficiency of 65%. They are working in the DARPA Super High Efficiency Diode Sources program. The goal is 80% electrical-to-optical efficiency in the generation of light from stacks of semiconductor diode laser bars, and a power level of 500W/cm2 per diode bar operating continuously.


This is one of those areas where progress is happening so fast that it can be hard to keep up with all the newest technology.

Two decades ago, everyone knew that laser weapons would use chemical lasers, like deuterium fluoride (DF) or chemical oxygen iodine laser (COIL) lasers. The beam quality was abysmal, but that was the only way you could get the power levels needed. One of my professors described chemical lasers as more like a flashlight than any sort of focused beam.

One decade ago, everyone knew that chemical lasers were a giant steamping pile of crud. Diode-pumped slab solid state lasers were the way of the future. You didn't have to carry around huge vats of toxic caustic chemicals, you could just use cheap electricity to efficiently generate your beam. Slab solid state lasers lead to all of the issues described in the linked article but lab prototypes were developed that operated at ~10 kW with beams that were only about 2 to 5 times worse than diffraction limited (going by memory here, there's a chance these numbers may be off by more than I'm recalling).

Then about 5 years ago some folks bundled together a bunch of fiber lasers into a high powered laser weapon demonstrator that was cheaper and more robust and smaller than any slab solid state laser. They used incoherent beam combining — just shining all the lasers at the same spot, so the beam quality was total crud. But it worked. You could blow up boats and rockets and UAVs and mortar shells in flight at respectable distances and do all sorts of other nifty stuff. All this was made possible by advances in industrial fiber lasers used for materials processing that allowed outputs of multiple kilowatts from individual fibers. Each fiber is essentially diffraction limited, and because the beam is generated inside of a very long fiber optic cable you have a huge surface area available for cooling.

The next trick is figuring out how to put the high quality ~kW beams together into one single high quality beam with ~100 kW or ~MW power levels. Lockheed Martin started using spectral beam combining in the last few years to do just this with lasers initially starting at around 20 kW and now exceeding 60 kW of power. It is expected that spectral beam combining can take you up to ~100 to 150 kW power before you start hitting limitations of the mechanism.

But people are already looking in to methods to go way beyond this. Coherent beam combining techniques are being developed that allow near diffraction-limited combined beams by controlling the phases of the individual beams. One method that would provide the highest quality beams uses diffraction gratings with phase control of the incoming beams to interfere constructively on only one of the diffraction lobes and destructively at all other lobes. Using this, you could daisy chain an unlimited number of lasers together into a single high quality beam. The other method I've seen involves controlling the phases of a bunch of beams that exit side-by-side, making a laser phased array. The beam quality will be a bit worse, but you have the benefit of allowing instantaneous control over the beam wavefront so you can instantly tilt the beam without needing to slew your beam pointer around (in addition to doing all sorts of nifty stuff like adaptive optics and active focusing just with the relative beam phases rather than cumbersome optical elements). With some development, you might even get around the fill factor issues by getting component beams that are nearly uniform in power level across the beam-front to allow laser phased arrays with nearly perfect diffraction limited performance.

The first coherently combined beams will undoubtedly use fiber lasers, but current research is already looking beyond that. Coherent combination of diode lasers could get around the problems that have plagued high powered diode lasers for decades. This could get around a significant source of loss in using diode lasers to pump fiber lasers, going from 30% efficiency to 50 or 60% efficiency for wallplug-to-light conversion (some laboratory diode lasers have even achieved 70% efficiency). In addition, diode lasers allow some degree of frequency agility, so that you could shift the wavelength of your beam on the fly (within limits). I would not be at all surprised if, a decade from now, this was the obvious future of laser weapons. Or maybe it will be something else completely unforeseen.

We = (1.0 - Ce)


  • We = Waste power percentage
  • Ce = Efficiency of Laser Cannon

WP = CP - BP


  • WP = Waste Power (megawatts)
  • CP = Laser Cannon total power (megawatts)
  • BP = Beam Power at laser aperture (megawatts)

Getting rid of the waste heat from a laser is a problem if you don't dare extend your heat radiators because you are afraid they will be shot off. A strictly limited solution is storing the waste in a heat sink, like a huge block of ice. "Limited" because the ice can only absorb so much until it melts and starts to boil. If your radiator is retracted and your heat sink is full, firing your laser will do more damage to you than to the target.

Eric Rozier has this analysis of heat sink mass:

One common mistake people make is assuming that lasers are infinite fire weapons. With proper radiators extended, this is true, but with them drawn in, to avoid being shot off, we're limited by the heat capacity of our sinking material, as you well know.

An interesting question to ask is: "Without radiators, how many shots can I get off for some mass of coolant and some sort of laser?"

Given single laser of Bp megawatts at aperture, and an efficiency of eff, duty cycle of dc, and firing time of Tf, we get the waste heat Wh (in MWseconds) as:

Wh = Tf * (Bp/eff * dc) * (1 - eff)

Wh is then the waste heat generated by a single blast from our lasers. To figure out how many times we can fire our lasers we need to perform some calculations based on our coolant, the data of interest is:

  • Mass of coolant dedicated to lasers (Mc) in kg
  • Atomic mass of coolant (Ma) in g/mol
  • Heat capacity of coolant (Hc) in J/(mol * K)
  • Melting point of coolant (Km) in K
  • Boiling point of coolant (Kb) in K

Given this, we can find the number of shots we can fire (S) as follows:

S = ((Mc / Ma) * Hc * (Km - Kb)) / 1000 / Wh

If you do not have the atomic mass of coolant or heat capacity of coolant, you can instead use the specific Heat capacity of coolant. This is useful if the coolant is a compound instead of an element in the periodic table.

  • Specific Heat capacity of coolant (Hck) in J/(kg K)
  • Energy Capacity of coolant in MW seconds (or MegaJoules if you prefer)

Ec = (Mc * HcK * (Km - Kb)) / 1000000

S = Ec / Wh

There is an online calculator for this here.

This assumes the coolant is just melted before firing the laser, and just boiling after firing all available shots. In reality, you want to set Kb at some level below the real boiling point, and Km at some level above the melting point.

As a worked example, a 100MW laser with efficiency of 0.2, 0.5 duty cycle, and 0.1s firing time generates 20 MWseconds of waste heat each time it fires. 1000kg of Lithium, (with about 1140K between melting and boiling) can contain enough heat to fire the laser roughly 204 times.

This, I think, helps show some of the heat limitations of lasers, and constrains them (especially as point defense weapons). You end up having to lug a lot of lithium around if you want to fire them often.

I think this is most interesting when thinking about point defense. Lasers fielded as a CIWS are pretty scary, and if you could fire them infinitely often, they probably keep missiles from hitting you. So in order to constrain you from using lasers for point defense, I simply pull into laser range, threatening your radiators, and forcing you to withdraw them. As such, you can no longer afford to use a laser CIWS, and have to switch to something projectile/missile based, which is liable to be less effective.

Eric Rozier

Winchell Chung:

Luke Campbell, a question occurred to me, and you are currently the only laser scientist I know. If this question is the equivalent to a graduate thesis, just forget it.

Occasionally science fiction authors try to figure the mass and volume of their spacecraft. Especially warships. So what is the average mass and volume of an anti-ship laser weapon? Does is scale with beam output power?

Luke Campbell:

At this point, there is no good way to estimate the mass and volume of an anti-ship laser. To do so requires knowing two things: the beam power or beam energy needed to defeat a target ship, and the specific power or specific energy (power divided by mass or energy divided by mass, respectively) of the laser.

(ed note: Energy is joules, Power is joules-per-second or watts)

The beam power or energy requires could in principle be determined for a given engagement scenario — engagement time and distance; target size and armor. This will, of course, depend on the tech choices made elsewhere in the setting, so no single value can be quoted. Using modern ocean-going warships as a proxy and the sorts of heat ray lasers that are currently being built and fielded, many tens of kilowatts to disable sensors, communications, and soft surface targets seems reasonable, while tens of megawatts could burn through the hull to kill propulsion, power generators, or explode on-board magazines. Longer ranges, shorter engagement times, or more massive or more heavily armored ships all tilt you toward needing more beam power.

The specific power of modern war fighting lasers has been rising rapidly, and there is no reason it shouldn't keep dropping in the foreseeable future. Some recent advances have got the specific power down to better than 0.25 kW/kg

(better because the listed performance also includes the batteries to power the laser for a number of seconds). The specific energy of pulsed lasers has also been increasing, although none are now a reasonable candidate for weaponization.

You can expect the laser mass to scale with beam power for heat rays, and pulse energy for blasters with an extra helping of other equipment scaling with beam power for power handling and control and heat rejection. The minimum area of the focal array will be set by the beam power and beam energy, but in practice you will probably find that you want a larger aperture than this minimum area in order to get a reasonable range. How the mass of the beam pointer telescope scales with the aperture's area I will leave to mechanical engineers.

From a thread on Google Plus (2015)

(ed note: The topic is Free Electron Lasers (FEL) as weapons.

There's a lot of engineering that goes into getting good efficiency. A design like an energy recovery linac can turn something like 99.9% of the electron beam energy into laser energy (with caveats that it is actually recycling a lot of its energy back into the beam, using energy that would normally be wasted at the beam dump to pump up the fields in the accelerating cavities and use that to accelerate the electron beam). So the problem comes down to efficiently accelerating the electron beam.

Most of the energy use is not in making the beam so much as in overhead, such as running the refrigerators to cool your RF cavities down to superconducting temperatures. I read one study that was looking at putting an FEL on a 747. They could use the jet turbines as compressors for their refrigeration to essentially get cryogenics for free while the plane was under way. This really helped the efficiency by a lot.

A heat pump can move heat from 100 K to 1000 K. It just generates a lot more heat in the process. For every watt you remove from the 100 K bath, you will need to radiate away 10 watts from your 1000 K radiators.

Luke Campbell from a thread on Google Plus (2016)

The U.S. military, of course, wanted something smaller than a cement truck. And another of the HEL-JTO programs, the Robust Electric Laser Initiative, managed to do it. With a mandate to develop solid-state lasers that were better suited for the battlefield, HEL-JTO set itself a goal of building a 100-kW laser that occupied about 1.2 cubic meters and could generate more than 150 watts per kilogram, operating at 30 percent efficiency or better. Two of the four projects HEL-JTO launched considered new variations on a hot technology for laser machine tools: fiber lasers.

A fiber laser is essentially an optical fiber with some important modifications. It has a central core with a slightly higher refractive index than the surrounding glass cladding. A telecom fiber uses that structure to guide optical signals from laser transmitters through its central core, which is made of extremely pure and nearly lossless silica. In a fiber laser, however, this central core contains light-emitting atoms, usually ytterbium.

Fiber lasers also have an extra layer, between the light-emitting central core and the outer cladding. This intermediate layer, called the outer core or inner cladding, has a refractive index in between that of the core and the outer cladding. The inner cladding is also made of high-⁠purity glass because its job is to guide light from external diode pump lasers directed into the outer cladding through separate optical fibers. From there, the light bounces along inside the outer core as it travels the length of the fiber, repeatedly passing through the inner core, where the ytterbium atoms grab the photons and emit laser light. The outer core is deliberately shaped unevenly—a D shape, an ellipse, even a rectangle⁠—to ensure that as much light as possible is directed through the central core.

Like the signal in a telecommunication fiber, the light emitted by ytterbium atoms in a fiber laser remains confined within the light-guiding central core. But instead of traveling tens of kilometers in one direction to the next optical amplifier or receiver, the light in a fiber laser bounces back and forth between a pair of reflectors fabricated into each end of the fiber. With each pass, more ytterbium atoms amplify the light, building up the laser power.

The tight connection between the inner and outer cores ensures that most of the pump light is absorbed by ytterbium atoms. And in 2016, IPG Photonics reported converting just over half of the electric power to light in the lab, well above what you could get from the bulk crystal or glass of older, solid-state laser schemes. Generating light in the long, thin fiber core also produces a beam that can be focused tightly over long distances, which is exactly what’s needed for delivering lethal energy to targets a few kilometers away. Because fiber lasers are thin—with diameters in the range of 125 to 400 micrometers—they have a high surface-to-volume ratio, allowing them to dissipate heat much faster than shorter and thicker lasers.

Fiber lasers started small, largely as spin-offs of the development of fiber amplifiers for long-haul telecommunications in the 1990s. The push to high power came from IPG. Starting with a 1-W fiber laser in 1995, the company has basically added an order of magnitude to that figure every three years through 2012. The company grew along with the power of its lasers. Its 2017 sales of $1.4 billion accounted for about a third of the revenue of the entire market for industrial lasers that year.

Industrial fiber lasers can be made very powerful. IPG recently sold a 100-⁠fiber laser to the NADEX Laser R&D Center in Japan that can weld metal parts up to 30 centimeters thick. But that high of a power output comes at the sacrifice of the ability to focus the beam over a distance. Cutting and welding tools need to operate only centimeters from their targets, after all. The highest power from single fiber lasers with beams good enough to focus onto objects hundreds of meters or more away is much less—10 kW. Still, that’s adequate for stationary targets like unexploded ordnance left on a battlefield, because you can keep the laser trained on the explosive long enough to detonate it.

Of course, 10 kW won’t stop a speeding boat before it can deliver a bomb. The Navy laser demonstration on the USS Ponce was actually half a dozen IPG industrial fiber lasers, each rated at 5.5 kW, shot through the same telescope to form a 30-kW beam. But simply feeding the light from even more industrial fiber lasers into a bigger telescope would not produce a 100-kW beam that would retain the tight focus needed to destroy or disable fast-⁠moving, far-off targets. The Pentagon needed a single 100-kW-class system for that. The laser would track the target’s motion, dwelling on a vulnerable spot, such as its engine or explosive payload, until the beam destroyed it.

Alas, that’s not going to happen with the existing approach. “If I could build a 100-kW laser with a single fiber, it would be great, but I can’t,” says Lockheed’s Afzal. “The scaling of a single-fiber laser to high power falls apart.” Delivering that much firepower requires new technology, he adds. The leading candidate is a way to combine the beams from many separate fiber lasers in a more controlled way than by simply firing them all through the same telescope. Two approaches looked promising.

One idea was to precisely match the phase of the light waves emerging from several identical fiber lasers so they add together to form a single, much more powerful beam. The light waves of each fiber laser are coherent, meaning all emitted waves march along in lockstep, with every crest locked in synchrony with every other crest, and every trough with every other trough, and so on. In principle, coherently combining the beams of several different fiber lasers should make a powerful beam that could be tightly focused onto targets kilometers away. Phased-array antennas can combine, in synchrony, the coherent outputs of many radio transmitters, but the trick is much more difficult with light. That’s because light wavelengths are orders of magnitude shorter—around 1 micrometer compared with centimeters for radar—making it extremely hard to align the waves precisely enough for them to add together constructively rather than interfere with one another.

The other approach is to ignore phase and combine beams from many fiber lasers that each have optics that limit them to emitting in a unique spectral slot. The resulting beams each occupy a different wavelength. So when they are combined into a single beam, that beam spans a range of wavelengths, which don’t interfere with one another. Called “spectral beam combining,” the technique is adapted from wavelength-division multiplexing technology, which has been enormously successful in packing more data into fiber-optic communications channels.

To implement the technology, Lockheed developed special optics that bend light from separate fiber lasers at angles that differ slightly depending on their wavelength, the same way prisms separate the colors of the spectrum. That bending merges their outputs to form a single beam. In 2014, the company “built and tested on our own money a 30-⁠kW laser to figure out the physics and basic engineering,” says Afzal. That system combined 96 beams of 300 W each at different wavelengths into a single beam with a total power of 30 kW. The lasers produce higher-quality beams when run at such relatively low powers, and it is easier to combine their output to produce a high-power beam than to build a single high-power laser with the same beam quality, says Afzal.

Lockheed scaled that technology to 60 kW in a laser it delivered to the U.S. Army Space and Missile Defense Systems Command, in Huntsville, Ala., last year for installation in a battlefield-ready military truck. That laser “set a world record for [weapons-grade] solid-state laser efficiency, in excess of 40 percent,” claims Adam Aberle, lead of the command’s high-energy laser technology development and demonstration. Such high efficiency greatly eases the problem of thermal management. With that efficiency, a laser system whose beam is at 100 kW generates less than 150 kW of waste heat. Compare that with more than 400 kW of waste heat, which is what Northrop Grumman’s 2009 nonfiber laser put out while delivering a beam of the same power. On 1 March, Lockheed announced that by 2020, it would supply the U.S. Navy with two copies of a similar laser, called HELIOS, that will deliver at least as much power. The Navy will install one on a destroyer and integrate it with the ship’s battle management system, and it will test the second on land at the White Sands Missile Range, in New Mexico.

“We view development of the high-power, beam-combined fiber laser as the final piece of the puzzle,” says Afzal. Maybe so, but the quest for laser weapons is far from over. Now that a high-energy laser technology looks viable, armed services around the world will need to figure out how to deploy it in combat, and against what. Those challenges, in turn, will require designing, building, testing, and refining the hardware needed to turn a powerful laser into a mobile weapon system, including trucks, ships, and aircraft to carry the laser; sensors and computer systems to spot and track targets; power management systems to deliver the electricity to the laser; cooling systems to keep it from overheating; and optics to focus the powerful beam onto moving targets long enough to destroy or disable them.


Back in 2003 DARPA started their Super High Efficiency Diode Source (SHEDS) program. In 2005 the nLIGHT company presented a couple of papers:

They reported some rather remarkable power conversion efficiencies, ones to bring a smile to any laser-weapon-smith's face.

Power Conversion Efficiency
980-nm wavelength
Diode cooled toEfficiency
(Room Temperature)

Attack Vector: Tactical Lasers

Ken Burnside's masterful tabletop wargame Attack Vector: Tactical is fictional, but it was prepared with expert help from real live physicists and other scientists. More to the point, design choices were made to make an interesting game. Which means they would also be design choices that would make an interesting science fiction novel.

In the game, there are various types of lasers of increasingly shorter wavelengths, which due to the diffraction equation have increasingly longer range (by which I mean the spot intensity decreases more slowly). These lasers also have a decreasing level of efficiency of converting power into laser beam, I am unsure if this is due to a physical limit or it is an arbitrary thing used to balance the game.

Short Range Laser2400 nmNear Infrared20%
Close Range Laser1600 nmNear Infrared16.6%
Medium Range Laser1200 nmNear Infrared12.5%
Extended Range Laser800 nmNear Infrared9%
Long Range Laser600 nmOrange6%
Extreme Range Laser400 nmIndigo3%
Ultraviolet Laser200 nmUltraviolet1.5%

In addition, each laser type comes in seven sizes (with focusing mirrors ranging in size from 3 meters radius to 6 meters radius) and assorted energy requirements. The basic game only has short range and medium range lasers:

Short Range
Laser 2
3 m3 GW20%0.6 GW80 km300 km
Short Range
Laser 3
3.5 m4.5 GW20%0.9 GW100 km440 km
Short Range
Laser 4
4 m6 GW20%1.2 GW120 km560 km
Short Range
Laser 5
4.5 m7.5 GW20%1.5 GW140 km740 km
Short Range
Laser 6
5 m9 GW20%1.8 GW160 km900 km
Short Range
Laser 7
5.5 m10.5 GW20%2.1 GW160 km1,040 km
Short Range
Laser 8
6 m12 GW20%2.4 GW180 km1,200 km
Medium Range
Laser 2
3 m2 GW12.5%0.25 GW180 km400 km
Medium Range
Laser 3
3.5 m3 GW12.5%0.375 GW200 km600 km
Medium Range
Laser 4
4 m4 GW12.5%0.5 GW240 km800 km
Medium Range
Laser 5
4.5 m5 GW12.5%0.625 GW280 km1,000 km
Medium Range
Laser 6
5 m6 GW12.5%0.75 GW300 km1,200 km
Medium Range
Laser 7
5.5 m7 GW12.5%0.875 GW340 km1,400 km
Medium Range
Laser 8
6 m8 GW12.5%1 GW360 km1,800 km

The mirror radius is the size of the lens or reflector (RL in the diffraction equation). The input energy is fed as power into the laser, after suffering the horrific effects of typical abysmal laser efficiency the laser beam emerges from the business end containing the aperture energy and leaps out to impale the hapless target. The gigawatts of waste heat are absorbed by the internal heat sink, because extending your heat radiator is just asking for it to get shot off.

The effective range and maximum range are not directly applicable, they are artifacts of the beam damage model used by the Attack Vector: Tactical game. But they do provide some basis of comparison. In the game each "damage point" inflicted upon an enemy ship represents 50 megajoules in an eight centimeter diameter circle inflicted in 1/100th of a second. The effective range is the farthest range that the laser can inflict its full damage. The maximum range is the farthest range that the laser can inflict at least one point of damage. This is all required because Attack Vector is not a computer game, it is an incredible paper and cardboard wargame where all the scientific accuracy and scary mathematics are handled painlessly with cunning player aides.

I would hazard a guess this is the reason for the values chosen for input energy and ranges, to calibrate each laser to 50 megajoules in an eight centimeter spot size.

For our purposes, it might make more sense to use the Brightness equation. Then you can assign hardness values for the target's armor.

Short Range Laser 2
80 km7.8 cm1.55×109 J/m2
100 km9.8 cm9.9×108 J/m2
140 km13.7 cm5.05×108 J/m2
180 km17.6 cm3.06×108 J/m2
220 km21.5 cm2.05×108 J/m2
300 km29.3 cm1.1×108 J/m2
Short Range Laser 8
180 km8.8 cm3.06×108 J/m2
200 km9.8 cm2.48×108 J/m2
240 km11.7 cm1.72×108 J/m2
300 km14.6 cm1.10×108 J/m2
380 km18.5 cm6.86×107 J/m2
520 km25.4 cm3.66×107 J/m2
840 km41.0 cm1.40×107 J/m2
1,200 km58.6 cm6.88×106 J/m2
Medium Range Laser 2
180 km8.8 cm5.09×108 J/m2
240 km11.7 cm2.86×108 J/m2
300 km14.6 cm1.83×108 J/m2
400 km19.5 cm1.03×108 J/m2
Medium Range Laser 8
360 km8.8 cm1.27×108 J/m2
420 km10.2 cm9.35×107 J/m2
500 km12.2 cm6.60×107 J/m2
620 km15.1 cm4.29×107 J/m2
860 km21.0 cm2.23×107 J/m2
1,220 km29.8 cm1.11×107 J/m2
1,600 km39.0 cm6.45×106 J/m2

Combat Mirror

A more scientifically plausible but much less dramatic laser weapon is the combat mirror. In this scheme, the spacecraft doesn't have a laser, just a large parabolic mirror. The laser is several million miles away, on a freaking huge solar power array orbiting your home planet. You angle the mirror so it will do a bank shot from the distant laser off the mirror and into your target, then radio the laser station to let'er rip. About fifteen minutes later the diffuse laser beam arrives, and your parabolic mirror focuses it down to a megaJoule pinpoint on your target.

The combination of a powersat and a combat mirror is called a Powersat Weapon.

The advantage is that the spacecraft does not have to lug around the laser, the power supply, the heat radiators, and other massive elements of the laser weapon. The spacecraft can have a higher acceleration or increased payload. The beam can also be of a power level associated with laser equipment that is not considered "portable by spacecraft", if the laser generator is a few miles in diameter your spacecraft could care less.

Disadvantages include the lag time between ordering a shot and its arrival, and the vulnerable nature of the combat mirror (generally little more than a large Mylar balloon).

Mirror Armor

Now I know all you older science fiction fans still remember Jonny Quest and The Mystery Of The Lizard Men where Dr. Quest demonstrates that one can defend oneself against a weapon-grade laser beam with a dressing-room mirror. Sorry, it doesn't work that way in reality. No mirror is 100% efficient, and at these power levels, the fraction that leaks through is more than enough to vaporize the mirror armor. The same goes for "ablative armor." One zap and the impact point is abruptly as bare of armor as a baby's behind.

Inside a laser cannon, a relatively diffuse laser beam is generated. This prevents the beam from vaporizing the cannon's internal optics. At the business end, a parabolic mirror focuses the diffuse beam down to the aforementioned megaJoule pinpoint on the hapless target.


The (above text) is alright, but it leaves the possibility open that someone loosely researches and finds some 99.999% efficient mirror for his or her purposes, similar to the waste heat into electrical power thing a while back (an equation in the "Efficiency" section above, with erroneous assumptions which Kerr pointed out. Said equation has been removed ).

Not only is the beam diffuse, but there are also specialized optics being used here, you will usually not see some polished tin foil in there but high-tech dielectric mirrors, the problem using them as armor is that you can always shift your wavelength or polarization one way or another, with will drastically change how efficiently the mirror reflects the beam, there are broadband mirrors that are somewhat immune to the wavelength changes (still not so much to the polarization) and vice versa.

But using them as the armor is comparable to assuming that using a technology that barely operates, even under laboratory conditions, could be taken to the battlefield.

You know what you fire against your own optics, with mirror armor you will not.

by Kerr (2018)


And don't think that lasers will automatically hit their targets either. There are many factors that can cause a miss. Off the top of his head, Dr. John Schilling mentions:

  • Uncertain target location due to finite sensor resolution
  • Uncertain target motion due to sensor glint or shape effects
  • Sensor boresight error due to finite manufacturing tolerances
  • Target motion during sensor integration time
  • Analog-to-digital conversion errors of sensor data
  • Software errors in fire control system
  • Hardware errors in fire control system
  • Digital-to-analog conversion errors of gunlaying servo commands
  • Target motion during weapon aiming time
  • Weapon boresight error due to finite manufacturing tolerances
  • Weapon structural distortion due to inertial effects of rapid slew
  • Weapon structural distortion due to external or internal vibration
  • Weapon structural distortion due to thermal expansion during firing

And we haven't even begun to include target countermeasures...

Kerr points out that the above list is fine, but outdated (list was compiled in the 1990s). Some factors ignore the capability of modern computing. "Modern" being defined as "circa 2018".


Airbourne Laser

What about a laser turret? It can be so inconvenient to have to move the entire ship in order to aim the blasted beam. As it turns out, the US Air Force has a solution created for their Airborne Laser project.

I hear you ask "but why doesn't the beam slice up the inside of the turret?" The key is power density.

For instance, a naughty little boy will find that sunlight does not do much to his skin except warm it up a bit. However, if you whip out a magnifying glass you can focus the sunlight to a white-hot pinpoint that will easily incinerate ants. The magnifying glass increases the power density of the sunlight. So inside the turret, the weapon beam is something like 20 centimeters in diameter which means a power density too low to fry the internal mirrors. At the end, the beam expander mirror evenly shines the laser beam over the primary mirror. That mirror then acts like the magnifying glass in the hands of the anticidal little boy, focusing the diffuse laser beam down to an incinerating pin-point on the hapless target.

Isaac Kuo points out that another factor keeping the laser from chopping up the turret is that the internal mirrors are dielectric mirrors. Those babies can be up to 99.999% reflective. Meanwhile if target has conventional mirror plating it will only be 95% reflective, absorbing 5,000 times as much laser energy. Dielectric mirrors would be difficult if not impossible to manufacture in pieces large enough to cover a missile or spacecraft.

The actual US Air Force Air Borne Laser is a megawatt class chemical oxygen iodide laser (COIL) operating at a frequency of 1.315 microns or 1.315e-6 meters (near infrared). With a 1.5 meter mirror, this gives a divergence angle of 1.07e-6 radians. If my slide rule is correct, this means at a range of one kilometer it will have a spot size of one millimeter radius, and a beam brightness of about 300,000 megawatts per square meter. However, I've seen suggestions that the actual spot size is more like several centimeters, demonstrating the room for improvement.

The US Air Force is understandably reluctant to give any figures on the performance of the Air Borne Laser. The best figures I could find suggest that it could destroy a flimsy unarmored hypergolic fueled missile (with fuel still in the tanks) by expending a three to five second burst up to a range of about 370 kilometers. Three to five seconds is an awfully long time to keep the beam focused on the same spot on a streaking missile. The dwell time will have to be longer if the missile is armored or if it uses solid fuel or other inherently stable fuel.

The giant primary mirror will contain adaptive optics (i.e., it will be a "rubber mirror"). This will allow the mirror to change its focus to accommodate the range to target. In diagram "a" to the right, the flexible mirror is laid over a slab of piezoelectric material that changes shape as power is applied to the electrodes. In diagram "b" individual actuators are used. The image on the right is a 19-actuator deformable mirror built by Rockwell International. The mirror is only 40 cm in diameter. The actuator density is about 150 actuators per square meter, so the 1.5 meter ABL mirror would require about 270. (surface area of a circular 1.5 meter mirror is about 1.8 square meters, times 150 actuators per square meters give 270 total actuators)

Luke Campbell's Turret

Luke Campbell has his own design for a laser turret. Cararra 5 was used to create the 3D mesh and to render the images.


Rick Robinson has a more serious concern. You know how it is a very bad idea to look through a telescope at the Sun? Well, for the same reason it is bad to unshutter your laser cannon optics and point them at a hostile ship which might zap you with its laser. Your cannon's optics would funnel their beam right down into the delicate interior of your cannon. The optics would also concentrate their beam to 10x or 100x the intensity. This means that if your lasers are unshuttered and your opponents are shuttered, you have the drop on them. The instant you detect their shutters trembling you give them a zap. Their shutters will still be opening when your bolt scrags their laser.

However, Ken Burnside says:

I will point out that the likeliest result of "shooting down the barrel of a laser" is to destroy one of the mirror elements on the focal array. Since those elements are likely to be used with adaptive optics, this won't even hurt the laser that much. It's only if the mirrors are hit at exactly the right angle that they'll direct energy back into the Free Electron Laser itself.

Ken Burnside

One solution is to aim the laser by using a flotilla of external combat mirrors. The laser cannon shoots a diffuse beam that the combat mirror focuses on the target. If the enemy returns fire the combat mirror will defocus the hostile beam.

Anthony Jackson has another messy solution. One can design a laser cannon without a mirror or lens, if one uses a phased array. Currently we can create phased arrays for microwaves and radars, but have no idea how to do it with visible light. It would take a major technological break-through, but it is not actually forbidden by the laws of physics. Kerr points out that as of 2018 there are indeed optical phased arrays, depending on how elastic is your defintion of "phased array." But there do exist things resembling an optical analog to a microwave phased array.

Another nifty effect of phased array emitters is that they're flat and can fire at any angle (range will suffer at extreme angles), without requiring a turret assembly.

Dr. Yo came to the horrified realization that the logical acronym for PHased Array laSER was ... aiieee!

Eric Henry prefers that particular name for Free-electron laSER.

It is possible to armor laser mirrors, and it's also possible to use optics which are inherently difficult to damage. We've had extensive discussions about this (with Rick Robinson and others) on sfconsim-l.

Armor is based on protecting an otherwise delicate mirror with grids of armor. This assumes the use of a pulsed laser. Each armor grid is a bundle of parallel sheets. When the grid is rotated, it briefly lines up with the target in passing—that's when a pulse laser can fire. With two or more grids, the window of vulnerability can be made arbitrarily short. And the duty cycle can be made unpredictable.

So, for example, a pulsed laser that could only pulse 1/10000 of the time. Incoming laser fire would only hit the mirror 1/1000 of the time. The other 99.99% of the time, it hits the grid armor.

If you want to get even fancier, you can space apart the grids by, say, 1/1000 light seconds (300km). This requires the use of an armor drone, or a pair of warships. This lets you have a duty cycle of almost 50% and still have armor protection 100% of the time. The time delay is sufficient that your photons can pass through to the target, while photons going the other way will get blocked by either one grid or the other.

Still, this grid armor is very bulky. Assuming the grids block 10% of the outgoing photons, it takes 100cm thick grid armor to provide the equivalent protection of only 10cm of solid armor. And it's possible that damage to these grids may significantly diminish their efficiency.

Another interesting possibility is to use damage resistant optics. If you use diffraction rather than reflection or refraction, you can make your focusing element arbitrarily thick. Your focusing element is a zone plate drone some distance away from the beam generator ship. The zone plate is a sturdy thick set of concentric cylinders. It can be arbitrarily thick...if you want, it can be 1m thick. All that really matters is the pattern of concentric circles. Enemy lasers could blast away at this thing all day, and it still functions perfectly so long as there's enough left over to block the concentric circles.

Such a zone plate is not the most efficient focusing element—it only focuses about 25% of the source beam's energy on target. But if you want the ultimate in damage resistance, it can't be beat.

The bottom line is...don't bother shooting at the laser optics. It can be HEAVILY armored.

Isaac Kuo in a Google+ thread

Bomb-Pumped Lasers

A special type of laser is the bomb-pumped laser. This is generally found as a missile warhead. A "submunition" is a warhead that is a single-shot bomb-pumped gamma-ray laser. The original concept was developed by Edward Teller under the name "Excalibur." Teller and Excalibur were later discredited, but the basic idea wasn't.

Here's the problem: the lasing medium in a laser has to be "pumped" or flooded with the same frequency that the laser emits. This isn't a problem with infrared or visible light, but sadly there are not many good sources of x-rays and gamma-rays. About the only good source is a detonating nuclear device, which has the distressing side-effect of vaporizing the laser. So the idea is to make a laser that can frantically manufacture one good x-ray zap in the few microseconds before it is destroyed by the bomb blast. This is the reason it is "one-shot."

(Yes, in theory, hafnium-178m2 is also a good source of gamma rays, but it has problems.)

The Excalibur units had about one hundred x-ray laser rods mounted on a nuclear device. When the hordes of evil Soviet nuclear missiles climbed into view, all one hundred lasers would lock on to different targets, then the bomb was triggered. John Schilling said that due to inefficiency each laser would emit a pulse of only 5×106 Joules, but they'd have a range of up to one hundred kilometers. Unfortunately Dr. Schilling didn't mention whiat size bomb he was basing his estimate on. The unclassified literature about Excalibur is vague, only saying the pumping nuclear device will have a yield that is smaller than your average nuclear warhead. Which could mean almost anything. My guess is under the size of the Hiroshima bomb: 15 to 20 kiloton or so.

According to Directed Energy Missile Defense in Space, a one megaton (1,000 kiloton) nuclear device releases about four billion megajoules (4.184×1015 J), but only a few percent of this will end up in the x-ray laser beams, due to the inherent inefficiency. Call it a total of about 100 million megajoules (1.0×1014 J) of x-ray laser (efficiency of 2.5%). Unfortunately they do not specify how many laser rods they are assuming in their analysis. Assuming 50 laser rods, then each rod would have a beam of 2.0×1012 joules.

Bomb-pumped lasers do not use lenses or mirrors (because there ain't no such thing as an x-ray mirror). Brian Smith-Winsemius gently pointed out to me that I do not know what I am talking about, since he works with x-ray mirrors every day.

I happen to work on a EUV (13.5nm wavelength) prototype photolithography tool. So when I read "Bomb-pumped lasers do not use lenses or mirrors (because there ain't no such thing as an x-ray mirror)." I had to stop and write. The tool I work on uses multi-layer mirrors We have to use mirrors since there are no known lenses that work with 13.5nm or x-ray light. For example, the Chandra X-Ray observatory uses a collector mirror assembly which resembles our collector optic.

Brian Smith-Winsemius

According to The Star Wars Controversy: An "International Security" Reader (edited by Steven E. Miller and Stephen Van Evera, 1986), in order to calculate the beam divergence angle of a bomb-pumped laser, use the following:

θ = 2 * (w / l)


  • θ = beam divergence angle (radians)
  • w = width of lasing rod (meters)
  • l = length of lasing rod (meters)

A practical maximum length of a single laser rod is no more than five meters. Making the rod thinner decreases the divergence angle, but this is limited by diffraction, just like in more conventional lasers. Make the rod too narrow and diffraction actually makes the divergence angle larger. The width limit is:

1.22*L/l = 2*w/l


  • L = wavelength of laser beam (meters)
  • w = width of lasing rod (meters)
  • l = length of lasing rod (meters)

For an x-ray laser rod of one nanometer wavelength and rod length of five meters, the optimum rod width is 0.06 millimeters. The beam divergence angle will be 20 microradians.

This relatively huge divergence further degrades the laser performance. Our 100 million megajoules are now diluted into a 20 microradian cone. If all of this energy came from a single laser rod, on a target at ten megameters (10,000 km), it would deposit about 300 kJ/cm2 over a spot 200 meters wide. Divide the energy by the number of laser rods in the Excalibur, probably around 50. That would be 6 kJ/cm2 over a spot 200 meters wide. Which isn't quite enough if you are targeting enemy ICBMs with a hardness of 10 kJ/cm2.

Note the consequence of the absence of x-ray mirrors: each laser rod will fire a laser beam out both ends of the rod. The majority of the beam will exit from the end of the rod farther from the nuclear blast, however (i.e., most of the beam will travel in the same direction as the x-rays from the blast). If the rod is perpendicular to the blast, equal beams will emerge from both ends.

A bigger draw-back is the fact that while a laser cannon requires a targeting system, Excalibur requires a targeting system for every single laser rod. Such systems are not cheap.

A more minor problem is "bomb-jiggle." Many types of fission devices use conventional explosives to squeeze the core into a critical mass. While the nuclear blast is far too swift to jog the laser rods off their targets, the conventional explosives are not. They might cause the rods to miss-aim, so when the nuclear blast triggers the x-rays, the beams are off-target. This might be avoided by using a laser-initiated fusion device.

1.1.3 Nuclear-bomb-pumped X-ray lasers

     Some observers believe that one of the reasons behind President Reagan's March 23, 1983, speech on defense spending and defensive technology was the result of tests of an X-ray laser pumped by a nuclear blast. The possibility of induced transitions in quantum systems was shown by Einstein back in 1917. Starting off with purely thermodynamical considerations, without any relevance to specific systems, he derived a relationship between the coefficients of spontaneous (A) and induced (B) radiation:

     where λ is the wavelength of electromagnetic emission. It can be seen that the ratio grows rapidly as the wavelength falls. This accounts for the snags encountered by short-wave laser designers.

     A closer examination shows that as the wavelength decreases the required pumping power goes up. For example, for λ = 1 Å the requirement is 1017—1019 W cm-3. It should be emphasized that the pumping energy varies like the fourth power of the wavelength. Therefore, for λ = 10 Å (1-keV quanta) the required input is much lower: 1013—1015 W cm-3.

     But even these values are too high, and such conditions can only be realized in some 'exotic' cases, e.g., in a laser focus or a nuclear detonation. It was in these cases that it was possible to ensure the conditions necessary for X-ray lasing.

     X-ray lasers are thus pulsed lasers with rather short pulses. With so high an input the active medium of the laser will be a plasma, and a strongly ionized plasma at that.

     Some of the plausible realizations of an X-ray laser have long been getting a great deal of attention in the literature. To be more specific, we will take one form, the so-called recombination laser.

     Suppose the thermal radiation yield of a nuclear explosion (mostly X-rays with quanta of several keV) is sufficiently high to ionize fully a substance with atomic number z. Note that after the medium has been ionized fully it becomes transparent to X-rays, so that the substance will gradually be 'eaten up' if the passage time of the pulse front is long as compared with the ionization time.

     After the explosion the fully ionized plasma begins to cool down (with no energy inputs except for the Compton scattering of nuclear-explosion photons by the electrons of the substance), the electrons cooling faster. When the electron temperature has fallen sufficiently, the recombination process sets in. First of all, the electrons begin to descend on energy levels of fully ionized atoms (hydrogen-like ions, so called because all the energy levels coincide completely with those of the hydrogen atom, which has been well studied both theoretically and experimentally, the only difference being that the energy scale differs by the factor z2).

     Calculations of the kinetics of these processes show that the energy level whose principal quantum number n = 3 will be depleted in electrons, with the result that induced transitions are possible to this level from those corresponding to n = 4 or 5.

     For the 5 → 3 transition the energy of quanta emitted is

     To ionize fully a z-electron atom requires an energy of about three-four ionization potentials, i.e., about 40-50 z2 eV. Accordingly, the efficiency of an X-ray laser of this type can only be several per cent, a typical value for atomic and molecular-transition lasers.

     The temperature of the pumping radiation must be higher than some figure, which is, generally speaking, proportional to z2. It was shown that the density of electrons should not be too high to fulfil inverted population conditions. These conditions are met by atoms with z values close to 30 (e.g., iron, zinc, copper).

     In 1981 an unofficial report was published about an experiment on X-ray lasing during an underground nuclear detonation in Nevada, USA. The characteristics were reported to be: wavelength about 14 Å, pulse length more than 10-9 s, pulse energy about 100 kJ.

     The evidence is still too scant for a meaningful detailed analysis. Note only that the 5 → 3 transition in zinc corresponds to a wavelength of 14.2 Å.

     If the active medium started as a solid, then, during the short time of pumping (about 50 ns), its shape will change but slightly. The plasma produced will start expanding at about 50 km s-1. If the initial radius of the rod (as will be seen later the active medium must have this shape) is a fraction of a millimeter, it will take 30 ns for conditions to establish that favour induced emission, which lasts for no longer than l ns. The real diameter of the active medium will then be about 1.5 mm.

     It should be borne in mind that for wavelengths under 2,000 Å mirror optical systems fail and optical resonators can no longer be used to enhance, form, and focus laser radiation. X-ray lasers fall under this constraint. With them radiation is formed and focused by adequately choosing the geometry of active zone, since the beam convergence is governed by the ratio of transverse dimensions to longitudinal ones. Therefore, the best choice is a long slender cylindrical rod, or bar:

where L is the rod length, and d its diameter.

     The ratio L/d cannot, however, be made arbitrarily large. Here diffraction limits come upon the scene. They determine the minimal divergence

where λ is the laser wavelength.

     This reasoning reveals fundamental constraints on the angular divergence for a recombination X-ray laser: the effective diameter of the rod must be about l mm, implying that the real angular divergence for a 10-m rod will be about 10-4. It follows that the brightness of the X-ray laser tested by the USA in 1981 must have been 1011 — 1013 J sr-1 (for a rod of length 1—10 m)—still a long way from meeting the specifications. Note that the recommendations of the Fletcher panel indicate that the brightness of X-ray lasers must be raised over the next several years up to 1014 J sr-1, i.e., the above estimates are fairly reasonable.

     Kilovolt X-rays are strongly absorbed in all substances including air. For example, the effective mean free path of 14.6-Å radiation in nitrogen is about 2 × 10-4 g cm-2 (recall that the total effective thickness of the atmosphere is 1,000 g cm-2). And so a kilovolt X-ray beam is absorbed in the upper atmosphere (higher than 100 km). True, if the laser beam is sufficiently powerful, it might 'drill' through the atmosphere. But this property of X-ray lasers is best exploited by firing not downwards from space but upwards from an altitude of 80—90 km from under a relatively thin atmospheric layer when the target is in space.

     The X-ray beam has the same destruction mechanism as that of the pulsed lasers discussed earlier in the section. It is only to be noted that X-rays penetrate deeper into the material than follows from arguments in terms of thermal diffusivity. Appropriate figures for some of the typical structural materials are provided in Table 1.5. It is seen that the effective mean free path of X-rays is strongly dependent on the quantum energy and the nature of the material.

     We will now try to assess the potentialities of X-ray lasers from general considerations. To be sure, the form of the recombination.laser considered above is not the only feasible alternative for ballistic-missile-defense applications. There are reports of laboratory experiments with a partially-ionized-selenium laser. It has also been reported that in some underground laser tests at the Nevada Test Site the active medium was a material with large enough atomic number. But the assumption that the active medium is fully ionized does not militate the reasoning that follows.

     The energy of a laser is determined by the number of fully ionized atoms in the active rod (in our rough calculations we ignore the losses):

where A is the atomic mass, and ρ the density of the rod material. Since the divergence angle is proportional to d/L (ignoring the expansion of the active medium), the brightness for one rod will be

where q is the density of the laser energy, as defined by

Let Eγ = 1 ke V = 1.6 × 10-16 J, and note that for almost all chemical elements ρ/A is about 0.1. Then

     The rod length is not chosen in an arbitrary manner, it is dictated by the nuclear explosion yield Q, as it is imperative that even the rod's parts farthest from the blast center be fully ionized (recall that after the medium has been fully ionized it becomes transparent to an ionizing radiation).

     Our further analysis requires a knowledge of the arrangement of the rods. Clearly, there are two limiting cases:

  1. Strictly radial arrangement of rods.
  2. Equidistant positioning of rods on the cylinder's generatrix, with the nuclear explosive on the axis (central line) (Figure 1.5).

     It can be readily shown that case (a) is unattractive for energy considerations. In case (b) for simplicity we will consider that the distance from the explosion center to the end of the rod is equal to the rod's length. We now equate the amount of energy flowing through the rod to that required to ionize the entire rod:

     The total efficiency ε is composed of two factors, ε1 and ε2, where ε1 is the share of the ionizing X-rays in the total electromagnetic spectrum of the nuclear detonation (normally it varies from 0.1 for a moderate explosion to close to unity for megaton explosion), and ε2 is the laser efficiency, which for a recombination laser is about 2 per cent. Setting d/L ~ 10-5 and ε1 = 0.3 gives

     If the rod is 10 m long, its brightness is 1016 J sr-1 It follows from (1.33) that to have a lethal range of 2,000 km (brightness 1021 J sr-1) a 50-kiloton* nuclear yield (1 kiloton = 4×1012 J) and 105 rods are required. If we put d/L = 10-4, as we did earlier for the recombination laser, then the requisite explosion yield will increase by a factor of 10, the number of rods remaining the same.

     The kill range of an X-ray laser can be found from the formula

where B is given by the relationship (1.33), N is the number of rods directed at one target, and q0 an energy threshold of target destruction. For Q < Q0 the laser does not function, and for Q > Q0 its radius is no longer dependent on Q.

     It should be noted that formula (1.34) is equivalent to that provided in the first report of the Soviet Scientists' Committee for the Defense of Peace Against Nuclear Threat with N = 1 and Q1 substituted for Q0.

     All the lasers just discussed have one thing in common: they are all based on bound electrons, i.e., on transitions in closed quantum systems (atoms and molecules).


RE: "Bomb Jiggle"

It reminded me of a certain bit of trivia that I had read. I don't have exact references for you at the moment, but I am sure what I am about to say will be substantiated if you peruse the various material available on nuclear weapon operation and effects.

Basically, when the conventional explosives detonate to compress a primary, the fission chain reaction is complete (and the core now expanding) before the detonation front of the conventional explosives has moved more than about an inch from the surface of the device.

Ergo: A fission device has radiated all of its X-rays even before the device has begun to disassemble itself.

In a 2-stage device, the secondary will yet to be compressed, but the detonation of the secondary is necessarily complete before the outer casing holraum has been disassembled (the casing is vaporised by radiation diffusion and must remain largely intact-and-in-place until the compression of the secondary has taken place).

The secondary is compressed (by many processes, but mainly — ) by the reaction force of explosive ablation of its outer layers. So it is only compressed as it is illuminated.

Ergo: The secondary stage of a hydrogen device has radiated all of its X-rays before the outer casing has been fully vaporised/blown off.

This all goes to illustrate how much faster the EM mechanisms go, than the physical ones. This can be seen in the famous "rope-trick" photographs, where the ropes are explosively vaporised (by IR emitted by the fireball) well ahead of the expanding fireball (which is still in the radiative diffusion phase).

An X-ray pumped device will receive all of its pumping X-rays well before any physical shockwave can arrive, including any pressure/shock-waves conducting vibrations, or "jiggle", through physical members to the lasers themselves.

The first "jiggle" that the lasers themselves will feel from the detonation, will be the explosive vaporisation of the laser casing as the laser itself is firing. Physical waves will not have time to reach the laser before this — by quite a large margin.

Now that I think about it, that is more likely to cause "jiggle" — the vaporisation of the lasing medium itself.

From Peter Oliver (p1t1o .) (2017)

The destructive capabilities of Casaba Howitzers, as covered by Matter Beam's beam blog post, are extraordinary. But there was always the photonic cousin of the Casaba Howitzer, Excalibur. Conceived in the 1970s it would use the x-ray emissions of a nuclear device to pump lasants made out of zinc, in order to produce large amounts of semi-coherent x-ray pulses capable of hitting and potentially disabling ICBMs in their launch phase. Using some new techniques, a few scavenged formulas for nuclear-pumped lasers and a figure from Matter Beam's Nuclear EFP blog post I try to calculate some speculative capabilities for a nuclear-pumped laser weapon one might see in a hard SF space battle.

MIMS or metastable inner-shell molecular state, is an exotic state of matter that exists under extreme pressures. At several millions of bar, the atoms inside an element exist under such pressure that they can create bonds between their innermost K-shells. When the pressure is removed those bonds break within picoseconds and emit x-rays. By choosing the right elements or molecules and the right pressure it is possible to convert kinetic energy into narrow linewidth x-rays. Nuclear EFP blog post mentions a figure by Friedtward Winterberg about how 50% of the energy of a nuclear blast can be converted into kinetic energy through the use of a filler, using a Teller-Ulam design to compress the MIMS x-ray source would be more efficient in most cases, but I take the 50% figure as a lower bound efficiency for Nuclear-kinetic conversion efficiency. Efficiencies of up to 40% have been demonstrated in experiments using MIMS, by adding the two efficiencies I assume 20% of the energy of a nuclear device can be converted into a narrow spectrum of high energy x-rays.

The idea is then to use those high-energy x-rays to excite an element with a K-edge lower than the emitted x-rays, leading to the ejection of a K-shell electron which is then quickly filled by a electron from the outer shell, resulting in a x-ray photon being emitted with a narrow spectral linewidth (range of wavelengths). The x-rays are then self-amplified through spontaneous emission. Using gold we get 67 keV x-rays.

THE FEASIBILITY OF THE X-RAY LASER PUMPED WITH A NUCLEAR EXPLOSION gives us the formula to estimate the half-angle of the emitted x-ray pulse and the required width. The angle would be 1.6 * ( wavelength / length)^0.5 or 1.6 * sqrt(wavelength / length). And the width of the lasant rod would be 1.1 * (wavelength * length)^0.5. Which equates to a half-angle of roughly three microradians and a width for the rod of around ten micrometers. This means the x-ray beam will expand to a diameter of 6m at one thousand kilometers and 60m at ten thousand kilometers.

The efficiency for exciting the lasant medium won’t be 100%, my guess would that an additional efficiency ranging from (The rods would emit at both end if they aren't seeding or one end is pumped first, leading to asymmetric gain in on direction) 25 to 12.5% should give a decent representation for the total efficiency of such a device: 5 to 2.5%. Or 200-100 TJ per megaton.

As for the energy density of those rods, if we assume that each gold atom will have both its electrons knocked out and filled by an outer-shell electron we will get 134 keV per gold atom, 12.88GJ/mol and 65GJ per kilogram of gold. The MIMS x-ray source would require two particles per bond to emit two x-rays, if we also use gold for that we get values of around 30GJ/kg. It would take at least 1540kg gold for the lasant rods and 3330kg for the MIMS source, it might be possible to combine the x-ray source and the lasant rods into a single object, but that would be another engineering challenge to overcome. A single 5m x 10µm rod would emit around 500kJ when fully populated and with zero extra losses.

A 100TJ nuclear laser would weight between five to tens tons, which would make it considerably heavier than most Casaba Howitzers. But it does carry a series of advantages:

  1. The beam moves at the speed of light, making any active defense impossible.
  2. The beam full-angle is around 6 microradians compared to one hundred for a casaba howitzer.
  3. The beam consists out of hard x-rays instead out of sub-MeV particles, making it highly effective at soft kills against ships without any proper radiation shielding.
  4. A single device could also work for point defense and or target multiple ships at once.

It would make for an intermediate weapon in the nuclear DEW arsenal.

     Casaba Howitzers being light, short ranged and having high-velocity particle beams.
     Spaced Explosively Formed Projectiles (EFPs) are heavy, have infinite range and are very slow relatively speaking.
     X-rasers are long ranged, can soft kill through radiation, are heavy and they are multi-purpose.

Some numbers:

At 1,000 kilometers
A crater in armor steel: 35.8m wide and 15m deep.
A crater in CNT: 20.8m wide and 7.38m deep.
A crater in graphene: 16.8 m wide and 5.4m deep.

At 10,000 kilometers
A crater in steel: 66.4 m wide and 3.19 m deep (25,120kg/m2)
A crater in graphene: 60.6 m wide and 31.6cm deep (~665kg/m2)

     That's pretty awesome. Note that the tamper has to be much heavier than the nuclear material being heated (to prevent effective kinetic energy lost through momentum transfer) and I think the 10 micrometer wide lasing rod is a bit too narrow, but it is a workable idea.

     Matter Beam, that's some design detail that would most likely fit into the mass constraint of ten tons I gave.
     Considering the rods are made out of gold and we have like 3 tons (example) of it it will need around 0.15m3 area, and because they are 5m long the base is 0.03m2. If we put the rods in some lightweight low-Z material we simply have 10µm wide rods placed in some medium (maybe aerogel), which is more than doable with current tech. Or rather, you would see bundles of them, maybe each bundle has 1-10GJ each, allowing you to use your 10 ton 100TJ device to target 10,000-100,000 individual targets

     Interesting, it seems that efficiency is the achilles heel of the concept.

     Todd Zircher, I disagree, while the efficiency is unfortunate it doesn't make much of a difference. The energy per square meter (relates to the actual effect) at a distance of one thousand kilometers would be the same as if we used the 1 megaton device at 100% efficiency and exploded it at a distance 6.7m from the hull of the target. Point blank range, you can see this weapon as a deal: You trade several tons of equipment and a one megaton nuke for a 25 kT nuke that automatically teleports, past every defense, almost inside the armor of the ship and explodes.

     I love gooooooold

     Troy, The blingiest laser in space

     Kerr, still, you need to actually protect all of the tiny gold members inside the package. A similar Excalibur from extremely long range will slag every single gold member inside the weapon casing. To say nothing of regular laser attacks jostling with and destroying the weapon.
     And once the weapon is fired, it creates a gigantic, roiling cloud of blue-glowing gold plasma that bathes your fleet.

     Troy, As said to Matterbeam, you can emerge those rods in a suitable medium. Besides, the actual cross-section of the weapon would be rather small and could somewhat easily be shielded against.

     With 10µmm/5m long gold lasing rods they should call this the Rapunzel Bomb.
     One of the problems with your lasing rods is that you're relying on random collisions to achieve the lasing ratio. This thing has a hellish shotgun effect in addition to basically being a nuke in space.


There is a variant on the bomb-pumped laser in Larry Niven and Jerry Pournelle's classic novel Footfall, which is arguably the best "alien invasion" novel ever written. They noticed that bomb-pumped lasers is a concept that merges seamlessly with Orion drive spacecraft. In this case the submunitions do not need a bomb. They are thrown below the pusher plate, they take aim at the enemy, then the next propulsion bomb pushes the ship and simultaneously pumps the submunitions. You can find more detalis about the spacecraft here.

Impulsively Driven Laser

Andrew Presby found an interesting document entitled "On The Feasibility of an Impulsively Driven Gamma-ray Laser" (1979) at the Federation of American Scientists website. Please note this is for gamma-ray lasers, not x-ray lasers like the discussion above. That is probably why the x-ray laser rods had a maximum length of 5 meters while these graser rods have a length of 0.05 meters.

I wish I'd found the dumb thing years ago when I taking my graduate school lasers class and looking for physics papers on bomb pumped GRASERS. The Nevada experiment described herein sounds suspiciously like the bomb pumped XRASER (xray laser) experiments in the 70s/80s codenamed Excalibur that started the chain of events that got Teller in so much trouble. Thing I cannot figure is that the device described herein seems to produce GAMMA RAYS in the 6-8 MeV range (~0.002 Ångström) which is 10000 times higher photon energy than the stuff I've found in the literature that is available on Excalibur (which was in the ~14 Ångström range).

I've never heard if this worked or not... but there you go.

Andrew Presby

The document suggest using Tantalum-180 dissolved in Lithium-7 for the lasing rods, about one part in four thousand. Alternatives are Cobalt-109 and Molybdenum-99.

The design uses the Mössbauer effect, the recoil-free emission and absorption of gamma ray photons by atoms bound in a solid form. This is important. Laser light is coherent light, where all the photons are in perfect lock-step. The trouble with x-ray and gamma-ray emission is that they are powerful enough to make the excited atom recoil in reaction. This throws off the synchronization, so that the beam is not coherent, and thus not a laser beam. The Mössbauer effect prevents this by locking the lasing atoms in a matrix of anchor atoms, thus dealing with the recoil.

It was estimated that the grasing transition energy densities of tens of kilojoules per cubic centimeter. This means a one megajoule graser could fit in a breadbox, sans bomb of course. A laser beam composed of gamma rays impacting on, say, an incoming Soviet nuclear warhead would produce a flood of neutrons generated by gamma-ray/neutron recations, burning a nice hole. And the high-energy Compton-scattered electrons would create an enormous EMP, frying the warhead's electronics.

The document describes a test for the concept. A cylindrical package five centimeters long by five centimeters in radius would be packed with 20,000 lasing needles 25 µ diameter by 5 centimeters long (I assume that µ means micrometre or micron). The needles would be composed of Lithium-7 with 0.025% Tantalum-180. The needles would be aligned in parallel with 100 µ spacing between their axes, and arranges so that the centers of no three needles would be in a straight line.

The rod assembly package would be insulated from the bomb by insulating and moderating material (from the bomb: 15 cm of space, 7 cm of lead, 20 cm of heavy water, 5 cm to the center of the rod assembly). This will ensure that only the proper radiation strikes the assembly, and to allow the assembly to survive for the few microseconds required to create the graser beam. The lead [1] attenuates the gamma radiation from the bomb, [2] slows the debris motion, [3] and blocks the x-rays that would destroy the package. The heavy water moderates the neutron output.

The beam divergence is determined by the aspect ratio, which for this package is on the order of 0.5 milliradian. This is above the diffraction limit (about 8 milliradian).

In the proposed test, a one kiloton device would be detonated to pump the graser. The five centimeter needles have a calculated gain of 2 x 104. About 9% of the nuclear energy in the grasing transition will actually escape the needles, due to the short pathlength for 6.3 keV gamma rays. The energy available is 7.3 x 1016 MeV cm-3, which means the graser beam will be a piddling little 2.6 kilojoules. Keep in mind that is was intended as a test rig, not a functioning weapon.

Nuclear Reactor Lasers


A nuclear pumped laser is a laser pumped with the energy of fission fragments. The lasing medium is enclosed in a tube lined with uranium-235 and subjected to high neutron flux in a nuclear reactor core. The fission fragments of the uranium create excited plasma with inverse population of energy levels, which then lases. Other methods, e.g. the He-Ar laser, can use the He(n,p)H reaction, the transmutation of helium-3 in a neutron flux, as the energy source, or employing the energy of the alpha particles.

This technology may achieve high excitation rates with small laser volumes.

Some example lasing media:


Research in nuclear pumped lasers started in the early 1970s when researchers were unable to produce a laser with a wavelength shorter than 110 nm with the end goal of creating an x-ray laser. When laser wavelengths become that short the laser requires a huge amount of energy which must also be delivered in an extremely short period of time. In 1975 it was estimated, by George Chapline and Lowell Wood from the Lawrence Livermore National Laboratory, that “pumping a 10-keV (0.12-nm) laser would require around a watt per atom” in a pulse that was “10−15 seconds x the square of the wavelength in angstroms.” As this problem was unsolvable with the materials at hand and a laser oscillator was not working, research moved to creating pumps that used excited plasma. Early attempts used high-powered lasers to excite the plasma to create an even more highly powered laser. Results using this method were unsatisfying, and fell short of the goal. Livermore scientists first suggested using a nuclear reaction as a power source in 1975. By 1980 Livermore considered both nuclear bombs and nuclear reactors as viable energy sources for an x-ray laser. On November 14, 1980, the first successful test of the bomb-powered x-ray laser was conducted. The use of a bomb was initially supported over that of the reactor driven laser because it delivered a more intense beam. Livermore’s research was almost entirely devoted to missile defense using x-ray lasers. The idea was to mount a system of nuclear bombs in space where these bombs would each power approximately 50 lasers. Upon detonation these lasers would fire and theoretically destroy several dozen incoming nuclear missiles at once. Opponents of this plan found many faults in such an approach and questioned aspects such as the power, range, accuracy, politics, and cost of such deployments. In 1985 a test titled ‘Goldstone’ revealed the delivered power to be less than believed. Efforts to focus the laser also failed.

Fusion lasers (reactor driven lasers) started testing after the bomb-driven lasers proved successful. While prohibitively expensive (estimated at 30,000 dollars per test), research was easier in that tests could be performed several times a day and the equipment could be reused. In 1984, a test achieved wavelengths of less than 21 nm the closest to an official x-ray laser yet. (There are many definitions for an x-ray laser, some of which require a wavelength of less than 10 nm). The Livermore method was to remove the outer electrons in heavy atoms to create a “neon-like” substance. When presented at an American Physical Society meeting, the success of the test was shared by an experiment from Princeton University which was better in size, cost, measured wavelength, and amplification than Livermore’s test. Research has continued in the field of nuclear pumped lasers and it remains on the cutting edge of the field.


At least three uses for bomb pumped lasers have been proposed.


Laser propulsion is an alternative method of propulsion ideal for launching objects into orbit, as this method requires less fuel, meaning less mass must be launched. A nuclear pumped laser is ideal for this operation. A launch using laser propulsion requires high intensity, short pulses, good quality, and a high power output. A nuclear pumped laser would theoretically be capable of meeting these requirements.


The characteristics of the nuclear pumped laser make it ideal for applications in deep-cut welding, cutting thick materials, the heat treating of metals, vapor deposition of ceramics, and the production of sub-micron sized particles.


Titled Project Excalibur, the program was a part of President Reagan’s Strategic Defense Initiative. Livermore Laboratories conceived of the initial idea and Edward Teller developed and presented the idea to the president. Permission was granted to pursue the project though it has been reported Reagan was reluctant to incorporate nuclear devices in the nation’s plan against nuclear devices. While initial tests were promising, the results never reached acceptable levels. Later, lead scientists were accused of falsifying the reports. Project Excalibur was cancelled several years later.

From the Wikipedia entry for NUCLEAR PUMPED LASER

      Nuclear reactor lasers are devices that can generate lasers from nuclear energy with little to no intermediate conversion steps.

     We work out just how effective they can be, and how they stack up against conventional electrically-powered lasers. You might want to re-think your space warfare and power beaming after this.

     Nuclear energy and space have been intertwined since the dawn of the space age. Fission power is reliable, enduring, compact and powerful. These attributes make it ideal for spacecraft that must make every kilogram of mass as useful and as functional as possible, as any excess mass would cost several times its weight in extra propellant. They aim for equipment for the highest specific power (or power density PD), meaning that it produces the most watts per kilogram.

     Lasers use a lasing medium that is rapidly energized or ‘pumped’ by a power source. Modern lasers use electric discharges from capacitors to pump gases, or a current running through diodes. The electrical power source means that they need a generator and low temperature radiators in addition to a nuclear reactor… these are significant mass penalties to a spaceship.

     Fission reactions produce X-rays, neutrons and high energy ions. The idea to use them to pump a lasing medium has existed ever since the first coherent wavelengths were released from a ruby crystal in 1960.

     Much research has been done in the 80s and 90s into nuclear-pumped lasers, especially as part of the Strategic Defense Initiative. If laser power can be generated directly from a reactor, there could be significant gains in power density.

     The research findings on nuclear reactor lasers were promising in many cases but did not succeed in convincing the US and Russian governments to continue their development. Why were they unsuccessful and what alternative designs could realize their promise of high power density lasers?

Distinction between NBPLs and NRLs

     Most mentions of nuclear pumped lasers relate to nuclear bombpumped lasers. They are exemplified by project Excalibur: the idea was to use the output of a nuclear device to blast metal tubes with X-rays and have them produce coherent beams of their own.

     We will not be focusing on it.

     The concept has many problems that prevent it from being a useful replacement for conventional lasers. You first need to expend a nuclear warhead, which is a terribly wasteful use of fissile material. Only a tiny fraction of the warhead’s X-rays, which are emitted in all directions, are intercepted by the metal tube. From those, a tiny fraction of its energy is converted into coherent X-rays. If you multiply both fractions, you find an exceedingly low conversion ratio.

     Further research has revealed this to be on the order of <0.00001%. It also works for just a microsecond, each shot destroys its surroundings and its effective range is limited by relatively poor divergence of the beam. These downsides are acceptable for a system meant to take down a sudden and massive wave of ICBMs at ranges of 100 to 1000 kilometers, but not much else.

     Instead, we will be looking at nuclear reactor pumped lasers. These are lasers that draw power from the continuous output of a controlled fission reaction.


     We talk about efficiency and power density to compare the lasers mentioned in this post. How are we working them out?

     For efficiency, we multiply the reactor’s output by the individual efficiencies of the laser conversion steps, and assume all inefficiencies become waste heat. The waste heat is handled by flat double-sided radiator panels operating at the lowest temperature of all the components, which is usually the laser itself.

     This will give a slightly poorer performance than what could be obtained from a real world engineered concept. The choice of radiator is influenced by the need for easy comparison instead of maximizing performance in individual designs.

     We will note the individual efficiencies as Er for the reactor, El for the laser and Ex for other components. The overall efficiency will be OE.

OE = Er * Ex * El * Eh

     In most cases, Er and Eh can be approximated as equal to 1. As we are considering lasers for use in space with output on the order of several megawatts and beyond, it is more accurate to use the slope efficiency of a design rather than the reported efficiency. Laboratory tests on the milliwatt scale are dominated by the threshold pumping power, which cuts into output and reduces the efficiency. As the power is scaled up, the threshold power becomes a smaller and smaller fraction of the total power.

     Calculating power density (PD) in Watts per kg for several components working with each other’s outputs is a bit more complicated. As above, we’ll note them PDr, PDl, PDh, PDx and so on. The equation is:

PD = (PDr * OE) / (1 + PDr (Ex/PDx + Ex*El/PDl + (1 - Ex*El)/PDh))

     Generally, the reactor is a negligible contributor to the total mass of equipment, as it is in the several hundred kW/kg, so we can simplify the equation to:

PD = OE / (Ex/PDx + Ex*El/PDl + (1 - Ex*El)/PDh)

     Inputting PDx, PDl and PDh values in kW/kg creates a PD value also in kW/kg.

Direct Pumping

     The most straightforward way of creating a nuclear reactor laser is to have fission products interact directly with a lasing medium. Only gaseous lasing mediums, such as xenon or neon, could survive the conditions inside a nuclear reactor indefinitely, but this has not stopped attempts at pumping a solid lasing medium.

     Three methods of energizing or pumping a laser medium have been successful.

Wall pumping

     Wall pumping uses a channel through which a gaseous lasing medium flows while surrounded by nuclear fuel. The fuel is bombarded by neutrons from a nearby reactor. The walls then release fission fragments that collide with atoms in the lasing medium and transfer their energy to be released as photons. The fragments are large and slow so they don’t travel far into a gas and tend to concentrate their energy near the walls. If the channels are too wide, the center of the channel is untouched and the lasing medium is unevenly pumped. This can create a laser of very poor quality.

     To counter this, the channels are made as narrow as possible, giving the fragments less distance to travel. However, this multiplies the numbers of channels needed to produce a certain amount of power, and with it the mass penalty from having many walls filled with dense fissile fuel.

     The walls absorb half of the fission fragments they create immediately. They release the surviving fragments from both faces of fissile fuel wall. So, a large fraction of the fission fragment power is wasted. They are also limited by the melting temperatures of the fuel. If too many fission fragments are absorbed, the heat would the walls to fail, so active cooling is needed for high power output.

     The FALCON experiments achieved an efficiency of 2.5% when using xenon to produce a 1733 nm wavelength beam.

     Gas laser experiments at relatively low temperatures reported single-wavelength efficiencies as high as 3.6%. The best reported performance was 5.6% efficiency from an Argon-Xenon mix producing 1733 nm laser light, from Sandia National Laboratory.

     Producing shorter wavelengths using other lasing mediums, such as metal vapours, resulted in much worse performance (<0.01% efficiency).

     Higher efficiencies could be gained from a carbon monoxide or carbon dioxide lasing medium, with up to 70% possible, but their wavelengths are 5 and 10 micrometers respectively (which makes for a very short ranged laser) and a real efficiency of only 0.5% has been demonstrated.

     One estimate presented in this paper is a wall-pumped mix of Helium and Xenon that converts 400 MW of nuclear power into 1 MW of laser power with a 1733 nm wavelength. It is expected to mass 100 tons. That is an efficiency of 0.25% and a power density of just 10 W/kg.

     It illustrates the fact that designs meant to sit on the ground are not useful references.

     A chart from this NASA report reads as a direct pumped nuclear reactor laser with 10% overall efficiency having a power density of about 500 W/kg, brought down to 200 W/kg when including radiators, shielding and other components.

Volumetric pumping

     Volumetric pumping has Helium-3 mixed in with a gaseous lasing medium to absorb neutrons from a reactor.

     Neutrons are quite penetrating and can traverse large volumes of gas, while Helium 3 is very good at absorbing neutrons. When Helium-3 absorbs neutrons, it creates charged particles that in turn energize lasing atoms when they enter into contact with each other. Therefore, neutrons can fully energize the entire volume of gas. The main advantages of this type of laser pumping is the much reduced temperature restrictions and the lighter structures needed to handle the gas when compared to multiple narrow channels filled with dense fuel.

     However, Helium-3 converts neutrons into charged particles with very low efficiency, with volumetric pumping experiments reporting 0.1 to 1% efficiency overall. This is because the charged particles being created contain only a small portion of the energy the Helium-3 initially receives.

Semiconductor pumping

     The final successful pumping method is direct pumping of a semiconductor laser with fission fragments. The efficiency is respectable at 20%, and the compact laser allows for significant mass savings, but the lasing medium is quickly destroyed by the intense radiation. It consists of a thin layer of highly enriched uranium sitting on a silicon or gallium semiconductor, with diamond serving as both moderator and heatsink.

     There are very few details available on this type of pumping.

     A space-optimized semiconductor design from this paper that suggests that an overall power density of 5 kW/kg is possible. It notes later on that even 18 kW/kg is achievable. It is unknown how the radiation degradation issue could be solved and whether this includes waste heat management equipment. Without an operating temperature and a detailed breakdown of the component masses assumed, we cannot work it out on our own.

Other direct pumped designs

     Wall or volumetric pumping designs were conceived when nuclear technology was still new and fission fuel had to stay in dense and solid masses to achieve criticality. More modern advances allow for more effective forms for the fuel to take.

     The lasing medium could be made to interact directly with a self-sustaining reactor core. This involves mixing the lasing medium with uranium fluoride gas, uranium aerosols, uranium vapour at very high temperatures or uranium micro-particles at low temperatures.

     The trouble with uranium fluoride gas and aerosols or micro-particles is the tendency for them to re-absorb the energy (quenching) of excited lasing atoms. This has prevented any lasing action from being realized in all experiments so far. As this diagram shows, uranium fluoride gas absorbs most wavelengths very well, further reducing laser output.

     If there is a lasing medium that is not quenched by uranium fluoride, then there is potential for extraordinary performance.

     An early NASA report on an uranium fluoride reactor lasers for space gives a best figure of 73.3 W/kg from what is understood to be a 100 MW reactor converting 5% of its output into 340 nanometer wavelength laser light. With the radiators in the report, this falls to 56.8 W/kg.

     If we bump up the operating temperature to 1000K, reduce the moderator to the 20cm minimum, replace the pressure vessel with ceramics and use more modern carbon fiber radiators, we can expect the power density of that design to increase to 136 W/kg.

     Uranium vapours are another option. They require temperatures of 4000K and upwards but if the problem of handling those temperatures is solved (perhaps by using actively cooled graphite containers), then 80% of the nuclear output can be used to excite the lasing medium, for an overall efficiency that is increased four-fold over wall pumping designs.

     More speculative is encasing uranium inside a C60 Buckminsterfullerene sphere. Fission fragments could exit the sphere while also preventing the quenching of the lasing material. This would allow for excellent transmission of nuclear power into the lasing medium, without extreme temperature requirements.

Nuclear-electric comparison

     With these numbers in mind, it does not look like direct pumping is the revolutionary upgrade over electric lasers that was predicted in the 60s.

     Turbines, generators, radiators and laser diodes have improved by a lot, and they deliver a large fraction of a reactor’s output in laser light. We expect a space-optimized nuclear-electric powerplant with a diode laser to have rather good performance when using cutting edge technology available today.

     With a 100 kW/kg reactor core, a 50% efficient turbine at 10 kW/kg, an 80% efficient electrical generator at 5 kW/kg, powering 60% efficient diodes at 7 kW/kg and using 1.34 kW/kg radiators to get rid of waste heat (323K temperature), we get an overall efficiency of 24% and a power density of 323 W/kg.

     A more advanced system using a very powerful 1 MW/kg reactor core, a 60% efficient MHD generator at 100 kW/kg with 1000K 56.7 kW/kg radiators, powering a 50% efficient fiber laser cooled by 450K 2.3 kW/kg radiators, would get an overall efficiency of 30% and a power density of 2.5 kW/kg.

     Can we beat these figures with reactor lasers?

Indirect pumping

     The direct pumping method uses the small fraction of a reactor’s output that is released in the form of neutrons, or problematic fission fragments. Would it not be better to use the entire output of the nuclear reaction?

     Indirect pumping allows us to use 100% of the output in the form of heat. This heat can then be converted into laser light in various ways.

     Research and data for some of the following types of lasers comes from solar-heated designs that attempt to use concentrated sunlight to heat up an intermediate blackbody that in turn radiates onto a lasing medium. For our purposes, we are replacing the heat of the Sun with a reactor power source. It is sometimes called a ‘blackbody laser’ in that case.

Blackbody radiation pump

     At high temperatures, a blackbody emitter radiates strongly in certain wavelengths that lasing materials can be pumped with. A reactor can easily heat up a black carbon surface to temperatures of 2000 to 3000K – this is what nuclear rockets are expected to operate at anyhow.

     Some of the spectrum of a blackbody at those temperatures lies within the wavelengths that are absorbed well by certain crystal and gaseous lasing mediums.

     Neodymium-doped Ytrrium-Aluminium-Garnet (Nd:YAG) specifically is a crystal lasing medium that has been thoroughly investigated as a candidate for a blackbody-pumped laser. It produces 1060 nm beams.

     Efficiency figures vary.

     A simple single-pass configuration results in very poor efficiency (0.1 to 2%). This is because the lasing medium only absorbs a small portion of the entire blackbody spectrum. In simpler terms, if we shine everything from 100 nm to 10,000 nm onto a lasing medium, it will convert 0.1 to 2% of that light into a laser beam and turn the rest into waste heat. With this performance, blackbody pumped lasers are no better than direct pumped reactor laser designs from the previous section.

     Instead, researchers have come up with a way to recover the 99 to 99.9% of the blackbody spectrum that the lasing medium does not use. This is the recycled-heat blackbody pumped laser.

     An Nd:YAG crystal sits inside a ‘hot tube’. Blackbody radiation coming from the tube walls passes through the crystal. The crystal is thin and nearly transparent to all wavelengths. The illustration above uses Ti:Sapphire but the concept is the same for any laser crystal.

     Only about 2% of blackbody spectrum is absorbed with every pass through the crystal. The remaining 97 to 98% pass through to return to the hot tube’s walls. They are absorbed by a black carbon surface and recycled into heat. Over many radiation, absorption and recycling cycles, the fraction of total energy that becomes laser light increases for an excellent overall efficiency.

     35% efficiency with a Nd:YAG laser was achieved.

The only downside is that the Nd:YAG crystal needs intense radiation within it to start producing a beam. The previous document suggests that 150 MW/m^3 is needed. Another source indicates 800 MW/m^3. We also know that efficiency increases with intensity. If we aim for 1 GW/m^3, which corresponds to 268 Watts shining on each square centimetre of a 1 cm diameter lasing rod, we would need a 1:1 ratio of emitting to receiving area if the emitter has a temperature of at least 2622K.

     From a power conversion perspective, a 98% transparent crystal that converts 35% of spectrum it absorbs means it is only converting 0.7% of every Watt of blackbody radiation that shines through it. So, a crystal rod that receives 268 Watts on each square centimetre will release 1.87 W of laser light.

     We can use the 1:1 ratio of emitter and receiver area to reduce weight and increase power density. Ideally, we can stack emitter and receiver as flat surfaces separated by just enough space to prevent heat transfer through conduction.

     Reactor coolant channels, carbon emitting surface (1cm), filler gas, Nd:YAG crystal (1cm) and helium channels can be placed back to back. The volume could end up looking like a rectangular cuboid, interspaced by mirror cavities.

     20 kg/m^2 carbon layers and 45.5 kg/m^2 crystal layers that release 1.87 W per square centimetre, with a 15% weight surplus for other structures and coolant pipes, puts this component’s power density at about 250 W/kg.

     The laser crystal is cooled from 417K according to the set-up in this paper. Getting rid of megawatts at such a low temperature is troublesome. Huge radiator surface areas will be required.

     As we are using flat panel radiators throughout this post, we have only two variables: material density, material thickness and operating temperature. The latter is set by the referenced document.

     We will choose a 1mm thick radiator made of low density polyethylene. We obtain 0.46 kg/m^2 are plausible. When radiating at 417K, they could achieve 3.73 kW/kg.

     It is likely that they will operate at a slightly lower temperature to allow for a thermal gradient that transfers heat out of the lasing medium and into the panels, and the mass of piping and pumps is not to be ignored, but it is all very hard to estimate and is more easily included in a 15% overall power density penalty for unaccounted-for components.

A 100 kW/kg reactor, 250 W/kg emitter-laser stack and 3.73 kW/kg radiators would mean an overall power density of 188 W/kg, after applying the penalty.

     Gaseous lasing mediums could hold many advantages over a crystal lasing medium. They require much less radiation intensity (W/m^3) to start producing a laser beam. This research states that an iodine laser requires 450 times less intensity than an equivalent solid-state laser. It is also easier to cool a gas laser, as we can simply get the gas to flow through a radiator. On the other hand, turbulent flow and thermal lensing effects can deteriorate the quality of a beam into uselessness.

     No attempts have been reported on applying the heat recycling method from the Nd:YAG laser to greatly boost efficiency in a gas laser. Much research has been performed instead on direct solar-pumped lasers where the sunlight passes through a gaseous medium just once.

     The Sun can be considered to be a blackbody emitter at a temperature of 5850K. Scientists have found the lasing mediums best suited to being pumped by concentrated sunlight – they absorb the largest fraction of the sunlight’s energy.

     That fraction is low in absolute terms, meaning poor overall performance. An iodine-based lasing medium reported 0.2% efficiency. Even worse efficiency of 0.01% was achieved when using an optically-pumped bromine laser. Similarly, C3F7I, an iodine molecule which produces 1315 nm laser light, was considered the best at 1% efficiency.

     Solid blackbody emitters are limited to temperatures just above 3000K. There would be a great mismatch between the spectrum this sort of blackbody releases and the wavelengths the gaseous lasing mediums cited above require. In short, the efficiency would fall below 0.1% in all cases.

     One final option is Gallium-Arsenic-Phosphorus Vertical External Cavity Surface Emitting Laser (VECSEL) designed for use in solar-powered designs. It can absorb wavelengths between 300 and 900nm, which represents 65% of the solar wavelengths but only 20% of the radiation from a 3000K blackbody. This works out to an emitter with a power density of 45.9 kW/kg.

     The average efficiency is 50% when producing a 1100nm beam. Since it is extracting 20% of the wavelengths from the emitter, this amounts to 10% overall efficiency.

     Using the numbers in this paper, we can surmise that the VECSEL can handle just under 20 MW/kg. The mass of the laser is therefore negligible. With a 100 kW/kg reactor, we work out a power density of 3.1 kW/kg.

     VECSELs can operate at high temperatures, but they suffer from a significant efficiency loss. We will keep them at 300K at most. It is very troublesome as 20 MW of light is needed to be concentrated on the VECSEL to start producing a laser beam. 90% of that light is being turned into waste heat within a surface a few micrometers thick. Diamond heatsink helps in the short term but not in continuous operation.

     Radiator power density will suffer. Even lightweight plastic panels at 300K struggle to reach 1 kW/kg. When paired with the previous equipment and under a 15% penalty for unaccounted for components, it means an overall power density of 91 W/kg.

     This illustrates why an opaque pumping medium is unsuitable for direct pumping as it does not allow for recycling of the waste heat.

Filtered blackbody pumping

     A high temperature emitter radiates all of its wavelengths into the blackbody-pumped lasing medium. We described a method above for preventing the lasing medium from absorbing 98 to 99.9% of the incoming energy and turning it immediately into waste heat. The requirement was that the lasing medium be very transparent to simply let through the unwanted wavelengths.

     However, this imposes several design restrictions on the lasing medium. It has to be thin, it has to be cooled by transparent fluids, and it might have to sit right next to a source of high temperature heat while staying at a low temperature itself.

     We can instead filter out solely the laser pumping wavelengths from the blackbody spectrum and send those to the lasing medium while recycling the rest.

     The tool to do this is a diffraction grating. There are many other ways of extracting specific wavelengths from a blackbody radiation spectrum, such as luminescent dyes or simple filters, but this method is the most efficient.

     Like a prism, a diffraction grating can separate out wavelengths from white light and send them off in different directions. For most of those paths, we can put a mirror in the way that send the unwanted wavelengths back into the blackbody emitter. For a small number of them, we have a different mirror that reflects a specific wavelength into the lasing medium.

     A lasing medium that receives just a small selection of optimal wavelengths is called optically pumped. It is a common feature of a large number of lasers, most notably LED-pumped designs. We can use them as a reference for the potential performance of this method.

     We must note that while we can get high efficiencies, power is still limited, as in the previous section. Extracting a portion of the broadband spectrum that the lasing medium accepts also means that power output is reduced to that portion.

     Another limitation is the temperature of the material serving as a blackbody emitter. The nuclear reactor that supplies the heat to the emitter is limited to 3000K in most cases, so the emitter must be at that temperature or lower (even if a carbon emitter can handle 3915K at low pressures and up to 4800K at high pressures, while sublimating rapidly).

     Thankfully, the emission spectrum of a 3000K blackbody overlaps well with the range of wavelengths an infrared fiber laser can be pumped with.

     A good example is an erbium-doped lithium-lanthanide-fluoride lasing medium in fiber lasers. We could use it to produce green light as pictured above, but invisible infrared is more effective.

     As we can see from here, erbium absorbs wavelengths between 960 and 1000 nm rather well. It re-emits them at 1530 nm wavelength laser light with an efficiency reported to be 42% in the ‘high Al content’ configuration, which is close the 50% slope efficiency.

     In fact, the 960-1000 nm band represents 2.7% of the total energy emitted. It is absorbing 125 kW from each square meter of emitter. If the emitter is 1 cm thick plate of carbon and the diffraction grating, with other internal optics needed to guide light into the narrow fiber laser, are 90% efficient, then we can expect an emitter power density of about 5.6 kW/kg.

     Another example absorbs 1460 to 1530 nm light to produce a 1650 nm beam. This is 3.7% of the 3000K emitter’s spectrum, meaning an emitter power density of 7.7 kW/kg.

     The best numbers come from ytterbium fiber lasers. They have a wider band of wavelengths that can be pumped with, 850 to 1000 nm (which is 10.1% of the emitter’s output), and they convert it into 1060 nm laser light with a very high efficiency (90%). It would give the emitter an effective power density of 23.4 kW/kg. More importantly, we have examples operating at 773K.

     The respected Thorlabs manufacturer gives information about the fiber lasers themselves. They can handle 2.5 GW/m^2 continuously, up to 10GW/m^2 before destruction. Their largest LMA-20 core seems to be able to handle 38 kW/kg of pumping power. It is far from the limit.

     Based on numbers provided by this experiment, we estimate the fiber laser alone to be on the order of 95kW/kg. Another source works out a thermal-load-limited fiber laser with 84% efficiency to have a power density of 695 kW/kg before the polymer cladding melts at 473K.

We can try to estimate the overall power density of a fiber laser.

     A 100 kW/kg reactor is used to heat a 23.4 kW/kg emitter, where a diffraction grating filters out 90% of the output to be fed into a fiber laser with 90% efficiency and negligible mass. The waste heat is handled by 1mm thick carbon fiber panels operating at 773K for a power density of 20.2 kW/kg.

     Altogether, this gives us 11 kW/kg after we include the same penalty as before.

     If it is too difficult to direct light from a blackbody emitter into the narrow cores of fiber lasers, then a simple lasing crystal could be used. This is unlikely, as it has alreadybeen done, even in high radiation environments.

     Nd:YAG, liberated from the constraint of having to be nearly entirely transparent, can achieve good performance. It can sustain a temperature of 789K.

     We know that Nd:YAG can achieve excellent efficiency when being pumped by very intense 808nm light to produce a 1064nm beam, of 62%. It is hoped that this efficiency is maintained across the lasing crystal’s 730 to 830nm absorption band.

     A 3000K blackbody emitter releases 6% of its energy in that band. At 20 kg/m^2, this gives a power density of 13.8 kW/kg. We will cut off 10% due to losses involved in the filtering and internal optics.

     As before, the laser crystal itself handles enough pumping power on its own to have a negligible mass.

     The radiators operating at 789K will require carbon fiber panels. They’ll manage a power density of 22 kW/kg.

Optimistically, we can expect a power density of 3.7 kW/kg (reduced by 15%) when we include all the components necessary.

Ultra-high-temperature blackbody pumped laser

     We must increase the temperature of the blackbody emitter. It can radiate more energy across the entire spectrum, and concentrates it in a narrower selection of shorter wavelengths.

     Solid blackbody surfaces are insufficient. To go beyond temperatures of 4000K, we must consider liquid, gaseous and even plasma blackbody emitters. This requires us to abandon conventional solid-fuel reactors and look at more extreme designs.

     There is a synergy to be gained though. The nuclear fuel can also act as blackbody emitter if light is allowed to escape the reactor.

     Let us consider two very high to ultra-high temperature reactor designs that can do that: a 4200K liquid uranium core with a gas-layer-protected transparent quartz window and a 19,000K gaseous uranium-fluoride ‘lightbulb’ reactor.

     For each design, we will try to find an appropriate laser that makes the best use of the blackbody spectrum that is available.


     Uranium melts at 1450K and boils at 4500K. It can therefore be held as a dense liquid at 4200K. We base ourselves on this liquid-core nuclear thermal rocket, where a layer of fissile fuel is held against the walls of a drum by centrifugal effects. The walls are 10% reflective and 90% transparent.

     The reflective sections hold neutron moderators to maintain criticality. This will be beryllium protected by a protected silver mirror. It absorbs wavelengths shorter than 250 nm and reflects longer wavelengths with 98% reflectivity.

     We expect the neutron moderator in the reflective sections, combined with a very highly enriched uranium fuel, to still manage criticality. The spinning liquid should spread the heat evenly and create a somewhat uniform 4200K surface acting as a blackbody emitter.

     The transparent sections are multi-layered fused quartz. It is very transparent to the wavelengths a 4200K blackbody emitter radiates – this means it does not heat up much by absorbing the light passing through.

     We cannot have the molten uranium touch the drum walls. We need a low thermal conductivity gas layer to separate the fuel from the walls and act like a cushion of air for the spinning fuel to sit on. Neon is perfect for this. It is mentioned as ideal for being placed between quartz walls and fission fuel in nuclear lightbulb reactor designs. The density difference between hot neon gas and uranium fuel is great enough to prevent mixing, and the low thermal conductivity (coupled with high gas velocity) reduces heat transfer through conduction. We might aim to have neon enter the core at 1000K and exit at 2000K.

     There is still some transfer of energy between the fuel and the walls because the mirrors are not perfect; about 1.8% of the reactor’s emitted light is absorbed as heat in the walls. Another 0.7% in the form of neutrons and gamma rays enters the moderator. We therefore require an active cooling solution to channel coolant through the beryllium and between the quartz layers. Helium can be used. It has the one of the highest heat capacities of all simple gases, is inert and is even more transparent than quartz.

     Beryllium and silver can survive 1000K temperatures, so that will set our helium gas temperature limit.

     A heat exchanger can transfer the heat the neon picks up to the cooler helium loop. The helium is first expanded through a turbine. It radiates its accumulated heat at 1000K. It is then compressed by a shaft driven by the turbine.

     If we assume that the reactor has power density levels similar to this liquid core rocket (1 MW/kg) and that 2.5% of its output becomes waste heat, then it can act as a blackbody emitter with a power density of 980 kW/kg. Getting rid of the waste heat requires 1 mm thick carbon fiber radiators operating at 1400K. Adding in the weight of those radiators and we get 676 kW/kg.

     A good fit might be a titanium-sapphire laser. It would absorb the large range of wavelengths between 400 and 650 nm.

     That’s 18.5% of a 4200K emitter’s spectrum. If we use a diffraction grating to filter out just those wavelengths, and include some losses due to internal optics, we get 125 kW of useful wavelengths per kg of reactor-emitter.

     The crystal can operate at up to 450K temperature, with 40% efficiency. Other experiments into the temperature sensitivity of the Ti:Al2O3 crystal reveals lasing action even at 500K, with mention of a 10% reduction to efficiency. We will use the 36% figure for the laser to be on the safe side. Based on data from this flashpumping experiment and this crystal database, we know that it can easily handle 1.88 MW/kg. The mass contribution of the laser itself is negligible.

     Any wavelengths that get absorbed but are not turned into laser light become waste heat. At 450K temperature, we can still use the lower density by HDPE plastic panels to get a waste heat management solution with 4.6 kW/kg.

     Putting all the components together and applying a 15% penalty just to be conservative, we obtain an overall power density of 2.2 kW/kg.


     If we want to go hotter, we have to go for fissioning gases. Gas-core ‘lightbulb’ nuclear reactors will be our model.

     The closed-cycle ‘lightbulb’ design has uranium heat up to the point where it is a very high temperature gas. That gas radiated most of its energy in the form of ultraviolet light. A rocket engine, as described in the ‘NASA reference’ designs, would have the ultraviolet be absorbed by small tungsten particles seeded within a hydrogen propellant flow. 4600 MW of power was released from an 8333K gas held by quartz tubes, with a total engine mass of 32 tons.

We want to use the uranium gas as a light source. More specifically, we want to maximize the amount of energy released in wavelengths between 120 and 190 nm. 19,000K is required. It is within reach, as is shown here.

     Unlike a rocket engine, we cannot have a hydrogen propellant absorb waste heat and release it through a nozzle. The NASA reference was designed around reducing waste heat to remove the need for radiators, but we will need them. Compared to the reference design, we would have 27 times the output due to the higher temperatures, but then we have to add the mass of the extra radiators.

     About 15% of the reactor’s output is lost as waste heat in the original design. It was expected that all the remaining output is absorbed by the propellant. We will be having a lasing gas instead of propellant in between the quartz tube and the reactor walls. The gas is too thin to absorb all the radiation, so to prevent it all from being absorbed by the gas walls, we will use mirrors.

     Polished, UV-grade aluminium can handle the UV radiation. It reflects it back through the laser medium and into the quartz tubes to be recycled into heat. Just like the blackbody-pumped Nd:YAG laser, we can create a situation where the pumping light makes multiple passes through the lasing medium until the maximum fraction is absorbed.

     Based on this calculator and this UV enhanced coating, we can say that >95% of the wavelengths emitted by a 19,000K blackbody surface are reflected.

     In total, 20% of the reactor’s output becomes waste heat.

     Since aluminium melts at 933K, we will keep a safe temperature margin and operate at 800K. This should have only a marginal effect on the mirror’s reflective properties. Waste heat must be removed at this temperature. As in the liquid fuel reactor, the coolant fluid passes through a turbine, into a radiator and is compressed on its way back into the reactor. Neon is used for the quartz tube, helium for the reactor walls and the gaseous lasing medium is its own coolant.

     Based on the reference design, the reactor would have 4.56 MW/kg in output, or 3.65 MW/kg after inefficiencies. If the radiators operate at 750K and use carbon fiber fins, we can expect a power density for the reactor-emitter of 70.57 kW/kg.

     28.9% of the radiation emitted by a 19,000K blackbody surface, specifically wavelengths between 120 and 190nm, is absorbed by a Xenon-Fluoride gas laser.

     They are converted into a 350nm beam with 10% efficiency in a single-pass experiment. In our case, the lasing medium is optically thin. Much of the radiated energy passes through un-absorbed. The mirrors on the walls recycles those wavelengths for multiple passes, similar to the Nd:YAG design mentioned previously. Efficiency could rise as high as the maximal 43%. This paper suggests the maximal efficiency for converting between absorbed and emitted light is 39%. We’ll use an in-between figure of 30%. This means that the effective power density of the reactor-emitter-laser system is 6.12 kW/kg.

     The XeF lasing medium is mostly unaffected by temperatures of 800K, so long as the proper density is maintained. We can therefore cool down the lasing medium with same radiators as for the reactor-emitter (17.94 kW/kg). When we include the waste heat of the laser, we get an overall power density of 2.9 kW/kg, after applying a 15% penalty.

     A better power density can be obtained by having a separate radiator for each component that absorbs waste heat (quartz tubes, lasing medium, reactor walls) so that they operate at higher temperatures, but that would be much more complex.

Aerosol fluorescer reactor

     The design can be found with all its details in this paper.

     Tiny micrometer-sized particles of fissile fuel are surrounded in moderator and held at high temperatures. Their nuclear output, in the form of fission fragments, escapes the micro-particles and strikes Xenon-Fluoride or Iodine gas mixtures to create XeF* or I2* excimers. These return to their stable state by releasing photons of a specific wavelength through fluorescence. Their efficiency according to the following table is 19-50%.

     Simply, it is an excimer laser that is pumped by fission fragments instead of electron beams. I2* is preferred for its greater efficiency and ability to produce 342 nm beams. Technically, this is an indirect pumping method, but it shares most of its attributes with direct pumping reactor lasers.

     The overall design is conservatively estimated at 15 tons overall mass, but with improvements to the micro-particle composition (such as using plutonium or a reflective coating), it could be reduced even further. It is able to produce 1 MJ pulses of 1 millisecond duration. With one pulse a second, this a power density of 66 W/kg. One hundred pulses mean 6.6 kW/kg. One thousand pulses, or quasi-continuous operation, would yield 66 kW per kg.

     The only limit to the reactor-laser’s power density is heat build-up. At 5% efficiency, there is nineteen times more waste heat than laser power leaving the reactor.We expect that using the UV mirrors from the previous design could drastically improve this figure by recycling light that was not absorbed by the lasing medium in the first pass through.Thankfully, the 1000K temperature allows for some pretty effective management of waste heat.

     Carbon fiber panels of 1mm thickness, operating at 1000K would handle 56.7 kW/kg. It would give the reactor a maximum power density of 2.4 kW/kg, including a 15% penalty for other equipment.

     If the reactor can operate closer to the melting point of its beryllium moderator, perhaps 1400K, then it can increase its power density to 8.3 kW/kg.


     Reactor lasers, when designed appropriately, allow for high powered lasers from lightweight devices. We have multiple examples of designs, either from references or calculated, that output several kW of laser power per kg.

     The primary limitations of many of the designs can be adjusted in ways that drastically improve performance. The assumptions made (for instance, 1 cm thick carbon emitter or flat panel radiators) are solely for the sake of easy comparison. It is entirely acceptable to use 1mm thick emitting surfaces or one of the alternate heat radiator designs mentioned in this previous blog post. Even better, many of the lower temperature lasers can have their waste heat raised to a higher temperature using a heat pump. Smaller and lighter radiators can then be used for a small penalty in overall efficiency to power the heat pumps.

     Most of the lasers discussed have rather long wavelengths. This is not great for use in space, as the distances they beam has to traverse are huge and it multiplies the size of the focusing optics required. For this reason, a method of shortening the wavelengths, perhaps using frequency doubling, is recommended. Halving the wavelength doubles the effective range. However, there is a 20-30% efficiency penalty for using frequency doubling. Conversely, lasers which produce short wavelength beams have a great advantage.

     The list of laser options for each type of pumping is also by no means exhaustive. There might be options not considered here that would allow for much greater performance… but research on such options is very limited. For example, blackbody and LED pumping seems to be a ‘dead’ field of research, now that diodes can produce a single wavelength of the desired power. Up-to-date performance of those options is therefore non-existent and so we cannot fairly compare their performance to lasers which have been developed in their stead.

     It should be pointed out that a direct comparison between reactor and electric lasers is not the whole story. Reactor lasers can easily be converted into dual-mode use, where 100% of their heat is used for propulsion purposes. A spaceship with an electric laser can only a fraction of their output in an electric rocket. For example, the 4200K laser can have a performance close to the liquid-core rocket design it was derived from. Other, like the aerosol fluorescer laser, can both create a beam and heat propellant at the same time. A nuclear-electric system must choose where to send its electrical output and must accept the 60% reduction in overall power due to the conversion steps between heat and electricity at all times.

     Finally, certain reactor lasers have hidden strength when facing hostile forces.

     Mirrors work both ways. The same optics and mirrors that transport your laser beam from the lasing medium out into space and to an enemy target can be exploited by an enemy to get their beam to travel down the optics and mirrors and reach your lasing medium.

     The lasing medium, assumed to be diodes or other semiconductor lasers, has to operate at relatively low temperatures and so it will melt and be destroyed under the focused glare of the enemy beam.

     Tactics around using lasers and counter-lasers, something called ‘eyeball-frying contests’ can sometimes lead to a large and powerful warship being brought to a stalemate by a small counter-laser.

     A nuclear reactor laser’s lasing medium can be hot gas or fissioning fuel. They are pretty much immune to the extra heat from an enemy beam. It would render them much more resistant to ‘eye-frying’ tactics.

     This, and many other strengths and consequences, become available to you if you include nuclear reactor lasers in your science fiction.

     PS: I must apologize for using many sources that can only be fully accessed through a paywall. It was a necessity when researching this topic, on which little detail is available to the public. For this same reason, illustrations had to be derived from documents I cannot directly link to, but they are all referenced in links in this post.

Non-Bomb-Pumped Lasers

Laser guru Luke Campbell thinks it not impossible to make an x-ray laser which does NOT require a nuclear device to pump it. In theory a Free Electron laser can produce any wavelength. It is possible approximate an x-ray lens by having the rays make glancing blows off dense materials.

Bottom line is an x-ray laser is technologically very challenging, but if you manage to make one you have an Unstoppable Death Ray of Stupendous Range.

Let's take a 10 MW ERC pumped FEL at just above the lead K-edge. This particular wavelength is used because lead is pretty much the heaviest non-radioactive element you can get, and at just above the highest core level absorption for a material you can get total external reflection at grazing angles - so no absorption or heating of a lead grazing incidence mirror. We will use a 1 meter diameter mirror. The Pb K-edge x-ray transition radiates at 1.4E-11 m. This gives us a divergence angle of 1.4E-11 radians. At 1 light second, we get a spot size of 5 mm, and an intensity of 5E11 W/m2.

Looking at the NIST table of x-ray attenuation coefficients, and noting that 1.4E-11 m is a 88 keV photon, we find an attenuation coefficient of about 0.5 cm2/g for iron (we'll use this for steel), 0.15 cm2/g for graphite (we'll use this for high tech carbon materials) and 0.18 cm2/g for borosilicate glass (a very rough approximation for ceramics). Since graphite has a density of 1.7 g/cm3, we get a 1/e falloff distance (attenuation length) of 4 cm. Iron, with a density of 7.9 g/cm3, has an attenuation length of 0.25 cm. Glass, density 2.2 g/cm3, has an attenuation length of 2.5 cm.

At 1 light second, therefore, the beam is depositing 2E12 W/cm3 in iron at the surface and 7E11 W/cm3 at 0.25 cm depth; 1.2E11 W/cm3 in graphite at the surface and 5E10 W/cm3 at 4 cm depth; and 2E11 W/cm3 in glass at the surface and 7E10 W/cm3 at 2.5 cm depth. Using 6E4 J/cm3 to vaporize iron initially at 300 K, we find that iron flashes to vapor within a microsecond to a depth of 0.9 cm. The glass, assumed to take 4.5E4 J/cm3 to vaporize (roughly appropriate for quartz) will flash to vapor within a microsecond to a depth of 4 cm within a microsecond. Graphite, at 1E5 J/cm3 for vaporization, will flash to vapor to a depth of 0.7 cm within a microsecond (the laser performs better if we let it dwell on graphite for a bit longer, we get a vaporization depth of 10 cm after ten microseconds).

Net conclusion - ravening death beam at one light second.

Now lets look at one light minute. The beam is now 30 cm across. This is much deeper than the attenuation length in all cases, so we will just find the radiant intensity and the equilibrium black body temperature of that intensity. We have an area of 7E-2 m2, and an intensity of 1.4E8 W/m2. You need to reach 7000 K before the irradiated surface is radiating as much energy away as heat as it is receiving as coherent x-rays. The boiling point of iron is 3023 K, the boiling point of quartz is 2503 K, and the sublimation temperature of graphite is 3640 K. All of these will be vaporized long before they stop gaining heat. At this range, the iron is subject to 5.6E8 W/cm3 at the surface, the graphite to 3.3E7 W/cm3 at the surface, and the glass to 5.6E7 W/cm3 at the surface. Using the above values for energy of vaporization, we get about 0.1 milliseconds before the iron starts to vaporize, 0.8 milliseconds before the glass starts to vaporize, and 3 milliseconds before the graphite begins to vaporize (because of its long attenuation length, once it begins to sublimate, graphite sublimates rapidly to a deep depth, while you essentially have to remove the iron layer by layer).

Net conclusion - still a ravening death beam at one light minute.

What about at one light hour? The beam is 18 meters across. The equilibrium black body temperature is 900 K. This is well below the melting point of most structural materials. Ten megawatts, however, is a lot of ionizing radiation. Any unhardened vehicle will be radiation killed at these ranges.

Luke Campbell

However, he goes on to note that in order to boost electrons to the velocities required for an X-ray free electron laser, you will need an acceleration ring approximately one freaking kilometer in diameter. So this X-ray laser would only be suitable for exceedingly huge warships, orbital fortresses, and Death Stars.

Since the time he wrote the above, Luke Campbell has reconsidered the use of lead grazing incidence mirror. Now he favors using diffraction.

I have since come to realize that at x-ray energies this high, matter cannot act as a mirror even at grazing angles (the x-rays have such a short wavelength that they interact with the atoms individually, rather than seeing them as a flat sheet - and you can't really get grazing incidence off of an individual atom). This is why I now prefer diffraction for focusing.

Luke Campbell

So, after researching, and solving equations it seems like that XFELs are highly finicky, complex, and specific devices (Who would have thought), but it gets worse.

For one, the divergence of the undulator beam will be around the microradians, meaning you'd need kilometer separation distances between your (seed) XFEL and the aperture. Alternative coherent X-ray generation methods are usually plagued by high linewidth, abysmal efficiency, and photon energy limitations.

The undulator wavelength or magnetic period of the undulator profits from a smaller length, due to a lower Lorentz factor being required to produce said wavelength. The undulator wavelength is also determining the K wiggler strength parameter, which is ideally kept small as fewer photons with higher energy and narrower linewidth are emitted.

There are so-called micro undulators concepts, one presented a period of 50µm, the catch is a gap size of 20µm, which should pose significant limits on the electron beam size, and therefore also beam current.

For high beam powers (exceeding tens of MW, which is honestly still pretty amazing with such low divergence when focused) larger undulators need to be used, which consequently usually also have larger K parameters, the solution would be using a micro-undulator as a seed laser, which gets amplified by the high power pump x-ray free electron lasers, the seed laser can also be pre-focused, circumventing inefficiencies of x-ray optics.

Luckily, it turns out that synchrotron radiation from electron beam recycling is almost insignificant for beam energies much below ~10 GeV (At 10m turning radius, 10 GeV electrons lose nearly 1% of their energy as synchrotron energy, rivaling lower-end extraction efficiencies of conventional undulators.)

Assuming a pump undulator wavelength of 1mm, we require an beam energy of 2.9 GeV, and a beam current of one ampere we get a beam power of 2.9 GW. Most undulators achieve single-digit extraction efficiencies, but due to our usage of beam recycling, this beam will pass through the undulator multiple times, if we model this beam was a pulse, with the same parameters, and if the beam needs to cover 50m it will pass through the undulator 6 million times per second. Extracting 1% six million times will convert all of the beam energy into our desired laser light.

After some point, the beam energy is reduced by such a degree that it will emit a different wavelength, but due to the beam also passing through our accelerator we can add the energy back each time.

A near-perfectly efficient system, the energy consumption boils down to the RF source that drives the superconducting RF accelerator, 80% is readily available and modern technology allows for 90% electrical-RF efficiency and possibly more.

A few remaining problems.

One are the optics, assuming an undulator length of one meter the seed undulator will emit an x-ray beam at a divergence angle of 4 microradians, for it to expand to say, 50 millimeters, it needs to travel 12.5 kilometers.

Secondly, the entire contraption is hard to point, it would be possible to do some minor beam pointing by moving and angling the seed XFEL, and also deflect the electron beam slightly in combination with also rotating the pump undulator. But this would require macroscopic actuators with micrometer precision. Whereas optical lasers can rely on several adaptive optics and even phased array techniques to move their beam point much more easily.

Thirdly, while the spot size is small enough to be lethal at distances up to several light-seconds, the light lag and the sheer distances makes accurate pointing and hitting a challenge. Optical lasers could simply send drones, or even coilgun launched payloads with folded mirrors or metamaterial lenses which can focus, relay and even point the laser beam at distances only limited by the number of relay drones/units available.



     One odd possibility which Luke and I discussed on sfconsim-l is a "sheet laser", which takes advantage of the possibility of using a widened undulator. This means the beam can be very wide in one dimension. This isn't so useful for my main interests (laser sail swarm acceleration for a variant of Jordin Kare's sailbeam interstellar propulsion concept).
     But for a weapon a sheet laser might be useful. Because the beam generated is wide in one dimension, it can focus onto a spot that is narrow in that dimension. The beam spot on the target is thus a narrow line perpendicular to the plane of the sheet laser.
     At the same time, this weapon only presents a very narrow slit toward the enemy, which may make the system much less vulnerable to being damaged than other laser weapon systems.


     Isaac Kuo, huh, I also had sheet beams in mind, but for a different purpose. I thought it was maybe capable of making beam combining simpler, which would work by measuring the phase of the seed laser, adjusting the entire XFEL accordingly, so that the phases of all beams interfere constructively interfere into one.
     But what I am just noticing is that those sheet beams are ideal for countering anti-laser armor schemes, angling has it issues when facing multiple opponents, or even mirror drones.
     Rotating armor, however, is more problematic.
     My usual assumption is that it rotates infinitely fast so that the y-axis equals the circumference of the hull at any point. Meaning the rate at which armor is removed is dependant on the diameter on the x-axis.
     Which means if I use a sheet or ellipse-shaped beam spot I can reduce the effect of rotating armor on my lasers capability of doing damage.


     You mean rotating an entire armor shell as a single unit, right? I used to like that idea but it places a lot of annoying design constraints on the spacecraft and it has catastrophic failure modes. I mean, even if the rotation rate is pretty low we're talking an incredible amount of force and momentum if anything ever gets bent into a scrape.
     A more robust and flexible alternative is to use a shield wall. You have a bunch of robots holding shields. Each individual shield might rotate, and the robots might "march" around the hull if necessary to replace damaged shields with fresh shields.
     These robots might not be limbed robots. They could simply be small thruster units attached to the shields. This lets you space the armor much further away from the spacecraft, which can be useful for defending against incoming missiles or obscuring the true location of the main spacecraft.
     With this sort of system, you have a lot fewer design constraints on the main spacecraft. You can have large solar panels or radiators, or whatever...they don't need to fit within a rotating armor cylinder or cone or whatever.


     Isaac Kuo, I use "rotating armor" pretty vaguely, the exact design details aren't too important, but I neglected different configurations of rotating armor.
     Matter beam has came up with reflective, liquid cooled, rollings pins as a anti-laser armor scheme for his setting, for which I still have the same opinion about: I've you spend as much time (real), and in-setting resources for anti-kinetic armor the results would be breaking them almost entirely, to make it short: It is over designed, IMO.
     I like the robot idea, I usually think off segmented rotating parts that cancel each other out, and also multiple layers, to have an similar protective bonus against kinetic projectiles.


     It seems to me that the simplest way to have rotating armor is to use a drone ship, and spin the entire vessel at the desired rate. Assuming that the ship information and targeting systems can handle the rotation, an issue I might expect would be centrifugal forces interfering with radiator circulation.



     They say if you say X-Ray Laser 3 times in the mirror, Luke Campbell will appear!


     Separation of just 12.5 kilometers? Think more like thousands of kilometers! I mean, it depends on what you want to do with it. I want to be able to accelerate/power a swarm of graphite laser sails out to distances of light months to light years. This works well with a zone plate on the order of 1km and a target swarm which is perhaps 1m wide during the acceleration phase and 1km wide during the cruise phase (4.3 light years away).
     The sizes required to do the same with optical lasers easily get into the diameter of Earth or more.


     Yea, it depends on what exactly you want to do, the usual design is a ship with an XFEL with hundreds to thousands of kilometers of separation distance to a giant zone plate for maximum range.
     As with the optical relay drone argument, same applies to XFEL, IMO, drone swarms are usually a superior model than single large ships when it comes to combat, carrier ships equipped with drones is, therefore, my usual to-go choice.
     But the point being is that you can have drones equipped solely with XFEL and other only meant to focus the beams. Or even both at the same time, creating layered 3D formations, with separation distances at which the beam expands to the full size of the apertures.


     The problem with re-accelerating your electron bunches is that the bunches disperse more and more with each pass. You do have methods of re-focusing the bunches, but these only work up to a point. In synchrotrons, where they keep re-using the same electron bunches (sometimes for hours), you get nanosecond duration x-ray pulses. Spreading the pulses out like this makes it harder to get into the condition where the interaction of the radiation field in the wiggler with the electrons self-organizes the electrons to produce a nicely in-phase, transversely coherent beam.
     The usual way around this is to accelerate femtosecond electron bunches with a linac, then send them on a one-way trip through the wiggler. After they pass through, turn the bunch around and run it through the linac backward and out of phase with the driving RF cycles. This slows the electrons down and puts their energy back into the RF fields, so you can recover almost all of the energy you used to accelerate the bunch in the first place. This can then be used to accelerate the next bunch. This design is called an "energy recovery linac".


     Luke Campbell, thanks! I've completely forgotten about how energy recovery linacs work in that detail. I am bit surprised how elegantly the electron energy is turned back into the initial RF frequency? Probably due to the deceleration being equivalent to the initial acceleration of the electron beam.


     Particle Beams are usually plagued by their horrible beam divergence, cooling and neutralization help, but I am not sure how well you could cool your neutralized particle down to nanokelvin, condensation into droplets might work.
     Waves made of bosons much simpler to predict, completly right.
     If particle accelerators being more efficient? As in transferring momentum? Yes, if the beam velocity is close to the spacecraft velocity you could even transfer 100% of the beam energy into the craft.
     Power conversion efficiency? Well, laser diodes can achieve 75% efficiency already at room-temperatures, and free electron lasers have pretty much the same efficiency constraints as particle beams if well designed and sufficiently up-scaled.


     Kerr, you might want to check out a recent article where it was worked out that a laser beam could cut down on the particle beam divergence. Can't find it at the moment, I may have shared it.


     A free electron laser take significant cuts in efficiency due to:

1) Conversion efficiency from the electron beam to the photon beam (this might be made good with a sufficiently long undulator and/or energy recycling, but I wouldn't take it as a given)


2) Photons lost to the zone plate — at least 50% loss for a sinusoidal zone plate, and at least 75% loss for a less challenging binary zone plate.

     So, being able to use a particle beam might give you an order of magnitude more powerful beams (or require an order of magnitude less power) than an equivalent free electron laser.
     Laser diodes have numerous challenges of their own, including much longer wavelength. You might focus them using more efficient fresnel lenses rather than a zone plate, sure, but you'd have to make them very huge to get light-month ranges (not to mention the sizes required to reach out to 4.3 light years to provide power).


     Troy, yes, it's a weird but interesting idea. The required power levels and scale are a bit daunting, though, and I don't see any way to try and develop and test the thing except at full scale.
     It does make me wonder, though, about using a plasma beam strictly as a lens. It might be a suitable replacement for a fresnel lens. I'm not so optimistic about this being suitable for interstellar propulsion, but it might be an interesting SFnal laser weapon. A thin "exhaust cone" of plasma particles might be a lot less vulnerable to enemy weapons than an exposed fresnel lens.


     Isaac Kuo, in principle, you could shine a "seed" x-ray beam through a zone plate, and then amplify the beam that passed through the zone plate. The technical challenges seem a bit daunting, but this would get rid of the 50% loss when passing the full powered beam through the zone plate.

From a thread on Google+ by Kerr (2018)

Particle Beams

Particle beam weapons use a similar principle to the one being utilized in the computer monitor aimed at your face right now (unless you are one of those lucky people who has a flat-panel monitor) those ancient CRT monitors and TV screens they used to use in olden times. Electrons or ions are accelerated by charged grids into a beam. They work much better in the vacuum of space than in an atmosphere, which is why there is no air inside the cathode-ray tube of your ancient monitors. Laboratory scale electron beams can have efficiencies up to 90%, but scaling up the power into a weapon-grade beam will make that efficiency plummet.

Particle beams have a advantage over lasers in that the particles have more impact damage on the target than the massless photons of a laser beam (well photons have no rest mass at least. The light pressure exerted by a laser beam pales into insignificance compared to the impact of a particle beam). There is better penetration as well, with the penetration climbing rapidly as the energy per particle increases. Particle beams deposit their energy up to several centimeters into the target, compared to the surface deposit done by lasers.

They have a disadvantage of possessing a much shorter range. The beam tends to expand the further it travels, reducing the damage density ("electrostatic bloom"). This is because all the particles in the beam have the same charge, and like charges repel, remember? Self-repulsion severely limits the density of the beam, and thus its power.

They also can be deflected by charged fields, unlike lasers. Whether the fields are natural ones around planets or artificial defense fields around spacecraft, the same fields used to accelerate the particles in the weapon can be used to fend them off.

Particle beams can be generated by linear accelerators or circular accelerators (AKA "cyclotrons"). Circular accelerators are more compact, but require massive magnets to bend the beam into a circle. This is a liability on a spacecraft where every gram counts. Linear accelerators do not require such magnets, but they can be inconveniently long.

Another challenge of producing a viable particle beam weapon is that the accelerator requires both high current and high energy. We are talking current on the order of thousand of amperes and energy on the order of gigawatts. About 1e11 to 1e12 watts over a period of 100 nanoseconds. The short time scale probably means quick power from a slowly charged capacitor bank, similar to the arrangement in a typical camera strobe. You want a very thin beam with a very high particle density, the thinner the better and the more particles the better. The faster the particles move the more particles will be in the beam over a given time, i.e., the higher the "beam particle current" and the faster this current flows, the more energy the beam will contain.

The power density is such that the accelerator would probably burn out if operated in continuous mode. It will probably be used in nanosecond pulses.

Protons are 1836 times more massive than electrons, so proton beams expand only 1/1836 times as fast as electron beams and are 1836 times harder to deflect with charged fields. Of course they also require 1836 times as much power to accelerate the protons to the same velocity as the electrons.

It is possible to neutralize the beam by adding electrons to accelerated nuclei, or subtracting electrons from negative ions. While this will eliminate electrostatic bloom, the neutralization process will also defocus the beam (to a lesser extent). As a rough guess, maximum particle beam range will be about the same as a very short-ranged laser cannon.

For a neutral particle beam, the divergence angle is influenced by: traverse motion induced by accelerator, focusing magnets operating differently on particles of different energies, and glancing collision occurring during the neutralization process. The first two can be controlled, the last cannot (due to Heisenberg's Uncertainty Principle). The divergence angle will be from one to four microradians, compared to 0.2 for conventional lasers and 20 for bomb-pumped lasers.

The source of the particles for the beam come from sophisticated gadgets with weird names like "autoresonantors", "inertial homopolar generators", and "Dundnikov surface plasma negative ion sources".

Dr. Geoffrey A. Landis had this to say:

Particle beams disperse for a lot more reasons than laser beams, unfortunately, so it's harder to give a simple formula. It will depend on things like magnetic and electric fields in the region between the source and the target (if the particles have spin, for example, they will couple to the magnetic field gradient even if they are neutral).

However, for a neutral particle beam traversing empty, field-free space, the dispersion is proportional to the temperature of the beam. Using, for the sake of a simple example, a mercury ion beam (dispersion decreases proportional to square root of atomic mass, and mercury is a convenient high-mass atom that ionizes easily), the lateral (spreading rate) velocity of the beam is:

V = 1.4 SQRT(T) m/sec, for T in Kelvins

To calculate the actual angular spread of the beam, you need to know the beam velocity. For a quick calculation, you could say it's no more than the speed of light, 300,000,000 m/sec. So the dispersion in nano-radians is 5 SQRT(T).

So, for a beam with an effective temperature of, say, 1000K, dispersion for mercury is 150 nR, or 0.15 micro-radians. Dispersion at a distance of 100,000 km would be 0.015 km, or 15 meters. A hydrogen beam would disperse SQRT(80)= 9 times more.

[note that if the beam is actually relativistic, you have to apply a relativistic correction, which I'll ignore here.]

Dr. Geoffrey A. Landis

I'm not sure I have this correct, but to put this in useful form:

θ = (5e-9 * Sqrt[BT]) * Sqrt[80/Bn]


  • BT = beam temperature (Kelvin)
  • Bn = atomic number of element composing the beam (Uranium = 92, Mercury = 80, Zirconium = 30, Calcium = 20, Neon = 10, Hydrogen = 1)
  • θ = Beam divergence angle (radians)

RT = Tan(θ) * D


  • D = distance from particle beam emitter to target (m)
  • RT = radius of beam at target (m)

...making sure that Tan() is set to handle radians, not degrees. Or as one big ugly unified equation:

RT = Tan((5e-9 * Sqrt[BT]) * Sqrt[80/Bn]) * D

...again making sure that Tan() is set to handle radians, not degrees. I must stress I derived this equation myself, so there is a chance it is incorrect. Use at your own risk.


(ed note: this is in the context of the tabletop wargame Attack Vector: Tactical. One hexagon is 20 kilometers. Each armor layer is 5 g/cm2 of carbon.)

Building a practical particle beam that behaves in a gun-like manner at any plausible level of technology is a formidable challenge; a 1 GeV neutral hydrogen beam has a minimum theoretical beam spread of around 1 microradian, or 8 cm at a 4 hex range (80 km). Reaching this limit seems unlikely, so using a standard damage model for particle beams seems unlikely.

However, particles at energies in excess of 1 GeV/nucleon have quite excessive penetration; 1/e distance for initial penetration are on the order of 70 g/cm2 in typical shielding materials, and if you count in the effects of cascade radiation can climb over 100 g/cm2, which means you need 20 layers of AV armor to get a 1/e reduction. This allows a particle beam to kill ships without actually piercing armor.

Hardened electronics tends to have severe problems at 100-1000 grays, or 2.5 to 25 megajoules per hullspace average dose; 1 damage point to a hullspace will kill it pretty reliably. This makes a PAW a bit more lethal, per unit energy, than conventional energy weapons, but it only damages a fairly limited class of targets. Note that 5 grays is likely lethal to a human, and incapacitation in combat-relevant time takes 40+ grays. A beam intensity of 1 megajoule per square meter, with a penetration of 100 g/cm2, results in 1000 grays to surface components.

While photonic equipment is more resistant than standard electronics to transient effects caused by radiation, radiation also directly physically damages components, and there's no really good way to make them tougher other than making them bigger (and thus slower) or adding lots of backups.

The incapacitation mechanic, for a PAW, is thus chosen as having the weapon damage X components, requiring a save for each component at a specified difficulty; it then cascades down to the next layer at some reduction in power (on average, 1/10 the dose per 10 meters of length; a 10m ship gives -1 in the first region, -3 in the second, -5 in the third). X depends on the beam width; for a beam that hits a 10 square meter area, X is 1.

For simplicity in handling shielding effects of internal components, we define a 'shielding depth' for the ship, equal to 1/8 of the relevant dimension, in meters. We also assume that the components in the hull layer are behind half a shielding depth.

Particle Beam Rules

1) Shielding and Shielding Depth

To determine a ship's shielding, add 1/8 of its armor and 1/32 of its hull dimension from the relevant direction, and drop fractions; thus, a Rafik has a shielding factor of 5/8 + 33/32 or 1, from more or less any side; a Wasp has a shielding factor of 12/8 + 84/32 or 4 from the front, 1/8 + 17/32 or 0 from the side. This is a bit of a simplification, but works tolerably well unless the ship is very large. Two points of shielding depth roughly halve dose.

To determine a ship's shielding depth, simply divide relevant dimension by 8. In the above examples, the Rafik uses 4 in all directions, the Wasp uses 10 from the front, 2 from the sides.

2) PAW Effects

A PAW hits one or more surface areas. The weapon table tells you how many surface areas it hits, and the power of the attack at each area. If more areas are hit than the actual surface of the ship, any excess is lost (if it's more than the area of one region, spread to another region). To determine the actual number of components in the first region damaged, multiply the area hit by shielding depth, and divide by 5. Then, reduce power by the ship's shielding. The result is the difficulty of component saves. Certain components are more or less vulnerable, see below. If it seems useful, you may spread; each doubling in area hit reduces damage by 2.

Once you've damaged surface components, you get to cascade. Subtract the shielding depth of the ship from the weapon power, and proceed to damage the core, hitting it the same number of times as you hit the surface. Then, subtract the shielding depth again and damage the core a second time; finally, subtract the shielding depth a third time and damage the far side of the ship. Note that damage below 0 does matter on certain vulnerable components.

If you wish to add some complexity, the core is actually fairly small; if you hit more than 1/5 of the exposed surface, the remainder must be spread to the sides of the ship instead of the core.

3) PAW weapons

A standard THS weapon delivers 80 MJ per 15 meters length per 16 seconds. This will deliver 8,000 grays to the surface of one location, which is pretty much an autokill unless the location has a lot of shielding; the save is set to 10 on 1 hex. The following table gives the effects of a PAW at varying ranges (minimum area is 4, to reduce jitter)


4) Component Damage

All Drive, Electronics, Reactor, and Weapons locations can be damaged by PAWs; damage control is assumed effective, though if a damage control team is in an area when it's hit by a PAW, the damage control team must save. Other mechanical components may also be vulnerable.

The Bridge location can be damaged by a PAW and suffers a +6 difficulty because it requires sophisticated computers. A light storm shelter reduces difficulty by 12, a heavy by 18.

Other locations will generally have noncritical but annoying damage to environment control, switches, loaders, and the like. Some sorts of cargo will be damaged by radiation.

Personnel, in any location, can be disabled and suffer a +6 difficulty to avoid immediate incapacitation (3200 rads = +0), and a +15 difficulty to survive long-term (140 rads = +0). Unless there is a reason for them to be elsewhere, personnel are on the bridge. The main reason for being off the bridge is damage control, though a surprised ship might have people in quarters.

Cybershells are disabled disabled like personnel; cybershells may use hardened computers if desired. Damage control teams are normally run by hardened cybershells. Radiation effects are a combination of physical damage to switches and transient effects.

Anthony Jackson (2005)

(ed note: Redditor poster MatterBeam has a brilliant suggestion. They make the case that science fiction authors who postulate spacecraft combat using particle beams will allow the authors to justify many of the cherished space combat tropes common in media SF. There is some room for argument, but it does provide authors with a lot of cover.)

Particle beam weapons are the ultimate scifi weapon for hard science fiction authors and worldbuilders.

What is it?

You know about particle accelerators: A handful of atoms are ionized (stripped of their electrons) and accelerated to near light speed. A particle beam is the same concept, with much greater energies and many more atoms, and it is open ended. The relativistic stream of particles can hit targets thousands of kilometers away with great accuracy.

How are they different from lasers?

Lasers are focused with large, fragile mirrors. Particle beams are focused using magnets.

Lasers have greater range due to their smaller spot size.

Particle beams have several damage modes, lasers have only one. Lasers do surface thermal damage. Continuous laser beams gradually melt through the target, while pulsed beams try to make the surface material heat up so quickly, it explodes away in chunks. Particle beams penetrate through armor, depositing energy throughout the entire target volume. They are also capable of being pulsed. They have a secondary damage mechanic that is called Bremsstrahlung radiation. Charge particles, when slowed down by armor, emit X-rays inside the target. This is very damaging to electronics.

Lasers are less efficient than particle beams due to the necessity of converting electrical energy into thermal/optical energy.

Lasers travel at light speed and can only be stopped by physical barriers. Particle beam weapons can use several different particles (from the lightest electrons to the heaviest uranium ions) and travel at varying near-light speeds. Their path can be altered by magnetic and electrostatic fields if not properly neutralized.

Why are they the ultimate scifi weapon?

They allow authors to justify the majority of tropes that make science fiction 'fun'. With lasers and their extreme range, battles are no more than point-click minigames between legions of automated drones bouncing and refocusing a beam from a laser-generating battlestation.

With particle beams:

-We can justify humans in space warships. Due to Bremsstrahlung radiation, electronics are especially vulnerable to particle beam weapons. Humans serve as a backup, and the simple act of placing them on the warship creates a large variety of warship design options that do not require greater investment, mainly the ability to do repairs, second-by-second decision making and recovering vessels from partial destruction (soft-kills).

-It is easier to defend against lasers than particle beams: while lasers focus more energy per area than particle beams at all distances, they are much more vulnerable to reflective surfaces or armor that dissipates surface heat. Particle beams will penetrate deep into armor material instead.

-We can justify dedicated armor. Against lasers, the most efficient armor is simply placing your propellant outside of your hull. Kilogram by kilogram, nothing is more mass-efficient than a block of shapeless propellant with your spaceship embedded inside. Due to to the penetrative capability of particle beams, you can justify having proper warships: while lasers can be no more than an ice trawler with a laser generator attached, particle beam warships will have to be properly protected with high-z materials, that is, materials with a lot of electrons per mass unit. Examples include metal foams filled with hydrogen or water.

-Battle ranges are shorter. While lasers can deposit their energies over vast distances, particle beams are more limited by bloom effects, even more so if they are charged. For example, a 1MJ pulse of mercury particles, neutralized by an electron beam, would have a spot size of 15m at 100000km. A laser would have a spot size of a few cm at that same distance. Why is this important? Maneuvering requires dedicated high-thrust engines instead of feeble milligee drives. You don't have to deal with light lag. The targets aren't thermal specks at the limit of your imagery resolution, but spaceships orbiting the same planet as you are...

-We can justify 'shell' designs. Laser warships come in two flavours: the telescope and the battlestation. The telescope is a flimsy assemblage of struts, nuclear reactor and laser generator working at the the shortest frequency manageable. On top of all this is a massive focusing mirror. It accelerates slowly and doesn't do anything except shoot at targets so far away you can only resolve a drive signature. This is because range is king. The second flavor is a single, huge space station containing several reactors dumping their waste heat into a hollowed out asteroid or an ice cube of several kilotons. The laser beam is bounced from mirror drone to mirror drone, refocused at each step, over millions of kilometers. This means spaceships start being focused and melted before they even leave their orbits... from another planet away. It is the end of 'spaceships', but actual planets shooting at each other. In both cases, the 'warships' resemble something NASA built.

Particle beam warships would need to be enclosed in armor, and their firing ports are millimeters wide. They would resemble the traditional science fiction warship design, based on naval warships, much closer.

-We can justify the conversion of space technology to military use Lasers can be used for tight-beam communication, but so can radio. There is no reason for a spacefaring nation to develop high intensity laser technology unless it is for military use. It becomes hard for the scifi author to explain how we went from peaceful space transport to megawatt beams in a short span of time. Particle beam technology could be no more than a repurposing of the magnetic focusing assemblies found in thermo-electric and plasma rocket drives. It is a much more plausible transition in purpose from peaceful to military.

-We can create more interesting tactical choices: Particle beams can use several types of 'ammunition'. Electron beams are short-ranged, but cause deadly Bremsstrahlung radiation. Heavy ions disperse much less and penetrate armor better. Neutralized beams need two parallel beams positively and negatively charged ions, but have the least dispersion. Magnetic shielding can reduce the damage caused by ion beams, and even deflect them entirely. Neutralized beams can be slightly destabilized by magnetic fields, or even shot down by electron beams. All these are much more ineteresting choices than the default 'shoot as soon as targets are detected' that comes with lasers.

-We can do away with drone sub-weapon fleets; As mentioned before, a laser battlestation with even moderate power levels and a flett of cheap mirror drones can shoot down spaceships before they leave Mars. It would end exciting space warfare. With the ability to incapacitate 'cheap' autonomous drones, ion beams can quickly make them less cost effective than 'full' warships carrying humans.


Using beam weapons to zap ballistic missiles has been a dream since Ronald Reagan’s “Star Wars” initiative.

Now the U.S. Missile Defense Agency is looking for technologies that will enable space-based particle beam weapons to shot down missiles.

More specifically, MDA wants a neutral particle beam (NPB) weapon. “A conceptual NPB system would generate, accelerate, focus, and direct a stream of highly energetic electrically-neutral atomic particles, traveling at near the speed of light, unperturbed by the earth’s magnetic field, at exo-atmospheric targets,” explains MDA’s research solicitation. “Particle interactions with target matter can cause damage and generate measurable emissions allowing target characterization.”

In other words, an NPB is a sort of sub-molecular machine gun that can damage a missile’s components and heat up its skin. The MDA wants to build upon on the 1989 Beam Experiment Aboard Rocket (BEAR) experiment, which lofted and tested a particle beam weapon in outer space.

MDA also wants a particle beam weapon “capable of operating in sub-orbital (pop-up) or orbital (space-based) mode.” This suggests that the system could be either a device permanently orbiting the earth, or a launch-on-demand system in which a rocket boosts the weapon to sub-orbital height, from which it will shoot down ICBMs before plunging back to Earth.

To make this happen, MDA is looking for six enabling technologies. These comprise:

  • Lightweight, compact, and energy efficient particle accelerators
  • Compact power sources
  • Particle neutralizers that exhibit minimal scatter, have extended operational life, and have minimal impact on operating environment
  • Anion sources, extractors, and injectors
  • Beam transport, collimator, focusing, steering, sensing, and tracking components
  • Sensors capable of detecting emissions from targeted objects

In March, MDA released budget estimates that asked Congress to authorize $380 million to be spent in Fiscal Year 2020 on developing NPB. “The Neutral Particle Beam is a game changing space-based directed energy capability for strategic and regional missile defense,” MDA wrote. “MDA will design, develop and conduct a feasibility demonstration of a first stage accelerator subsystem.”

In turn, the NPB is part of a massive MDA effort to develop space-based energy weapons for the U.S. Ballistic Missile Defense System. The agency is requesting $304 million to bring several missile defense technology projects to maturation, including lasers and NPB.

“Working with national laboratories and industry, MDA will address laser scaling by investing in the laser component technology required to demonstrate efficient electric lasers,” according to the agency’s budget documents. “MDA will conduct component demonstration to prove out laser capability. The addition of the Neutral Particle Beam effort will design, develop, and conduct a feasibility demonstration for a Space-Based Directed Energy intercept layer. NPB efforts will leverage past and current work on particle beam and related enabling technologies as well as laser scaling, pointing, and stability to provide a component technology to improve the cost-benefit and size, weight and power for an operational system. This future system will offer new kill options for the BMDS and adds another layer of protection for the homeland.”

The lure of space-based energy weapons, like particle beams and lasers, to zap ICBMs is understandable. To destroy missiles in space, before the warheads enter the atmosphere. the U.S. has just 44 interceptor-missiles deployed in Alaska and California. That may – or based on test failures, may not – be sufficient to stop a couple of North Korean missiles aimed at the West Coast. It is most certainly not sufficient to handle a swarm of ICBMs with multiple warheads and decoys. Energy weapons, firing at or near the speed of light, and with a plentiful supply of electrical ammunition, seem ideal.

But they also have their obstacles to overcome, such as size, weight and especially power requirements. MDA will have to surmount these issues before space-based energy weapons become a reality.


Science fiction is missing a realistic and grounded look at particle beams. We plan to do just that now.

After reading this, you might decide to give particle beams their rightful place alongside lasers as a means of transmitting power, propelling spacecraft or dealing damage at long distances.

This post focuses on particle beams deployed and used in space. All claims and calculations here are based on paper and studies referenced through links throughout. The first sections focus on the hard science behind particle beams and the performance achieved by existing accelerators. We then move on plausibly extrapolated performance and then to informed speculation on how they can be designed and used before ending on topics most relevant to sci-fi authors and worldbuilders.

Particle Beams

A particle beam is a stream of electrons, ions or neutral atoms that have been accelerated to a high velocity by an accelerator from a particle source. Particle beams are used in a huge variety of ways. Everything from electron microscopes to cancer treatment involves a particle beam. A common example of a particle accelerator is a medical X-ray. It produces a beam of electrons that emit X-ray light when they hit a metal target.

They are used in research extensively. Some of the most expensive research projects ever are centred around particle accelerators, such as the Large Hadron Collider or the Stanford Linear Accelerator Center. The beams produced there are usually composed of electrons or protons, but also heavy ions such as lead and uranium. In fact, any charged particle can be accelerated in a particle accelerator.

This technology was also a focus of the Strategic Defense Initiative back in the 1980s, which culminated in an accelerator-equipped satellite being launched into space to test the performance of particle beams at different altitudes.

To describe the characteristics of particle beams, we could use standard units such as velocity in meters per second or particle energy in joules. However, the typical beam is highly relativistic (90%+ the speed of light or 0.9 C) and each particle has a very small amount of energy (a hundredth billionth of a joule or less).

A specialized set of units is used instead and a relativistic energy calculator is the best tool to handle them.

We use the Beta factor (β), with values between 0 and 1, to describe the ratio of particle velocity to the speed of light (in a vacuum). β = 0.875 means that the beam is travelling at 0.875 C (87.5% the speed of light in a vacuum).

The Lorentz or Gamma factor (γ) describes the intensity of the relativistic effects. A 0.875 C, a particle has a gamma factor of 2.065, meaning that it experiences time 2.065 times slower than anyone else around.

The relativistic energy calculator provides these values. If we input an ion mass (carbon has 12 g/mol molar mass so put ‘12’ in the mp box) and an ion energy (3.2 * 10^-8 joules, equivalent to about 2 * 10^9 electronvolts or 2 GeV), we obtain a Beta of 0.528 and a Gamma of 1.177. If we have a current of these carbon ions travelling in a beam (for example, 0.00001 Amps or 10 μA), we can multiply it by the particle energy in eV to work out the total beam power in watts (2 GeV * 10 μA : 20,000 watts or 20 kW).

These figures will be critical to understanding the performance and requirements of a particle accelerator.

The Accelerator

The characteristics of a particle accelerator are resumed in their efficiency (%), acceleration gradient (volts per meter or V/m) and mass per meter length (kg/m). Launching and building equipment in space is inherently expensive. Moving it around is even more so. The expense is proportional to the equipment mass, so the best accelerator is therefore the one which has the highest performance per kg. High efficiency is good, because it means less mass dedicated to cooling systems. A high acceleration gradient is desirable for shorter and lighter accelerator. A low mass per meter is also needed.

It is with these characteristics that we evaluate the major types of particle accelerator.

The first and oldest type is the electrostatic accelerator. It works by applying a strong voltage difference between an anode and a cathode, separated by a gap. The maximum voltage possible is limited by electrostatic breakdown, which is when electrons jump across the gap on their own.

Van de Graff accelerators are the primary example of this design. Currently, the maximum voltage is roughly 25 million volts (MV), with the acceleration gradient averaging 0.5 MV/m.

Tandem electrostatic generators have achieved 40 MV in total.

To achieve higher energies and better acceleration gradients, induction accelerators are used.

Betatrons are an example of this design, and they are a type of cyclotron. The acceleration gradient is about 1MV/m, but it quickly falls when the particles start reaching relativistic velocities.

Radio-frequency accelerators are the dominant type of high-energy accelerator in use today.

They use radiofrequency (RF) cavities to produce a voltage difference that particles are accelerated over. The cavities are simply 'mirror boxes' for radio waves. They bounce up and down at a very specific rate within the boxes. When a particle beam enters one end of the cavity, it encounters the radio wave. The wave has an electric field that pulls the beam along, which corresponds to a voltage.

Once the particle beam exits the cavity, it enters a drift tube that shields it from the radio wave's pull in the opposite direction. A series of cavities continuously accelerates the beam in this way. Dividing the voltage difference between the ends of the cavities by the distance the beam crosses gives us an acceleration gradient. Typical particle accelerators have an acceleration gradient of 20 MV/m. They are limited by RF waves being absorbed in the walls as heat.

The alternative is to use superconducting RF accelerators.

Cryogenically cooled cavities made of niobium metal have no electric resistance and do not absorb the RF waves. This means that very high acceleration gradients are possible without worrying about heating problems.

Superconducting RF (SRF) accelerators regularly reach 25 to 40 MV/m.

Certain configurations, such as travelling wave accelerators, are needed for highly relativistic electrons, but it is not the case for much more massive ions. This allows very short accelerators reach very high energies.

SRF accelerators can be circular or linear.

Circular accelerators allow a short acceleration length to be used again and again.

However, it needs powerful and therefore heavy magnets to keep bending a beam into a circle as the particle energies increase. Furthermore, bending a beam releases synchrotron radiation that drains particle energy. A small circular accelerator that can fit inside a spaceship would be limited in the particle energies it can achieve and would have multiple sources of inefficiency.

Linear accelerators or ‘linacs’ do not bend the beam. All energy expended goes towards accelerating the beam. Only a single pass is possible however, so strong acceleration gradients are needed.

You don’t have to choose strictly one or the other. A circular accelerator can be used to bring particles up to speed and then pass them onto a linac for the final boost. A recirculating linac could be selected as a sort of hybrid: after passing through the accelerating section, the beam is turned 180 degrees for a second pass.

Whatever the choice of the exact configuration, the SRF accelerator on a spaceship will have a length and therefore mass proportional to the particle energy we want to achieve. If we want particles with an energy of 100 MeV, we divide the energy by the number of charges and the acceleration gradient to find the accelerator’s length. For example, Oxygen 2+ ions and a 25 MV/m gradient would reach 100 MeV in just 2 meters while Lithium 1+ ions and a 10 MV/m gradient would need 10 meters.

A new accelerator technology has emerged in recent years: plasma wakefield accelerators.

They use an intense laser pulse to create a tube of plasma emptied of electrons. The electrons rush back in as a wave. Multiple pulses create a series of waves travelling at relativistic velocity. They can pull along particles in their ‘wake’, allowing for extreme acceleration gradients on the order of 10 GV/m. However, their efficiency is abysmal (~0.1%) and their acceleration lengths are in the centimetres, making them unsuited for anything but researchers. Even more recent developments could remedy their faults.

For the rest of this post, we will assume that SRF linacs are being used.

Particle beam divergence

In space, distances are huge. Particle beams would have to traverse thousands of kilometres to be useful. Divergence is very important in space because of these distances.

Divergence is the ratio of lateral spread to forward motion, noted in radians. For most cases described here, we will use milliradians ‘mrad’ or microradians ‘μrad’. To correct for relativistic factors, it must be further divided by the gamma factor ‘γ’.

A high divergence means that the beam spreads its energy over a large area within a short distance, making it hard to use for purposes such as power transmission or propulsion. A low divergence allows it to be focused onto a spot small enough to become a damaging weapon. The lower the divergence, the greater the range at which a beam remains useful.

Particle beams are said to spread too quickly to be used over long distances. This is true… for charged particle beams.

All accelerators produce charged particle beams. The self-repulsion between ions of similar charge causes electrostatic bloom. This is a very rapid widening of the beam that de-focuses it and spreads its energy rapidly. Even worse, if a beam were near a planet’s magnetic field, its trajectory would be bent off-course. Shooting charged particle beams also confers a strong electrostatic charge to the firing platform, which could lead to dangerous sparks and arcs.

The radius doubling distance for a charged particle beam is:

RDD = 5586 * BR * β^1.5 * γ^1.5 * (M / (Z * IB))^0.5

RDD is the radius doubling distance in meters
BR is the initial beam radius in meters
β is the Beta factor
γ is the Gamma factor
M is the ion mass in g/mol
IB is the beam current in Amps
Z is the particle charge

We can work out that a 0.1 mA beam of 200 MeV carbon ions with a charge of 3+ (β: 0.186, γ: 1.02, IM: 12 and Z: 3) and an initial radius of 0.1 m would have a radius doubling distance of 9,232 meters. It crosses this distance in 165 microseconds. Because the radius increase causes the doubling distance to also increase, it would take 330 microseconds for the radius to double from 0.2 to 0.4 m, and 660 microseconds to increase from 0.4 to 0.8 meters and so on.

The exponential nature of the radius doubling distance means that to find out the distance at which a beam expands by a ratio

Charged particle beams cannot cross the thousands to tens of thousands of kilometers that separate objects and ships in space without expanding to huge sizes.

It doesn’t have to be this way though.

Electrostatic bloom can be prevented by taking an extra step after a charged particle beam passes through an accelerator: neutralization. This converts charged particles into neutral atoms, either by adding or subtracting electrons. Neutral beams do not suffer from electrostatic bloom but are still affected by thermal expansion.

Thermal expansion is due to the random motion of particles within the beam. This motion is the same as that of molecules within a gas and is proportional to the temperature and molar mass of the particles.

Perfect gas laws allow us to work out the velocity of the particles that results in thermal expansion. The velocity of particles in a gas depends on their temperature and molar mass. Specifically, the velocity in meters per second is equal to 17009.6 * (Temperature/Molar mass)^0.5, if we use electronvolts for temperature and g/mol for molar mass.

Lithium particles with a temperature of 1 eV and a molar mass of 7g/mol would expand by 6.43 km/s in all directions. This is negligible velocity in the longitudinal direction (the lithium particles would be accelerated to several thousands of km/s by the accelerator) but is critical in the transverse directions.

Divergence is the simple ratio between the beam’s rate of expansion and rate of travel. If we divide the transverse velocity by the beam velocity, we get a divergence in radians. Multiplying that divergence by the distance the beam must travel gives the beam radius at the distance. It is also called the spot radius, analogous to the size of a spotlight’s spot on the ground.

If a lithium beam were accelerated to a velocity of 72,330 km/s (a beam energy of 200 MeV), and it had a temperature of 1 eV, we can work out a divergence of 0.0000889 radians, or 88.9 microradians. If the beam must travel 1,000 km, it would have a beam radius of 88.9 meters (and a beam diameter of 177.8 meters). Its energy would be spread over the surface area of that spot.

By reducing the temperature or increasing the particle mass, we could expect a lower divergence. If we used ions with a temperature of 0.1 eV instead of 1 eV, we would expect a 3.16 times lower divergence. If we switched out the lithium ions (7 g/mol) for Cesium ions (133 g/mol), we would expect a 4.36 times lower divergence. A lower divergence allows for a smaller spot size at all distances and a better focusing of the beam’s energy.

This is where most writing on particle beams ends. Further research has shown that particle beam divergence is not so simple.

A heavier particle, for example, would also be travelling proportionally slower. Divergence is a ratio, and if both the transverse and longitudinal velocity are reduced by the same amount, the ratio is maintained.

Beam temperature is a complex topic. Superconducting accelerators with good control over the beam should cause next to no heating of the particles. What determines the temperature in the first place then?

What of all the other factors that go into determining the rate of beam spread? Why does ‘divergence’ not give many search results online?

This is because actual particle physicists use a different measure for the performance of accelerators: emittance. Let’s try to explain what it is and use it to answer our questions.

Emittance, emittance growth and ion sources

In scientific literature, the divergence of a particle beam is rarely given or used. ‘Emittance’ is used in its place. It is the result of multiplying the divergence of a beam by its radius to produce a measure in ‘meters-radians’. Because of the low values in most accelerators, ‘millimeters-milliradians’ or mm-mrad is preferred. One m-rad is a million mm-mrad.

Emittance describes the average spread of particles, like divergence does, but it also helps factors in the width of the beam, any perturbations or errors, any imperfections in the accelerator and other factors.

A ‘normalized’ emittance divides the measured emittance by the gamma factor to account for any relativistic effects.

Emittance is more useful that simple divergence because it is flexible and can be applies to different accelerators that can be scaled, stretched or used in different ways… so long as the parameters determining the emittance are similar.

To get divergence back from emittance, use this:

Divergence: Emittance / (Beam radius * 10^6)

Divergence will be in radians
Emittance is in mm-mrad
Beam radius is in meters

Emittance is a very useful measure for predicting the performance of future accelerators. If we took the results of a small laboratory accelerator with a 1 mm wide beam, we can work out the divergence of a beam from a scaled-up version with a 10 cm wide beam.

Sadly, emittance is reported very inconsistently. One emittance reading in one paper will mean something different from another reading in another publication. The way emittance is reported has changed over time too. Early studies could give a figure in ‘mm-mrad’ that did not take into account relativistic effects. More recent paper would give ‘normalized’ emittance in ‘π mm-mrad’. To convert from one to another, you’d have to divide by π and calculate the gamma factor… despite both being called ‘emittance’. Also pay attention to whether the value is reported at the entrance, midway or at the exit of the accelerator. To muddle things further, emittance can count the beam radius as starting from different distances from the beam centre, creating hugely varied readings for the same beam.

With all these caveats in mind, we can start to take a quick look at the emittance of past and present accelerators.

As we can see, there is potential to improve. If you look into the documents linked above, you will see multiple emittances reported, at the exit of injectors or at the entrance of accelerators and so on. As the beam travels through the accelerator, it is disturbed a small amount by magnetic fields and heated up slightly by inter-particle collisions. This leads to a gradual increase in emittance from entry to exit. We call this ‘emittance growth’.

Much effort has been put into reducing emittance growth.

As we can see from these studies, emittance growth in modern accelerators can be as low as 5% or as high as 90%.

The valuable truth is stated in the introduction of this paper: emittance is due mainly to the ion source.

Ion sources are therefore the primary determinants of an accelerator’s emittance. We can see in the BEAR experiment that the emittance at the exit of the ion injector is the same as that at the exit of the entire accelerator.

An ion source, as the name states, is the device that feeds an accelerator with ions. There are a large number of options with different currents (charged particles per second released), current densities (current per area), efficiencies, voltages and other parameters.

We won’t detail the entire list. In general, ion sources are a small fraction of the power consumption, weight and size of a particle accelerator. However, the properties of the beam produced by an ion source determine the overall performance. It makes sense that we would select ion sources that produce high quality beams even if we must sacrifice efficiency or equipment mass to produce them.

As we will prove again later, having an ion source with a low emittance is crucial to a low final divergence of the particle beam. Searching through published performance of ion sources finds emittances as low as 0.004 (hydrogen) to 0.0075 (argon) mm-mrad.

It is consistent with an ion temperature of about 0.1 eV and an aperture of 3 mm when using this equation from a study on heavy ion beams accelerated by the MBE-4 linacs:

Ion Source Emittance = 65 * Aperture Radius * (T/M)^0.5

Emittance will be in mm-mrad
Aperture radius must be in meters
T is in eV
M is molar mass in g/mol

Inputting the figures from the study (0.1 eV Argon 1+ beam of 18 g/mol, leaving through a 1.5 mm radius aperture) we find a very similar emittance of 0.0073 mm-mrad.

To bring this back to divergence for a moment, we can work out that the MBE-4 linacs have a divergence of 4.8 microradians.

The equation also suggests that the smaller the aperture of the ion source, the smaller the emittance. However, the ion current is proportional to the surface area of the aperture, so this might limit how much current is available… unless multiple small radius ion sources are combined into one beam to have the best of both worlds: lowest emittance and high current.

Another way around a low current is to use a pulsed mode of operation. A small, lightweight low-energy storage ring can accumulate the output of an ion source working continuously and release it periodically in a high current burst.

The low emittance from an ion source like the one used in the MBE-4 linac is only possible because it produces ions with single charges. They require the least heating and the least intense magnetic fields to handle.

In many cases, an ion with multiple charges is desirable. An ion with more charges gains energy proportionally faster than an ion with less charges. An Uranium 12+ ion, for example, would gain 120 MeV of energy after passing through a 10 MV accelerating gradient. An Uranium 35+ ion would gain 350 MeV instead. The potential reduction in the accelerator length required to reach a certain energy level is very interesting as it would lead to great reductions in accelerator mass.

The best source for highly charged ions is the Electron Cyclotron Resonance ion source.

It is capable of handling all elements and achieving very high charge states by bombarding ions with an energetic electron beam again and again. The collisions deliver the required ionization energy to the ions, which can reach several keV.

The ions are forced to orbit within a small circle by magnetic fields so that they can be contained. However, the rotation within the magnetic fields adds a radial velocity to the ions. The result is an emittance dominated by the strength of the magnetic fields and the charge to mass ratio of the ions.

The equation for the emittance of an ideal ECR ion source is:

ECRIS emittance: 0.032 * Aperture Radius^2 * B / MCR

Emittance is in mm-mrad.

Aperture Radius is in millimeters.

B is the magnetic field strength in Tesla.

MCR is the mass to charge ratio.

For heavy ions, B is about 0.5 to 2 Tesla and the MCR for something like Oxygen 2+ is 16 over 2 (which is 8). We find emittances as low as 0.03 to 0.05 mm-mrad using heavier elements Bismuth and Krypton. With an ECRIS, we want the heaviest ions and the smallest apertures to minimize emittance.

ECRs can become rather heavy. They need large magnets and consequent cooling systems. For cases where achieving the lowest possible emittance is not a priority but producing highly charged ions is, there exists an alternative: foil or gas strippers.

It involves two steps. First, an ion is given a small charge and accelerated to moderately high energies by a separate accelerator. The ion then impacts the stripper, which is a certain length of gas (light ions) or a certain thickness of metal (heavy ions). The impact releases enough energy to strip off a large portion of the electrons around the ion. Extreme charge states are possible, such as Pb 82+, if the particles were given sufficient energy to start with.

The stripping process leaves most of the beam’s energy preserved, but emittance suffers. Modern ion strippers achieve emittances on the order of 0.1 mm-mrad.

Emittance alone is not enough to make a particle beam useful. A very low emittance in a beam released through a very small opening still makes for a high divergence beam. In ion sources, trying to achieve a lower emittance also involves making their aperture even smaller, which does not lead to improvements in divergence.

If particle beams cannot achieve low enough divergence, then lasers will remain as the better option...

Beam optics

The beam radius can be increased through the use of beam optics. Increasing the radius of a beam with low emittance will lead to a very low divergence. Just like beams of light that can be bent, focused or defocused by lenses, particle beams can be manipulated using electrostatic or magnetic lenses.

Electrostatic lenses work by introducing a voltage gradient from a particle beam’s centre to its edge. A charged particle travelling near the centre is unaffected. A particle travelling nearer the edges is either pushed inwards (focusing) or pulled outwards (expanding) by the voltage gradient.

Electrostatic lenses become less effective as the beam velocity increases. This means that they work fine for non-relativistic beams but the voltage gradients needed to act on high energy beams quickly become impractical (electrostatic lenses are limited by the same 10MV/m as electrostatic accelerators).

Electromagnetic lenses use magnetic fields to deflect ions.

They become more effective as the beam velocity increases, allowing them to handle relativistic beams much more easily. They are larger and heavier than electrostatic lenses for the same focusing ability due to the need for strong magnets however.

Two lenses working together can decrease divergence. The beam would first be expanded from its narrow diameter to a larger diameter. Then its expansion would be corrected and it would be focused on a far-away spot. Emittance does not change during this process.

A 1 mm radius beam with 0.1 mm-mrad emittance would have a divergence of 0.1 mrad without beam optics. If it is expanded to 20cm, it would have a new divergence of 0.0005 mrad.

Beam expansion to reduce divergence can be found most prominently in the neutral particle beam space experiment ‘BEAR’ from the Los Alamos National Laboratory. It was and still is the only high powered particle beam flown into space. The accelerator produced a negatively charged hydrogen beam with a beam radius of 2mm, which was then expanded to 11mm by electrostatic optics. This would theoretically allow the divergence to fall by a factor 5.5 before neutralization.

The effect of magnetic lens radius on the size of beam spot at a certain distance is determined by:

Spot radius = Emittance * Distance * 10^-6 / Lens Radius

Spot radius will be calculated in meters.

Emittance is in mm-mrad.

Distance must be given in meters.

Lens radius is also in meters.

You might notice that this is the equation used by lasers to determine spot size, if the wavelength of the photons were replaced by the emittance of the particles. In other words, a particle beam of emittance 0.1 mm-mrad has the same performance, given any distance and lens radius, as a laser of wavelength 100 nanometers (soft X-rays).

The implication is that particle accelerators can produce and handle beams with performance equal to lasers with extremely short wavelengths.


This is the step that allows a tightly focused particle beam to reach its destination without spreading into uselessness. Necessarily, it is the last step in a particle’s journey from ion source to space. After an ion becomes a neutral particle, it can no longer interact with magnetic fields and so cannot be further cooled, accelerated, focused or aimed.

Neutralization disturbs the particles in a beam. It imposes a minimum divergence that depends on the charge state of the ion, its energy and mass, and most importantly on the neutralization method being used. All neutralization requires an input of energy to strip an electron off a neutral ion, or releases energy when adding electrons to a positive ion. This energy is equal to the ionization energy.

Three main neutralization methods exist: using charge exchange, using electron beams or using lasers.

Charge exchange neutralization requires that an ion from a particle beam travel through a gas, plasma or foil.

When the ion strikes a component of that gas, plasma or foil, it gains or loses electrons and becomes a neutral atom. The advantage is that this method requires no power input (the neutralization energy comes from the beam itself) and can be a very lightweight solution.

The major downside is that impacts between an ion and a neutralizing particle tends to scatter the beam significantly. Gas or plasma neutralizers have the extra disadvantage of requiring heavy flow through a pressurized chamber, which is directly contrary to the requirement for keeping the accelerator tube in a perfect vacuum.

Design documents on the DEMO neutral beam injectors state that plasma neutralization becomes exceedingly inefficiency as particle energy increases above the 100s of keV. Gas neutralization fails above 1 keV. This is not a good solution for high energy particle beams.

Electron beam neutralization combines the ion beam with an electron beam of the same velocity.

The two beams merge into a plasma with an overall neutral charge. Within microseconds, the ions pull on the electrons to become neutral atoms. This is known as ‘recombination’. Recombination energy is equal to ionization energy.

As the electrons are travelling at the same speed as the ions, there are no impacts that scatter the beam. The massive mass difference between an electron and an ion means that the electrons retain almost all the energy being released by recombination. The electrons emit that energy as photons of specific wavelengths. The downside to this method is that you need an additional accelerator for the electrons and can only neutralize positive ions, but it is a small price to pay for the low divergence beams that are produced.

The latest option being developed is neutralization by lasers, also called photo-neutralization.

High energy photons from a short wavelength laser are sent to interact with an ion. The photons are absorbed by the outermost electrons of the ion. If enough energy is delivered to an electron, it jumps out of position. Photo-neutralization can turn negative ions into neutral atoms by removing electrons in this manner. The advantage is that photons are the most delicate neutralization tool and disturb the beam’s ions the least. However, it only works on negative ions and the laser power needed to strip high velocity beams after they have been expanded by beam optics is incredibly high.

Photo-neutralization power = 8.853 * 10^-5 * BV * BR / Laser wavelength

Photo-neutralization power will be in watts.

BV is the beam velocity in m/s.

BR is the beam radius in meters.

Laser wavelength is also in meters.

That equation applies only to negative H ions. We work out that at 1 GeV energy (262,000 km/s) and in a beam 1 m wide (BR 0.5), we would need a laser power of over 11.6 GW when using the longest practical wavelength of 1 micrometer. This is to neutralize just 63% of the beam. Neutralizing a full 98% of the beam requires 46.4 GW.

This paper describes the development of an optical cavity that can bounce the laser up to 10,000 times through the particle beam to reduce the power required down by a factor 10,000. In our case, it is a reduction down to 4.64 MW. In non-laboratory conditions, that cavity might not have the same performance, but the real problem is that your multi-megawatt particle accelerator also needs a multi-megawatt laser to neutralize it.

Considering the characteristics of all these methods, we will focus on electron beam neutralization. There will be designs for which the other methods make sense, such as a single-use close range particle beam using a foil stripper or an interplanetary ultra-low-divergence power transmission beam using a photo-neutralizer, but we won’t focus on those here.

Let's continue to look at electron beam neutralization.

When adding or removing charges from an ion, they get a ‘momentum kick’ that can be seen as the difference in beam velocity before and after neutralization. The minimum divergence imposed by neutralization is:

Neutralization divergence = (0.56 * IE/M) / (B * C * y)

Neutralization divergence is given in radians.

IE is Ionization energy in eV.

M is Molar mass is in g/mol.

B is the particle beta.

C is the speed of light, about 3 * 10^8 m/s.

y is the Lorentz Factor.

For a hydrogen ion, ionization energy is 13.6 eV. At 100 MeV, beta is 0.428 and y is 1.1065. We can work out that the minimum divergence of such a beam is 53.6 nanoradians. If it is accelerated to 1 GeV energy, beta becomes 0.875, y is 2.065 and the minimum divergence becomes 14 nanoradians.

This divergence is to be added to that of the beam before neutralization. In the real world, the neutralization disturbance will be greater than the theoretical minimum.

You will notice that the ions with the lowest ionization energy per mass, accelerated to the highest energies, will have the lowest minimum divergence. Cesium, for example, is particularly good. It has an ionization energy of just 3.89 eV while having a mass of 133 g/mol. At 250 MeV of energy, Cesium would have a minimum divergence of 0.86 nanoradians. Francium is even better but it is rare and very radioactive.

Bright beams?

The neutralization step releases the excess energy from recombination in the form of photons. Recombination usually involves the release of a photons with a total energy equal to the ionization energy.

The SDI proposal for neutral particle beams used gas strippers for hydrogen atoms. It was expected for about 7% of the atoms to exit the stripper in a metastable excited state. Shining a laser on those metastable atoms would have caused them to quickly release their energy as 656 nm wavelength photons, which is a bright cherry red. Without the laser, it would take about 125 milliseconds for the photons to be released.

Different ions emit different photon wavelengths as a ‘Radiative Recombination Continuum’. Going straight from the excited state (the electron has just arrived) to the ground state (all excess energy has been released) is rare, with a graduated release much more likely.

For example, a lithium atom would release a photon with an energy of 5.39 eV and a Cesium atom would release photons with an energy of 3.89 eV. Any division of these energies would correspond to visible wavelengths.

Multiplying the ionization energy (1 eV = 1.6 * 10^-19 Joules) by the current (1 A = 6.242 * 10^18 atoms per second) gives the total watts of visible light being emitted. For 1 Amp of Cesium atoms, this is 3.89 Watts. For a 250 MeV beam, this means that 1.6 millionth of a percent of the beam energy becomes visible light. This ratio only gets worse for beams with higher particle energies. These watts are spread over the distance the beam travels during its recombination time.

In other words, particle beams could be visible, and will certainly be detected by sensors across even large distances, but they are mostly invisible to the naked eye.

As the beam traverses interplanetary space, it encounters about five million protons per cubic meter near Earth, falling to 300,000 per m^3 at Saturn’s orbit. A 10 nanoradian divergence beam would traverse a volume of about 0.015 m^3 over a distance of 10,000 km. It encounters 78.5 thousand particles at most. Even if even proton is is struck, and all of the collision energy between the protons and beam particles were absorbed, and all of that energy was to be re-radiated as visible wavelength photons, then this would only amount to 2.34 femtowatts per meter for 0.063 C particle, or 0.45 nanowatts per meter for 1 GeV particles.

Neither makes for visible beam.

The situation changes near a planet. The particle density above an atmosphere is much higher than in the interplanetary medium, even when hundreds of kilometers over the surface. At 1000 km altitude above Earth, there are enough particles to create a mass density of 5.85 * 10^-15 kg/m^3. This would release 0.8 W/m from a 1 m diameter 0.063 C beam and 201 W/m from a 0.875 C beam. Relativistic beams are likely to be visible to the naked eye when fired over an atmosphere.

Near the top of Earth's atmosphere, at 200 km altitude, we would expect very bright beams of 55.9 kW/m (0.063 C) or 10.78 MW/m (0.875 C). The huge energy losses experienced by fast beams make them impossible to use in such conditions unless they are very, very small (mm wide beams).

All in all, the particle beams are likely to be detected by sensors but unlikely to be visible to bystanders.

Final divergence

We now have all the elements in place to work out the divergence of a very good particle accelerator.

Final divergence= ((SE/LR * EG * 10^-6 + 0.56 * IE/(M * BV))/y

SE is source emittance in mm-mrad (refer to the ion source equations).

LR is the lens radius in meters.

EG is the emittance growth throughout the accelerator, dimensionless.

IE is the ionization energy in eV.

M is the molar mass in g/mol.

BV is the beam velocity in m/s.

y is the gamma factor.

We can work out that a 10 meter long accelerator built using modern technology, using a Microwave Ion Source to produce extract single-charge Cesium ions with 0.0018 mm-mrad emittance, expanding the beam from 1 mm radius to 0.05 meter radius (LR = 0.05), causing 10% emittance growth (EG = 1.1) and using electron beam neutralization (IE 3.89, M 133, BV 18,900,000), could be expected to produce 250 MeV particles with a divergence of just 40.5 nanoradians.

This beam would cross a distance of 1,000 km in about fifty milliseconds and would remain focused within a spot just 8.1 cm wide.

Even better focused beams could be produced if negatively charged ions are accelerated.

The ionization energy for a negative ion can be very low, such as 0.47 eV for Cesium instead of 3.89 eV.

Bigger accelerators can use larger optics and achieve higher particle energies, making particle beam performance scale up favourably.

Equipment design

The mass of a particle accelerator system seems to be dominated by the RF power generators and the cooling system, at least according to a footnote on the SDI report on the feasibility of Neutral Particle Beam weapons for ballistic missile defence.

RF power, specifically in the frequencies that heavy ion SRF accelerators use, can be generated by solid-state devices. The best example of commercially available performance is from the Nautel generators produced specifically for the VASIMR rocket.

They operate at over 98% efficiency and have a power density of 2 kW/kg. However, they lose efficiency as the RF frequency asked of them increases.

For the dozens of MHz minimum that accelerators need, they are closer to 65% output efficiency.

Inductive Output tubes are another option.

This design by Relltubes produces an impressive 16 kW/kg at 73% output efficiency.

The low frequencies achieved by solid state devices or Inductive Output tubes limit them to accelerating the heaviest ions to rather low velocities. Higher frequencies are needed for light ions or to achieve relativistic velocities.

For higher RF frequencies required to push light particles to relativistic velocities, a magnetron is the best option.

The most modern designs boast 14.7 kW/kg at 88% output efficiency.

Solid state amplifiers, inductive output tubes or magnetrons can all expect to operate at rather warm temperatures. The amplifiers obtain good efficiency at room temperature (298 K) but can sacrifice efficiency down to operate at up to 473 K. The same goes for inductive output tubes, while magnetron performance seem to be unaffected by temperature even when operating at 423 K.

The Klystons needed for the highest frequencies struggle to surpass 1 kW/kg.

However, NASA designs for klystrons to be used in the SPS program were to achieve 1.96 kW/kg before cooling equipment was included.

These temperatures are critical for telling us whether the waste heat from the RF source can be radiated directly or requires heat pumps to increase the radiating temperature (at the cost of more electricity and equipment mass). Lighter radiators can accommodate lower temperature waste heat. Better heat pumps significantly reduces radiator mass.

For example a 1 MW magnetron would mass 68 kg and would need 95 kg of 1 mm thick graphite radiators radiating at 400 K to get rid of 120 kW of waste heat.

The RF power reflected in an accelerator’s cavities is not absorbed. Over 100 MW of RF power per meter length of accelerator is possible.

However, the superconducting walls are subjected to eddy currents from the megavolt electric field gradients running through them. These currents encounter a very small resistance, on the order of nanoOhms. Even cooling below 2 Kelvin temperatures cannot eliminate this ‘residual’ resistance.

Typical SRF efficiency is therefore about 99.9%. Residual resistance causes about 0.1% of the power that an accelerator handles to become heat in the cavity walls. A 1 MW accelerator, for example, would cause 1 kW of heating.

Most superconducting accelerators operate at 4.5 Kelvin temperatures to handle this heating.

The empty spaces around a cavity’s walls are actually filled with helium. Helium boils at 4.2 Kelvin in standard atmospheric pressure. Having the cavity walls sit at a temperature just above the boiling point of helium allows any heating to be carried away by helium’s phase transition from liquid to gas state.

The transition absorbs 20 kJ of heat per kg of helium. Accelerators that operate in the 4 to 5 Kelvin temperature range are made possible today through the use of niobium-tin alloys. A 1 MW accelerator should be prepared to lose 50 grams of helium per second.

For a spaceship that only intends to use the accelerator in short bursts, releasing the helium vapours into space is acceptable. If the usage period extends to many hours, it is advisable to use a cryogenic heat pump to compress the vapours and increase their temperature from 4.2 K to 13.8 K. The latter temperature is where liquid hydrogen boils in near vacuum. Using hydrogen as an expendable coolant instead of helium is much more interesting, as it can absorb 455 kJ/kg. Even with the increased heat load of the pumps, the coolant expenditure is reduced by a factor 10 with liquid hydrogen.

A closed loop alternative to expending helium or hydrogen is to install many more heat pumps to raise temperatures to the point where the heat can be effectively emitted from a radiator’s surface. A 300 Kelvin radiator emits 459.3 W/m^2 of exposed area. Pumping heat from 4.2 K to 300 K adds an additional 7042% to the heat load. If we want to get rid of 1 kW of heat, 7043 kW need to be emitted from 7667 m^2 of double-sided radiators.

The question is whether the mass dedicated to the heat pumps (14 tons at 500 W/kg as deduced from Lockheed’s aerospace cryocooler) and the radiators (17.6 tons for 1mm thick graphite fins) is advantageous compared to few grams per second of liquid hydrogen expenditure using the previous solution. Only serious improvements to heat pump technology can reduce the mass of equipment needed to carry heat across large temperature differences and make closed loop cooling a better alternative.

After the RF power source and the cooling equipment comes the mass of the accelerator cavities themselves.

We can work this out. A half-wavelength cavity made for particles of moderate relativistic velocity (0.6 to 0.9 C) has 59 kg of niobium per meter length according to this design. With its titanium structure, it comes out to 130 kg/m.

Other figures that we can use are those of the non-superconducting BEAR accelerator at 53.7 kg/m, the Indian IUAC at 316 kg/m or the much more modern cavities of the superconducting LHC at 125 kg/m. The main reason behind the mass per meter difference between the superconducting and non-superconducting cavities is the addition of a pressurized helium tank. We can settle on 130 kg/m as being a reasonable estimate. A 40 m long accelerator is expected to add 5.2 tons to equipment mass. This is expected to fall as technology progresses.

The beam must pass through an electromagnetic lens and a neutralizing step.

The High Energy Beam Transport section of the BEAR accelerator is an example of an electromagnetic lens. This is another example. All figures available online for magnetic lenses assume energetic beams being focused to a spot just a few centimeters to meters away from the lens. Deflecting the beam over such a short distance requires strong magnets, hence the improve magnet masses you can find. A particle accelerator in space will want to focus its beam over thousands to hundreds of thousands of meters. This greatly reduces the magnet strengths needed.

For example, a typical magnetic lens with an aperture of 10 millimeters will focus a beam over a distance of 1 meter. Our lens would have an aperture of 1 meter and focus a beam over a distance of 100,000 meters at a minimum. The magnetic field requirements for our lens would be about a thousand times lower than a typical magnetic lens.

For example, a 0.5m wide magnetic lens trying to focus 250 MeV heavy Cesium ions a spot 100 km away needs a magnetic field strength of just 0.000188 Tesla. In other words, the mass of magnetic optics for long range particle beams is negligible.

The neutralizing step requires an electron accelerator. Electrons of the same velocity as a heavy ion are very low energy particles. Producing and accelerating them therefore requires very little mass dedicated to electron accelerators, on the order of kilograms. For a 10 MW beam of 250 MeV particles, a Cesium current of 40 milliAmps is required. 40 milliAmps of electrons would be needed to neutralize the ions. The Cesium ions are travelling at 18,947 km/s so the electrons would need an energy of just 1 keV to reach the same velocity.

A 40 mA, 1 keV beam of electrons can be created by a <1 kg device.

Other equipment such as an ion source are a small contribution to overall mass.

A permanent magnet ECR called LAPECR1 managed 2.5 mA using just 25 kg of equipment.

An even better example is the Dresden ECRIS-2.45M ion source for low charge ions, where 10 mA can be produced by a device of just 35 kg. 40 mA of Cesium might need less than 0.14 tons.

Using the figures for modern accelerators, we can expect a 10 MW 250 MeV beam to require 0.14 tons for the ion source, 1.3 tons for the cavities, 0.68 tons for the RF power source, and 0.64 tons for 400 K radiators. We add a 25% ‘other equipment’ margin to bring the total mass to 3.45 tons. About 50.2 grams of liquid hydrogen coolant per second is the ‘ammunition’. The accelerator can fire for one hour with 180.7 kg of hydrogen on-board or for a full day (delivering 864 GJ) with 4.3 tons. Cesium consumption is negligible, at just 55 micrograms per second.

At this scale, the entire accelerator assembly would have a power density of 2.89 kW/kg. When more advanced technologies are included, such as better heat pumps or lighter radiators, the figure increases even further. For the rest of this post, we will use three designs:

Modern Accelerator

Output: 10 MW

Divergence: 40.5 nanoradians

Beam velocity: 18,900 km/s

Total mass: 3.45 tons.

The modern accelerator is built out of existing components as described above. The biggest contributors to the device’s mass are the cavities and the RF power source.

Huge Accelerator

Output: 500 MW

Divergence: 16.7 nanoradians

Beam velocity: 18,900 km/s

Total mass: 203 tons.

Some design changes made sense at a larger scale. Better radiators in the form of ‘wire radiators’ show benefits when 185 MW of waste heat must be removed from the RF generators. At smaller scales, the support structure needed to handle the 1 mm thick carbon fiber wires makes them uninteresting. The SRF cavities are heated significantly more by 500 MW of input power. Ejecting a huge load of hydrogen is wasteful at this scale, so a closed loop solution using 65.6 tons of heat pumps and 8.2 tons of nylon radiators operating at 300 K was selected. It ends up more mass efficient than open loop cooling after 8.8 hours of operation. A larger set of lens was also used, with 0.25 m width. Together, a power density of 2.46 kW/kg (even with +25% for other equipment) is achieved and the beam can be focused to a spot 33.4 cm wide at 10,000 km distance.

Advanced Accelerator

Output: 1000 MW

Divergence: 3.9 nanoradians

Beam velocity: 48,270 km/s

Total mass: 131.2 tons

In the advanced accelerator, we assume some technological progress has taken place. The RF power source is more efficient, at 85%, which increases its power density to 18.6 kW/kg. Heat pump technology moves to using superconducting electric motors to drive Brayton cycle compressors, increasing their power density to 5 kW/kg, which in turn allows them to be used to increase the temperature of all waste heat. The heat from RF generator and the SRF cavities is pumped up to 600 K, which allows for a very lightweight bubble membrane radiator to be used. Stronger materials can also allow for lighter SRF cavities, reducing them to 50 kg/m. We can therefore use a longer accelerator (50 m long at 33 MV/m) and a larger lens (1m wide). Adding on improvements to the ion source, we end up with an overall power density of 7.6 kW/kg and the ability to focus a 48,270 km/s beam to a spot just 39 cm wide at a distance of 50,000 km.

The particle beam cannot be bent after neutralization, and it becomes very hard to steer it using electromagnetic optics after it has reached high energies near the end of the accelerator. A reasonable configuration of all these components is to have a fixed ion source and low energy accelerator stages, and a moving high energy stage topped with a neutralizer. It would resemble a turret.

Power transmission and propulsion

The ability to focus a beam of high velocity particles onto a small spot over long distances has applications in transmitting power or spacecraft propulsion.

For power transmission, you need a beam accelerator and a receiver, separated by the distance you want to cross.

The beam accelerator is as described above. The receiver has three parts. The first part is the beam stripper, most likely a metal foil. A neutral beam cannot be converted into electricity without turning it back into a charged beam. After passing through the stripper, the beam becomes a plasma of electrons and ions. This plasma travels into the next part: the beam optics. Electromagnetic lenses (for relativistic beams) or electrostatic optics (for slow beams) attempt to brake and bend the beam. The effect on the lighter electrons is much greater than on the heavy ions, which leads to the electrons slowing down more and bending away from the main ion beam.

Once separated from its electrons, the ions are directed through the third part: the beam recuperator. It works like an accelerator in reverse and is a commonly proposed for use in fusion reactors to convert alpha products: instead of using electric fields to accelerate particles, it slows them down and converts its energy into electricity.

Direct energy conversion turns kinetic energy into electric energy with no intermediate steps. ‘Travelling Wave’ or ‘Inverse Cyclotron’ direct energy converters have a maximum efficiency of over 90% and can handle high particle energies. Similar power density is expected at either end of the power transmission, with RF generators replaced by power processing units at the receiving end.

A direct conversion receiver works best over distances where the beam does not spread too much.

A very wide beam would have to be handled by equally large beam optics, which become very heavy when scaled up. For example, the Huge Accelerator would produce a beam about 1 meter wide at a distance of 60,000 km. The Advanced Accelerator achieves this at a distance of 256,000 km. These are more than sufficient for carrying power between spacecraft, such as a booster mothership and a cargo tug, but not enough to transmit power over the distances between moons or planets. Increasing the transmission distance by a factor 10 would require beam optics over 100 times larger and heavier.

A different way of converting beam power into electricity can used to unlock the longer distances.

When a particle beam intersects a gas, collisions between the beam and gas molecules turn kinetic energy into heat.

A tube of gas can be used as a beam target, with the beam entering through a thin window of dense metal. The beam loses its energy by travelling through the gas, which is converted into heat with an efficiency approaching 100%. The hot gas is then used to power turbomachinery, much like a modern power reactor.

After passing through a compressor, turbine and radiator, the cooler gas is returned to the beaming tube.

The best type design is one where the particle accelerates the heaviest particles possible to velocities just high enough so that they reach high charge states when striking the metal window. Heavy particles disperse the least and slow down the quickest when travelling through a gas, which keeps the transmission range high and the beaming tube short. A high charge state also helps them to slow down faster. An ideal ion is Uranium 238, which has a high mass, low ionization energy and low radioactivity.

The beaming tube should be filled with a high molar weight gas with a low heat capacity. The high molar weight allows for a higher density (kg/m^3) to slow down the beam in a shorter distance, while the low heat capacity allows for the gas to heat up to high temperatures to improve thermodynamic efficiency. Iodine is a good example, as it is sufficiently dense even at high temperatures (1.2 kg/m^3 at 10 atm pressure and 2500 K temperature in the form of the molecule I2) while being not as rare and expensive as Xenon nor likely to condense in the radiators (it boils at 457 K).

Efficiency of the beaming tube power transmission design suffers due to the intermediate thermodynamic step for converting beam energy into kinetic energy. If the beaming tube is 90% efficient, the Brayton turbomachinery 60% efficient and the alternator and power handling steps 90% efficient, the overall efficiency is 48.6%. Power generators seeking the highest possible power density will have a higher temperature Brayton cycle that minimizes radiator size but cuts into efficiency even further, down to 24.3% perhaps. This is roughly the efficiency of solar power.

The beaming tube power generator can operate at extreme distances away from the power source, does not rely on the sun and can achieve overall high power density.

A dedicated power source would use the extra equipment required to reduce the divergence of its heavy ion beam to the lowest possible value, roughly equal to that caused by the neutralization disturbance. For a 1000 MeV Uranium 238 beam, this can be as low as 0.45 nanoradians. A 20 m beaming tube would intercept 100% of this beam at a distance of 22 million km.

Another way to use a particle beam is to bounce it off a magnetic field in a propulsion system known as the ‘mag-sail’.

The slower the particle beam, the better the thrust per watts of the propulsion. The efficiency falls as the ratio of mag-sail velocity to beam velocity increases, but it can be ignored for interplanetary trips. For example, a 100 MW beam of 0.3 C particles would deliver 2.2 Newtons of thrust to a stationary mag-sail (45.5 MW/Newton), but a 0.01 C beam would deliver 66.6 Newtons (1.5 MW/Newton). The main advantage of mag-sails is that they can create huge reflecting field areas using lightweight conducting coils. Mag-sails prefer the use of lighter particles that are more easily reflected by magnetic fields after they are ionized, but this tends to negatively affect divergence.

Using Zubrin’s estimates, superconducting coils that can handle 1000 MA/m^2 of current can produce a magnetic field of 1 Tesla in a bubble nearly 500 m in diameter using loops massing just 10 tons. This mag sail is large enough to fully intercept a 1 nrad beam at distance of 250 million km or 1.7 AU. It could potentially catch 15.7% of a nanoradian beam across the 4.2 AU distance that separated Earth from Jupiter.

A 20 ton spaceship with a 10 ton magsail riding a 1 GW beam of heavy particles at a velocity of 0.01 C would accelerate at a rate of 22.2 mm/s^2. This is enough to cross the distance between Earth and Jupiter in about 17.6 weeks.

The field area can be further boosted by ejecting plasma, as is done by the M2P2 Mini-Magnetospheric Plasma Propulsion system.

We can also imagine a Particle Beam Thermal Rocket engine, where the beam is used to directly heat propellant.

This is similar to the Laser Thermal Rocket engine. Instead of optical mirrors, a stripping foil with bending magnets behind it can direct a particle beam into a reaction chamber filled with propellant. Particle beams can efficiently heat up propellant without the need for seeding particles, allowing for pure hydrogen gas to be used for maximal exhaust velocity. They can also ionize a good portion of the propellant gases, allowing for electromagnetically confined propellant that can reach very high temperatures without touching the chamber walls.

The main disadvantage is that a Particle Beam Thermal Rocket cannot work in an atmosphere.

Weaponry and damage mechanics

The ability of particle accelerators to focus their output onto a small area at a great distance has an obvious application as a weapon system.

First of all, how does a particle beam deal damage?

The ‘Report to the American Physical Society of the study group on science and technology of directed energy weapons’ is the golden reference for its section on Neutral Particle Beam weapons.

Two damage mechanisms prevail for the heavy ion particle beams discussed so far: radiation dose and volumetric heating.

High energy particles are considered as penetrating radiation. They do not deposit all of their energy on a target’s surface, but travel through a certain depth of matter before stopping. The depth depends on the properties of the beam and density of the target material. All energies discussed in this post are more than enough completely strip any electrons from an impacting particle. In fact, the target material acts like a 100% effective stripper. This is why the particles from a neutral hydrogen beam will be referred to as protons, and why previously neutral particles are described as ion in the following sections.

The main way that particles lose energy when traversing matter is due to collisions with the electrons surrounding atoms in the matter. The equation that governs how far a particle penetrates into matter is based on that effect:

Penetration depth: 0.00331 * E^1.74 / (Z^2 * A^0.74 * D))

Penetration depth will be in centimetres.

E is the particle energy in MeV

Z is the particle charge state.

A is the particle molar mass in g/mol.

D is the target material’s density in g/cm^3

We can see that more energetic and lighter particles would penetrate the most, with protons being the best at traversing matter. In fact, any other particle than a proton is unlikely to penetrate significant lengths of any material due to 1/Z^2 factor.

A helium particle would gain 2 positive charges after impact while weighing 4 times more than a hydrogen particle. For the same energy, it penetrates 11.15 times less material than a hydrogen particle. This get much worse for heavier particles, with Cesium penetrating 112,817 times less than hydrogen.

We can safely ignore the penetrating effects of anything other than protons.

The penetration depth equation does not account for the changes in how protons interact with electrons at energy levels greater than 10 GeV.

The energy transfer from a proton to an electron increases rapidly beyond 1 GeV, which makes penetration rates fall below the expected values. At even higher energies, the protons cause multiple neutrons to be knocked out of the shielding material for every incident particle and can even create muons and pions… these are additional energy loss mechanisms that further affect penetration.

The shielding table from a CERN lecture empirically confirms that proton penetration rises more slowly for energies higher than 3 GeV. In other words, proton penetration at 3 GeV is the most efficient, but it can be increases further.

Another complication is that shielding full of hydrogen, such as water or plastic, is much more effective than the equation would suggest for the same g/cm^2 values.

From this table, we find a 29% discrepancy between the penetration depth calculated for 250 MeV protons (49 cm) and the value measured (38 cm).

It can all be summarized by the relative effectiveness of shielding materials:

We can see that water is again about 30% more effective than aluminium at great shielding amounts. Surprisingly, there are materials even more effective than water but are not liquid hydrogen, such polyethylene and lithium hydride requiring 45% less shielding than aluminium.

Considering all these complications, it is best to simply use the data collected in the physics databases made online by the National Institute for Standards and Technology. Using those databases, we will produce charts for the penetration of protons of 100 MeV to 10 GeV into polyethylene, water, carbon, steel, tungsten, lead and uranium.


Polyethylene has a density of 0.94 g/cm^3 so a 250 MeV proton would go through 38 cm and a 3 GeV one would go through 13 meters.

Water is 1 g/cm^3 so the y-axis can be read in centimeters. 250 MeV protons go through 35.7 cm and 3 GeV through 12.47 meters.

Graphite can have a density of 1.5 to 2.3 g/cm^3. Amorphous carbon has 2 g/cm^3 and diamond has 3.5 g/cm^3. For this graphite specifically, 250 MeV protons go through 24.9 cm and 3 GeV through 8.7 meters.

We use iron at 7.84 g/cm^3 to simulate steel. 250 MeV go through 6.92 cm and 3 GeV protons go through 2.31 meters.

Tungsten at 19.3 g/cm^3 is interesting as it is dense, temperature resistant and strong. It stops 250 MeV protons within 3.7 cm and 3 GeV protons within 1.21 meters.

Lead is disappointing as it requires 6.6 cm for 250 MeV protons and 2.08 meters for 3 GeV protons.

Uranium is great as it stops 250 MeV protons within 4.6 cm and 3 GeV after 1.3 meters, but there is the danger of significant secondary radiation in the form of neutrons.

The energy of a proton is not deposited continuously throughout the penetration depth. As the particle slows down, the material becomes more effective at slowing it down further. At a certain point, usually for protons of less than 100 MeV, material stopping power increases very rapidly up to a maximum at 1 MeV. The Bragg peak is situated in this region

The heavier the particle, the narrower and sharper the Bragg peak is. More importantly, the Bragg curves indicate that shielding that is too thin to fully absorb a beam let through a lot more radiation than what you’d expect, up to 40% of a 250 MeV proton or 3% of a 3 GeV proton.

Whatever passes through the radiation shielding is fully absorbed by people or electronics. People and electronics do not like being hit by high energy particles.

One rad of radiation is 0.01 J of particle energy per kg of matter. Sickness, nausea, anaemia and immunodeficiency is caused by 3 J/kg. 30 J/kg is enough to kill within a day after incapacitating the person. 300 J/kg kills most people on the spot, and no-one can survive 750 J/kg.

The full effects and calculations of radiation doses are given on the Atomic Rockets website.

The only saving grace here is that when the highest energy protons encounter very thin or no shielding, they don’t slow down at all keep on going through the walls, people and electronics before exiting without losing much of their energy.

This is the reason behind NASA stating that aluminium walls on their spacecraft makes Galactic Cosmic Ray radiation worse by causing them to release more of their energy in people.

A completely unshielded human modelled as a 30 g/cm^2 target would absorb only 10% of a 1 GeV proton or 0.7% of a 10 GeV proton.

However, particle beams can be tailored to deal maximum damage. An over-penetrating beam can easily be detected leaving the target from the other side. The particle energy would then be adjusted so that the Bragg peak sits inside people or electronics. A large portion of the beam’s energy would then be released in the most damaging manner.

This is used to a good end in proton radiation therapy: 250 MeV protons deposit most of their energy in the center of a person. Weaponized protons would designed to have at most 250 MeV left over after passing through shielding to prevent over-penetration.

Insufficient shielding against weaponized radiation beams will be deadly in short order.

A 100 MW accelerator shooting 1 GeV protons with a divergence of 0.1 urad, facing shielding that lets through 100 MeV of energy per particle, would cause immediately lethal doses of 300 J/kg at a distance of over 59,467 km… in one second.

If the beam can be held on the target for just one minute, it can be lethal at a distance of 0.46 million km.

Electronics do not fare much better.

Sensitive devices used in sensors would be even less resistant than people. Electronics can survive a dose of 100 kJ/kg if they are extremely radiation hardened (at the cost of weight and performance). This decreases the lethal distance by a factor 18.25.

It should be noted that a 1000 MW beam would terminally irradiate targets in a period 10 times shorter, or at a distance 3.16 times further, than a 100 MW beam.

Protecting against such a beam would be of capital importance to having human crews anywhere near a space battle. Armor and defense schemes will be discussed in the next section.

If a proton beam does not fully penetrate the shielding, it will have almost all of its energy converted into heat instead. We can use the following equation to determine how much heat energy is deposited per m^3 of shielding material:

Volumetric heating rate = BP / ((Divergence * D)^2 * 3.142*Penetration))

The heating rate is in W/m^3.

BP is Beam power in watts.

Divergence is in radians.

D is Distance in meters.

Penetration is in meters.

We can work out that the previous beam (100 MW, 1 GeV protons with a divergence of 0.1 urad), if encountering a thickness of shielding it cannot penetrate from 59,467 km away, would spread its energy over a volume 11.89 m wide and 2.15 m deep in graphite or 0.58 m deep in steel. The volumetric heating is 418.6kW/m^3 in graphite or 1552 kW/m^3 in steel. These figures can be converted into 182 and 197 W/kg respectively.

This heating can be ignored for temperature resistant materials such as graphite or steel, but could cause the best radiation shielding materials such as polyethylene or water to fail.

What is to be done if the particle beams cannot irradiate their target or cause sufficient volumetric heating?

You change the beam properties to maximize volumetric heating. Instead of a lightweight, penetrating particle, you choose a heavy atom with the lowest divergence possible. As we can see from the penetration equation, a higher mass and charge state reduces penetration. Heavy atoms striking solid matter quickly lose most or all of their electrons and achieve a multiply charged state.

A 250 MeV Cesium particle would only penetrate a distance of only 1.88 micrometers into graphite or 0.4 micrometers into steel. We will set 63 MJ/kg as the energy needed to vaporize carbon, which happens at a temperature of about 3600 K in vacuum. Steel sublimates at just 873 K in vacuum, requiring 6.3 MJ/kg. We can convert those figures into 144.9 GJ/m^3 for carbon and 54.2 GJ/m^3 for steel. If we divide the beam energy by the multiple of the beam area and the volumetric vaporization energy, we can get a penetration rate. This is the resulting equation:

Penetration rate = Beam Power/(Spot Area * VVE)

Beam P is beam power in Watts

SA is the beam Spot Area in m^2, equal to ((Divergence * Distance)^2 * 3.142)

VVE is the volumetric vaporization energy in J/m^3.

That equation is only useful at shorter ranges, where the beam intensity is rather high. At the shortest ranges (a few hundred km), the beam causes explosive expansion of the target material and gains an even greater penetration rate from the pressure breaking up and excavating more material. At longer ranges, the beam spreads out enough for thermal conduction and blackbody radiation to sap away its power and reduce penetration significantly, or even stop it.

For a more accurate result, we would best use this laser damage calculator. While it is designed for laser beams, the extremely low penetration of heavy ions allows the model to carry over accurately.

Let’s use the calculator to work the penetration rate of the three accelerator designs described previously against carbon (at 2.1 g/cm^3) and against steel (at 7.87 g/cm^3).

Modern Accelerator

100 km= 1.28 m/s in carbon, 2.61 m/s in steel.

1,000 km= 1.47 cm/s in carbon, 3.48 cm/s in steel.

2,000 km= 3.6 mm/s in carbon, 1.09 cm/s in steel.

Large Accelerator

100 km= 366 m/s in carbon, 2380 m/s in steel.

1,000 km= 3.75 m/s in carbon, 7.14 m/s in steel.

10,000 km= 4.32 cm/s in carbon, 8.76 cm/s in steel.

50,000 km= 1.66 mm/s in carbon, 3.87 cm/s in steel.

Advanced Accelerator

1,000 km= 1930 m/s in carbon, 1440 m/s in steel.

10,000 km= 1.38 m/s in carbon, 2.8 m/s in steel.

100,000 km= 1.58 cm/s in carbon, 3.28 cm/s in steel.

500,000 km= 0.57 mm/s in carbon, 1.47 mm/s in steel.

An ideal particle beam weapon would have a high power output, narrow divergence and minimal penetration. This is best done by using heavy particles such as Cesium or Uranium: when they strike the target material, they lose their electrons and acquire a very high charge state. This drastically reduces penetration depth and allows the beam’s energy to be concentrated into a thin layer on the target’s surface.

For practical reasons, the beam cannot have too low of a velocity.

If particles take 0.33 seconds to reach their target (100 MeV Uranium ions from 3,000 km away), then the target has the option of accelerating in any direction for 0.33 seconds before the beam’s aim can be adjusted. If the target acceleration is 1g, the beam’s position can be moved +/- 0.52 meters before it is adjusted. This might be enough to completely move the beam away from the area it has started burning through and expose fresh surfaces of armor. A target able to spread the beam’s damage across more of their armor surface would take considerably longer to destroy.

Pulsed particle beams, just like pulsed lasers, have additional damage mechanisms.

They produce pressures by vaporizing target material quickly enough to cause the mechanical failure of surrounding material. A pulse energy great enough to overcome the cratering energy of a material can rip out large chunk of material more efficiently than a continuous beam that if forced to fully vaporize that same material. Weak materials suffer the most from pulsed particle beams. Graphite, for example, takes about three hundred times less energy to break apart than it takes to completely vaporize it.

The penetration rates of a perfect pulsed particle beam can many times greater than a continuous particle beam.

Unlike a laser, they can ignore debris and plasma ejected from the target material into the path of the beam, allowing for very high pulse frequencies. Pulsing a beam’s power also allows it to better overcome the losses from thermal conduction or blackbody radiation at very long range.

There is also potential for a deeply penetrating, pulsed particle beam to exploit the Bragg peak of a particle to rapidly heat material inside the target’s volume.

This would have an effect equivalent to placing dynamite inside a boulder: all of the pulse’s energy will go towards straining the target material and causing shockwaves that crack and shatter the material. Multiple pulses can shake the material apart without having to vaporize it all.

The downside is the increased mass penalty from the pulsing equipment, as well as the challenges of producing and accelerating pulsed particle beams. Compressing a bunch of particles into short packets causes heating of the particles and greatly increases divergence. It is worse inside the accelerator because the particles are still charged ions and repel each other. Very strong magnets are needed to handle these packets of ions.

You would also need large capacitors to produce and accelerate the peak currents necessary for pulsed operation. Insufficient peak power would just warm up a larger volume of material than a continuous particle beam, making it far less efficient.

Defending against particle beams

Different approaches are needed to defend against the two main types of particle beam weapon: the penetrating proton beam and the vaporizing heavy ion beam.

The simple answer to the penetrating proton beam is to have sufficiently thick radiation shielding. ‘Sufficient’ is hard to judge when everything from the lowest energy 10 MeV accelerator to the kilometer-length 10 GeV beams are possible.

It would depend on accelerator technology, how long the engagements last and the degree of automation a space force employs. Better technology allows spaceships to use more powerful accelerators, which produce more penetrating beams. Longer engagements allow for a low dose to accumulate to damaging levels. More automation allows for less radiation-sensitive equipment and personnel to encounter the beams. Even better, good intelligence on the enemy and their equipment.

The shielding does not need to be one block of material on the outside of a spaceship. The outermost layers could be just enough to stop lower energy protons. An internal shell would contain more delicate equipment, with an innermost radiation shelter lined with sufficient shielding. The objective is to reduce the surface area the shielding has to cover to reduce the mass penalty of all this shielding. Even with polyethylene, it is 12.22 tons per square meter against 3 GeV beams. When using tungsten, this rises to 23.3 tons per square meter.

Simple mass shielding is therefore very bad for spacecraft. In the worst case scenario, a 10 meters diameter ship would need 1,819 ton slab on its nose to prevent radiation coming through. Providing protection for the flanks would be an even greater mass penalty.

A lot of research has gone into protecting astronauts from cosmic galactic rays and other particle radiation using electromagnetic fields as a lighter solution.

Electrostatic shielding is simple to understand.

There are three parts to it: stripper layer, electrostatic plates and backplate.

The stripper layer resembles a Whipple shield. Thin layers of metal strip the electrons off an incoming neutral particle. The electrostatic plates are the critical piece.

Two conducting plates can built up a large voltage difference.If they are also close together, they produce an electrostatic gradient that can be measured in the megavolts per meter. Sandwiching a dielectric material, the best of which is diamond, in between these plates allows for gradients of up to 1000 MV/m even when allowing for a safety margin. Charged particles travelling through these fields are slowed down. The backplate catches any excess energy from the particles and any secondary radiation they released when crashing through the plates.

Using equations for capacitors, we can work out that two plates separated by 1 millimeter, with the gap filled with diamond, maintaining a 10 MV potential in between them, would achieve a voltage gradient of 1 GV/m. The charged plates attract each other with a force per area equivalent to 425 MPa. This force can be handled by most structural materials, such as high strength steel or the diamonds serving as dielectric insulators themselves.

The plates are thin compared to the dielectric material in between them, so we can simplify the shielding to a solid stack of dielectric layers. For example, 1 GV/m shielding using diamond would be able to stop 1 GeV protons if it were a meter thick. Diamond has a density of 3510 kg/m^3, so this shielding would mass 3510 kg/m^2. That mass adds another 1.2 GeV worth of protection for a total of 2.2 GeV. Particle beams of less than 2.2 GeV energy will not go through. Particle beams with more than that would have their energy reduced by 2.2 GeV.

A particle beam striking the layers of electrostatic shielding would deplete the voltage potential between the charged plates. That potential must be recharged with onboard power. The beams also continuously degrade the charged plates, so they must be replaced eventually.

If a 2.2 GeV proton beam with 100 MW of power struck the diamond dielectric shielding described above, then 1 GeV (45.5%) of the beam’s power must be recharged plates and 1.2 GeV (54.5%) will have to be dissipated as heat.

As the shielding thickness increases, the protection from the electrostatic charge also increases (1 GV/m over 2 meters is 2 GV) but the contribution from mass shielding only rises by the power ^0.5747. More energetic particles follow the same relationship (a 2 GeV particle is 2^1.74 times less affected by mass shielding than a 1 GeV particle).

This means that the power required to recharge the shielding quickly matches the power of the incoming beam. In other words, radiation protection can become a tug of war between the power of the incoming beams and the power flowing through the shielding.

At this point, it might be worthwhile to consider the effects that volumetric heating and electric resistance heating have on the conductivity of the charged plates and therefore power requirements needed to recharge them.

High temperature stacked capacitors are a good design inspiration () and it would eventually be necessary to sacrifice some dielectric strength to be able to use liquid dielectric materials that can double as coolant.

Despite all those requirements and drawbacks, note that using electrostatic shielding on the front of a 10 m diameter spaceship against 3 GeV protons would not mass more than 300 tons.

Deflecting particle beams is a potentially even more efficient solution.

If a beam never strikes the spaceship, then only the mass of the deflecting equipment is needed, without any of the shielding. The risk, of course, is if the beam ever overcomes the deflection force and does hit the ship, then it will do so at full strength since it was not slowed down.

For magnetic shielding, we use the Larmor radius of an ion. It is the radius of the curvature of an ion’s trajectory through a magnetic field. Because of how the force a magnetic field applies on an ion increases with its velocity, the Larmor radius can be pretty small.

We work out that a 10 GeV proton beam can be bent 180 degrees by a magnetic field averaging 1 Tesla within a distance of 35.5 meters, and by a field of 10 Tesla within 3.6 meters.

Simple wires on the surface of a spaceship’s armor could project a magnetic field strong enough to deflect even the highest energy particles.

A current of 14.5 MA running through a wire is enough to produce a field with a strength of 10 Tesla at a distance of 3.65 meters from the wire. The critical current for superconducting wires is usually 15 MA/m^2, but it is preferable to use the same Niobium-Tin alloy as in SRF accelerators to achieve critical current densities of over 300 MA/m^2.

A Niobium-Tin wire handling 14.5 MA would mass about 1600 kg per meter of length (since it loop around to form a coil and needs a safety margin on top of that) to which must be added the mass of cooling, insulating and structural equipment. Each meter of superconducting coil would protect about 7.3 m^2, allowing for a shielding requirement of 213 kg/m^2 for the coils alone, likely 500 kg/m^2 with the additional equipment. If we only expect 3 GeV beams, the shielding requirement would fall to about 170 kg/m^2.

This compares favourably with other shielding options. The downside to relying on magnetic deflection is that unexpectedly powerful beams would hit the spaceship with full force, and that the wires themselves are rather vulnerable.

A temperature increase could cause them to tear themselves apart or vaporize instantly due to a quench. All momentum from the beam is transmitted directly to the wires, creating uneven stresses that could break them, especially from the hammering of a pulsed beam. Broken wires would leave gaps in the shielding, so a warship would likely have many hundreds of smaller coils that are redundant and easily replaced.

A strong magnetic field running through a spaceship is likely to have major deleterious effects. This is why all modern magnetic radiation shielding concepts include the use of another, internal set of coils to create a field-free volume.

The internal coils don’t have to be as strong as the external coils as a layer of conductors with very high magnetic permeability, such as nickel or gold, can be included to help the external magnetic field lines take a different path and avoid the protected volume.

Electromagnetic shielding only works if the particle beam is ionized before it interacts with the magnetic fields. Turning an incoming neutral beam into a charged beam is therefore of critical importance.

There are four potential methods for ionizing at a distance.

The first is to use an electron beam.

Just like an electron beam can be added to positive ions to neutralize them, another electron beam can be used to create electron/atom impacts to re-ionize them. Since the electron beam leaving the defending ship is travelling in the opposite direction as the incoming particle beam, there is no need for highly energetic electrons: the incoming beam is travelling fast enough to ionize itself with each collision. Even better, the electron beam can be easily steered using electromagnetic optics, allowing it to quickly change target within microseconds and handle multiple incoming beams.

There are many challenges though. The electron beam spreads quickly due to electrostatic self-repulsion. This makes it difficult to create the electron densities needed for full ionization within reasonable distances. For example, a 1 GeV 100 MW hydrogen beam with a divergence of 0.1 urad would have a current density of 31.8 mA/m^2 after travelling 10,000 km. A 1 MeV electron beam of the same total current and an initial beam diameter of 10 cm has a doubling distance of just 95 meters. The two beams would have the same current density at a distance just 4.5 km away from the defending spaceship. Increasing the electron energy to 10 MeV increases this distance to about 90 km.

The electron beam must be carefully aimed to not be bent off-course by the electromagnetic fields meant to protect the spaceship.

This difficulty in using electron beams is compounded by the fact that hydrogen beams are highly relativistic and would only give 4 milliseconds of warning over a distance of 10,000 km at 1 GeV of energy, or 0.12 milliseconds at 10 GeV, after the light signal from their firing arrives.

In short, it is very hard to ionize incoming radiation beams using electrons.

Ionizing slow, heavy particle beams is a different matter. The current density is usually higher owning to the lower per-particle energies, but the reaction time is measured in tenths of a second instead of milliseconds. For example, a 250 MeV beam of Cesium particles would take 0.529 seconds to cross 10,000 km, while light takes 0.033 seconds, giving a heads up of 0.495 seconds.

The slower beams can also be forced to suffer electrostatic bloom even over the short distances the electrons operate on. Fully ionizing an incoming 250 MeV cesium beam would cause it to reduce in intensity 16 times before it crosses 1.5 kilometers.

Having that warning time means that a second method is made possible: metal screens can be positioned between the beam and the ship.

This screen would act as a foil stripper and efficiently strip electrons from the heavy particles. It does not have to be a large screen, as a cloud of chaff will work equally well.

These metal screens work well against radiation beams if they are a few millimeters thick. They can ionize heavy beams with only a few micrometers of thickness but will destroy themselves in doing so.These screens can be moved into place by ‘interceptor drones’ or shot into position out of coilguns.

These foil screens are very vulnerable to being swept away by even weak laser beams. They would have to be released at the last possible moment, and be replaced quickly.

The third method is to use a plasma screen. A plasma acts somewhat like a foil stripper, except that a much greater thickness of plasma is needed to ionize a beam because the plasma is much less dense than a solid target. This paper suggests that 1 kg/m^2 of plasma is enough to ionize 4.2 GeV Uranium ions, which is more than enough for the other beams discussed here. Plasma screens of such density cannot be extended more than few meters to tens of meters away from the source of a containing magnetic field, so they can only serve to ionize incoming beams. They have the advantage of being easy to replenish.

A particle beam travelling through a relatively dense plasma will emit a lot of light and appear like a lightning bolt.

The fourth option is an ionizing laser.

A laser can react the quickest to an incoming beam. Ultraviolet lasers work to directly ionize atoms with every encounter between a photon and an outer electron of a neutral particle.

The relativistic doppler shift from an incoming beam works to the laser’s advantage by shortening the wavelength the neutral particles encounter down to the 90-100 nm optimum for ionizing hydrogen.

The only difficulty with ionizing lasers is that they have to work quickly against very low interaction probabilities due to the small ionization cross-sections, which means high laser power is needed. We can estimate that GWs are needed for relativistic hydrogen beams and tens of MWs for slower heavy beams.

It should be noted that there is always the option to move out of the way of a particle beam. Slower particle beams that take several tenths of a second to reach their target or correct their aim would create an opportunity to accelerate the spaceship randomly, in any direction, to frustrate the attacker’s efforts to keep the beam focused on one spot or even the hit the spaceship at all.

In half a second, a 1g acceleration can allow a spaceship to ‘jink’ by 1.22 meters. This is enough to prevent most beams from staying focused on the same spot.

A full study of these anti-particle beam, ionization-at-a-distance concepts and other defensive measures merits its own post.

Lasers vs Particle Beams

Lasers have been the best contender for long range power transmission, propulsion and weaponry in science fiction and the real world. Their ability to deliver energy to a narrow spot far away comes mainly from advances in laser technology allowing for the efficient production of short wavelength beams.

However, we are suggesting the particle beams can produce beams with even shorter ‘wavelengths’ and with even greater efficiency.

Their optics are much harder to damage than the mirrors of a laser and can have great effective ranges even when firing through small opening in armor. Using current technology, they are likely to have the upper hand in terms of power density too.

From a power transmission standpoint, particle beams can allow for very high efficiency at very long ranges.

Propulsion such as mag-sails also benefit from a better thrust per watt than lasers.

There are many advantages to a particle beam weapon instead of a laser weapon too. On top of the increase in potential beam intensities, they heat up armor material from the inside, leading to massively better penetration rates. When used as a radiation weapon, they can knock out electronics and crews from very long range as well.

While they are immune to damage reducing techniques such as reflective surfaces, and the danger of radiation beams can be greatly reduced by using appropriate shielding, it is still a powerful tool if it imposes on any enemy ship to have several meters of armor or superconducting wires all through its hull as a minimum requirement to enter battle. Deploying a more penetrating beam due to technological advances could suddenly render older warships with insufficient shielding obsolete. The shielding requirements also impose a minimum scale to the warships being deployed.

Smaller warships would have a bigger proportion of their mass dedicated to shielding, making them less effective on a ton per ton basis compared to larger warships. The smallest vehicles suffer the most, with cheap massed missile swarms becoming irrelevant due to the ability of a radiation beam to disable them in seconds.

There are plenty of secondary benefits and uses to particle beams.

Their development as part of the Strategic Defense Initiative focused on using them to discriminate between warheads and decoys. That same ability can be used to identify targets using penetrating beams that exit the other side carrying information on what they passed through.

Particle beams could also counter stealth.

When energetic particles strike a solid target, they release secondary radiation in form of gamma rays, as well as neutrons and X-rays. These signals do not care about the temperature and albedo of the target material. Randomly sweeping the surrounding volume of space with low powered radiation beams could reveal the position of cryogenically-cooled spaceships. Of course, the stealth ships are able to use electromagnetic shielding to ward off these beams, but the act of ionizing an incoming beam so that it is deflected by a magnetic field creates distinctive but more diffuse and inaccurate signals of its own.

Finally, while humans are soft targets that want to stay away from particle beams, it might be interesting to keep them nearby. The use of heavy particle beams to damage the exterior of a warship and then disabling it using a radiation attack would mean that there is a high chance of battles ending with most spaceships on either side mostly intact. Sending in a repair crew to swap out the sensitive electronics and computers of disabled warships could be the difference between losing a battle and winning a war.

With all this in mind, we cannot dismiss lasers either.

Lasers have utility and advantages that would want them in use alongside particles beams instead of one or the other.

Lasers are hard pressed to produce the ‘wavelengths’ of particle beams, but they can compensate for it by using large and lightweight mirrors. These mirrors can be tens of meters in diameter, allowing for extreme effective ranges.

The range of a laser can be further extended by the use of laser weapon webs.

Relaying a beam from one mirror to another is not a feat that particles beams can replicate.

Always travelling at C, lasers experience light-lag at distances exceeding 300,000 km. Slower particle beams suffer from the light-lag equivalent at shorter distances, with heavy particles having the worst of it even over distances of a few thousand kilometers.

The need for a moving turret to change a neutral particle beam’s direction makes it slow to switch target. Lasers only need to rotate a mirror. Phased array lasers can shift their output electronically, within microseconds, which makes them much better options for point defense. Lasers are also modular and divisible, so a single laser generator can split its beam into multiple channels or supplement a group of generators working together. They have the extra utility of allowing moderated responses (warning shots and low grade heating) and working in or through the upper atmosphere of planets. High energy particle beams meant for space are completely ineffective below about 150 km altitude around Earth.

Lasers are much easier to pulse than particle beams. We have devices that work on the scale of femtoseconds. Frequency doubling or tripling also makes them very useful for blinding sensors across many wavelength bands.

Lasers and particle beams will in practice cover for each other’s weaknesses. Lasers would start an engagement with their extreme range, but then particle beams are used to degrade an opponent’s reflective surfaces so that they can deal damage. Particle beams can quickly destroy the fragile mirrors of lasers being used for ‘counter-beaming’, in which they try to send laser beams back up an optics train to damage the internal components. Lasers in turn can wipe away metal foil screens and bypass electromagnetic defenses to start heating up the armor, perhaps causing the superconducting wires to fail.

Having an ultraviolet laser with several tens to hundred of megawatts of power in addition to a particle beam weapon gives more offensive options as well as defensive ones: the laser can ionize enemy particle beams at a distance, or burn channels through plasma screens to allow your own particle beams to get through.

What’s next?

This has taken a long time to prepare! Many scientists and researchers have contributed their knowledge, with help from the ToughSF community on twitter, G+ and our Discord.

The next steps are to respond to comments and then do a further study of the capabilities of protection mechanisms against particle beams, as well as a look into the more advanced techniques for creating and handling the, such as beam cooling, plasma wakefield accelerators and beam condensation.


We look at the various ways of accelerating micro-scale projectiles up to hypervelocity (10-10,000 km/s) and their use in space.

Going small to go fast

Macrons or macroscopic particles are tiny projectiles that sit on the border between the complex structures we see under a microscope and the far simpler molecules where we can count individual atoms.

A typical macron is a micrometre in diameter and has a very simple structure. Due to the small size, it exhibits an interesting feature: a very high surface area to mass ratio. A useful number of electrical charges can be placed on a macron’s exterior compared to how much they mass. This feature can be exploited by an electrostatic accelerator.

Tiny particles are too small to survive the heating and friction in a railgun, and cannot support large magnetic fields in a coilgun. However, an electrostatic accelerator can bring particles up to high velocities by using a voltage gradient between an anode and a cathode. Charged particles feel a force when placed in between electrodes, proportional to the voltage gradient multiplied by the particle’s charge. When we divide that force by the mass of the particle, we get force divided by mass, which is an acceleration. A macron, with its high charge to mass ratio, will experience a strong acceleration even under small voltages. The velocity gained by a non-relativistic charged particle is easy to calculate:

Particle Velocity = (2 * Voltage * Charge/Mass)^0.5

The velocity will be in meters per second.
Voltage is in volts.
Charge is in coulombs. Mass is in kg.
Charge to Mass ratio, the critical feature of macrons, is in C/kg.

Electrostatic acceleration is regularly used today to push small things to great speeds. For example, electric rocket engines such as colloid thrusters shoot out tiny liquid droplets at multiple kilometres per second, which is somewhat similar to how we want a macron accelerator to operate. One design accelerates them to 43km/s. We can also find electrostatic accelerators in the medical field. In fact, the majority of them today are used to generate X-rays for therapy.

The most powerful electrostatic accelerators are for nuclear research purposes. They operate at several megavolts and are used to accelerate electrons and ions.

Van de Graaff accelerators have been used to study the impacts of interplanetary dust grains. The original accelerator facility built by Friichtenicht in 1962 was able to accelerate 0.1 μm iron spheres to 14 km/s using a 2 MV potential. We have also designed Cockroft-Walton, Marx and Pelletron accelerators, each different in their way of creating and holding a large voltage potential.

How much voltage can be obtained in an accelerator?

A voltage ‘V’ between two surfaces separated by a distance ‘m’ will create a voltage gradient of V/m. 1,000 Volts across a 1 centimetre gap will give a gradient of 1,000/0.01 or 100,000 V/m. The gradient creates a force that accelerates charged particles, but can also give electrons within the two surfaces enough energy to jump across the gap. The electrons that escape gain energy and slam into the opposite electrode, damaging it and reducing its ability to maintain a voltage gradient.

Weak voltage gradients are enough to get electrons to jump across a gap filled with a conductor, like salty water. Stronger gradients are needed to cross insulated gaps, like pure vacuum. Charge will accumulate at the tip of any imperfections or contaminants on the surface of an electrode, creating stronger voltage gradients locally and reducing the overall voltage that is possible. Too high a gradient, and enough electrons jump across to create an electric arc. The arcs from too much voltage gradient are lost energy that does not go towards accelerating charged particles. In fact, that energy becomes heat that can burn out anodes and cathodes. A device that operates at the megawatt or gigawatt level will certainly not want electric arcs dissipating that power as heat internally!

Single stage accelerator today manage 10 to 15 MV in total. Getting more than that becomes exceedingly troublesome, as voltage multiplying circuits become larger and larger.

Tandem (or two stage) electrostatic accelerators double their maximum voltage by switching the charge on the particle being accelerated halfway down their length.

At the upper end, we see Pelletrons with 30 MV. However, the highest voltages are only possible because the electrode gap is filled with a pressurized insulating gas. We cannot use this option inside our macron accelerator as interactions between the charged particle and the gas could create enough friction heating to destroy it. We are therefore forced to rely on simple vacuum. Highly charged macrons cannot be quickly switched from a negative to a positive charge either; the charges that need to move quickly result in destructive currents. Tandem accelerators are not an option either.

A ‘Super Marx Generator’ was proposed for achieving voltages on the order of 1000 MV; it is 1500 meters long and therefore averages 0.6 MV/m. That design stored a gigajoule of energy. Our macrons do not need that much energy but the length requirements are similar; 100 MV would require 167 meters of capacitors in series.

Another option is a pulsed staged accelerator. An electrostatic accelerator can be broken down into a series of stages. Each stage consists of a pair of charged plates with a gap between them. The voltage gradient between each pair of plates, assuming excellent vacuum, no contamination and perfectly smooth surfaces, can be on the order of 1 to 10 MV/m, which is far better than the Super Marx generator design. More realistically, 3 MV/m is achievable.

If an electrical current is supplied to the pairs of plates for just the short period where a macron crosses through them, and then it switched off as the macron exits, we end up accelerator driven by pulses of electricity with multiple stages. This design was suggested and demonstrated (for 5 stages) here. The increased voltage gradient means that 100 MV only needs between 10 and 100 meters of length.

The downside is that switching the plates on and off is not a perfect process. The switches, likely to be solid state transistors, convert some of the electrical energy into heat and can become a major source of inefficiency.

We can also consider a circular accelerator.

Instead of thousands of stages, a single stage is reused multiple times. The macrons will be bent 180 degrees twice by U-shaped magnets to form a looping trajectory. They gain velocity with each revolution, so there is no ‘maximum voltage’. However, we cannot increase the velocity past the point where the magnets cannot bend the macron’s trajectory.

The maximum velocity achievable can be calculated with this equation:

Maximum Velocity = Bend Radius * Magnet Strength * Charge/Mass ratio

Maximum Velocity is in m/s.
Bend Radius is in meters.
Magnet strength is in Tesla.
Charge/Mass ratio is in C/kg.

All of these factors affect velocity linearly. You will notice that the voltage gradient does not come into play at all; it simply takes more revolutions to reach the maximum velocity if the voltage is weaker.

Large circles have the lowest magnetic strength requirements to reach a certain velocity. However, spacecraft might have certain constraints on their cross-section and size that prevents them from mounting circular accelerators above a certain radius, so a linear accelerator might be preferred for reaching high velocities. It should be noted that the velocity achieved in a linear accelerator is proportional to the square root of the charge to mass ratio, but it is directly proportional in a circular accelerator. This means that as C/kg values increase, the circular accelerator becomes more attractive.

In spacecraft with both length and radius restrictions, the circular and linear accelerators can work together to maximize the velocity possible.

After exiting an accelerator, macrons can be neutralized by passage through a thin plasma, and at the highest velocities, by a charged particle beam of the opposite charge. The tiny, rapidly cooling particle will become nearly impossible to detect or deflect until it hits a target.

Charge to Mass ratio

To reduce the weight of the accelerator, a lower voltage requirement is needed. To do this, charge to mass ratio must be maximized.

For a spherical macron, surface area to volume ratio increases at the same rate as radius decreases. A sphere with a radius 10 times smaller has a 10 times better surface area to volume ratio. This could mean a 10 times better charge to mass ratio.

A huge amount of charge can be added by various methods. How much charge can a sphere hold?

The total charge is given by:

Surface charge = 1.11*10^-10* Voltage Gradient * Radius^2

Surface charge is in Coulombs (C)
The voltage gradient within the projectile is in V/m
Radius is in m
The 1.11*10^-10 coefficient is (4*pi*Permittivity of Vacuum)

The charge divided by mass, or charge to mass ratio, for a sphere is:

Charge to mass ratio = 2.655 * 10^-11 * Vg/(Radius * Density)

Charge to mass ratio is in C/kg.
Vg is the voltage gradient within the projectile in V/m
Radius is in meters.
Density is in kg/m^3.

These equations show that want to maximize the charge to mass ratio, the radius has to be very small and the voltage gradient as high as possible. The maximum voltage gradient for a negatively charged particle is about 100 MV/m. For a positively charged particle, this increases to 1,000 MV/m. Other sources mention voltage gradients as high as 50,000 MV/m as being possible, but that is likely to be a theoretical limit. If the particle is charged too much, it will start releasing electrons through field emission and dissipating the excess potential charge. For tiny projectiles, this causes enough heat to destroy them.

We can suppose that any macron that we need to accelerate to very high velocities will be pushed to this limit.

Let’s take the example of a positively charged 1 mm wide iron sphere. Radius is half of the diameter, so 0.5 mm or 5*10^-4 meters. The density is 8600 kg/m^3. The maximum charge to mass ratio will be 0.006 C/kg.

Now let’s work out the C/kg for a positively charged 1 micrometre lithium sphere. Radius is 0.5 micrometres. Density is 534kg/m^3. The maximum charge to mass ratio for this macron is 99 C/kg.

The lithium macron is clearly superior to the iron particle, because it is much smaller and composed of a less dense material.

Another maximum is the strength of the macron’s materials. The voltage gradient creates a force that tensile strength must overcome. The equation for a macron stressed to the limits of its tensile strength is:

Strength-limited C/kg = (1.77 * 10^-11 * T)^0.5/(R * Density)

The charge to mass ratio is in C/kg.
T is the tensile strength in Pascals.
R is the radius in meters.
Density is in kg/m^3.

Using the previous examples, a 1mm iron sphere with a strength of 250 MPa could survive a charge to mass ratio of 0.015 C/kg. This is a quarter of the previous limit.

Lithium is rather weak with 15 MPa of tensile strength. A micrometre wide particle of lithium would only survive a charge to mass ratio of 0.99 C/kg, so it is strength limited to a hundredth of the previous value.

To achieve better C/kg, we need stronger materials. The tiny dimensions of macrons bring forward another advantage to help meet this requirement. At a very small scale, we can expect materials to be formed without any defects. This unlocks their full strength potential.

A good example of this small-scale advantage is iron.

Bulk iron has a strength of 250 MPa. However, a micrometre-long monocrystalline whisker of iron displays strengths of 14,000 MPa. The charge to mass ratio allowed by micro-scale iron’s strength is 0.12 C/kg.

This difference in strength between bulk and micro-materials can be demonstrated for graphite, aluminium, silicon and many others.

A silicon nitride whisker has a strength of 13,800 MPa and a density of 3200 kg/m^3. It can have a micro-scale charge to mass ratio of 309 C/kg.

The current champions of strength to weight ratio are carbon fibres. The Toray T1100G fibre is the strongest material commercially available for its weight, at 7,000 MPa for 1,790 kg/m^3. A micrometre-sized sphere of these fibres can support charge to mass ratios up to 393 C/kg.

At the microscopic scale, those same carbon fibres gain the incredible properties of carbon nanotubes. They have shown strength to weight ratios more than ten times better than Toray T1100G fibres (about 63,000 MPa for 1340kg/m^3), which means charge to mass ratios of at least 1,576 C/kg at the same scale.

How do we actually use the full potential of these small-scale materials if by making them stronger, we run again into the field emission limit on charge to mass ratio?

Shaping the macron

The solution to more C/kg is to move past simple spheres.

The spheres can be made hollow. This retains the surface area of a sphere but decreases the mass. We can call W the ratio of wall thickness to radius. W=0.5 means that the walls are half as thick as the sphere’s radius. W=0.01 means that the walls are a hundred times thinner than the sphere’s radius.

The wall thickness ratio can by multiplied against the density in the previous equations to give the field-emission-limited charge to mass ratio of a hollow shell:

Hollow C/kg = 0.02655 / (Radius * W * Density)

The charge to mass ratio is in C/kg.
R is the radius in meters.
W is the wall thickness ratio.
Density is in kg/m^3.

This limit improves by a factor 1/W as the wall to thickness ratio decreases. At W:0.1, the field-emission-limited C/kg is increased by a factor 10. At W:0.01, it is a hundred-fold better.

However, a hollow shell has W times less thickness to resist forces, and also has W times less mass to support. The strength-limited charge to mass ratio becomes:

Hollow C/kg = (1.77 * 10^-11 * T * W)^0.5 / (Radius * Density * W)

The charge to mass ratio is in C/kg.
T is the tensile strength in Pascals.
W is the wall thickness ratio.
R is the radius in meters.
Density is in kg/m^3.

Notice how this limit improves by a factor 1/W^0.5 as the wall to thickness ratio decreases. The benefit from W:0.1 is only 3.3x, and from W:0.01 is 10x better than a full-thickness sphere.

These equations for hollow spheres imply that as the walls get thinner, the strength of the projectiles becomes more important.

There is also the option to shape the macron into a cylinder.

Cylinders can be elongated to large length to width ratios, like in this paper. This gives them a better surface area to volume ratio than spheres.

The ratio between the lateral surface area of a tube of elongation G and a sphere of equal volume is:

Surface area ratio for cylinder vs sphere = 0.605*G^0.333

G is cylinder length divided by cylinder radius

A tube that is 1000 times longer than it is wide (G:2000), for example 1 um wide and 1 mm long, would have a surface area that is 7.6 times greater than a sphere of equal volume. Carbon nanotubes that are a few nanometres wide and up to several centimetres long would have G:10,000,000, so they are a 131 times better shape than a sphere.

Cylinders, of course, can be hollowed out to become tubes. The benefits of elongation and wall thickness ratio are multiplied in this case.

Ion beam for macron acceleration

An electrostatic accelerator can be used in an entirely different way to get a macron up to high velocities.

Instead of directly pushing and pulling on a macron using electric fields, it can act on it indirectly with a beam of electrons or protons. This has been called a ‘beam pushrod’ or a ‘beam blowpipe’.

The charged surface of a macron naturally repels objects of similar charge. If it has an internal voltage gradient of 1000 MV/m and a diameter of 1 millimetre, it can repel particles with an energy of up to 500 keV. A thousand times smaller particle can only deflect particles of up to 500 eV, but it will accelerate harder thanks to the square-cube law. A negatively charged macron would only produce internal voltage gradients of 100 MV/m, so it would be deflecting 50 keV beams at 1mm and 50 eV at 1 um.

Less energetic beams can be deflected further away from the particle, giving it a larger effective cross-section. For example, a macron that could deflect a maximum of 50 eV electrons would be able to deflect 25 eV with an effective cross-section twice its actual physical size. We will assume that electric or magnetic fields are used to focus the charged beam onto a spot equal to the size of the macron’s effective cross-section throughout the length of the accelerator, as has been proposed here. Low energy charged beams will tend to expand very rapidly once outside the focusing influence of these lenses, so acceleration past the last focusing element can be ignored.

The maximum acceleration that a macron can survive in these conditions is dependent on tensile strength:

Maximum acceleration = (0.75 * T) / (R * Density)

Maximum acceleration is in m/s^2.
T is tensile strength is in Pascals.
R is macron radius in meters.
Density is in kg/m^3.

The value is independent of the wall thickness ratio.

A millimetre-sized projectile made of a material such as aluminium 7075-T651 (570 MPa, 2800 kg/m^3) could be accelerated at up to 1.52*10^8 m/s^2.

Meanwhile, a micrometre-sized sphere of diamond (1600 MPa, 3510 kg/m^3) would accelerate at 3.42*10^11 m/s^2.

To accelerate a positively charged macron, a proton beam would be used. At 500 keV, protons have a velocity of 9,780 km/s. At 500 eV, this falls to 300 km/s.

A negatively charged macron can be pushed by an electron beam. Electrons with an energy of 50 keV travel at 123,000 km/s. At 50 eV, it is 4190 km/s.

These figures do not mean that the macron can only asymptotically approach the beam’s own velocity. They are the maximum relative velocity between the beam and the macron. If the macron is already travelling at 4190 km/s (50 eV electrons), then it can actually deflect 100 eV electrons (5929 km/s). A series of pulses from a particle accelerator, each tuned to have an energy that closely matches that of a macron, can bring that macron up to higher and higher velocities in steps. This is also good for transferring momentum to the macrons efficiently.

Pushing a macron with a charged beam has the advantage that almost any beam intensity can be used. Since the protons or electrons do not touch the macron and are instead deflected electrostatically, none of their energy is converted into heat. Also, the accelerating tube can be equipped with electrostatic or electromagnet lenses that can focus a charged beam and maintain high intensity throughout the duration of the acceleration. The beam energies are relatively low, so the focusing elements can be very lightweight and the acceleration tube extended without great mass penalties.

Other than the strength of the macrons, the limit on ‘pushrod’ acceleration is the beam’s charge density.

Protons or electrons do not like being bunched up behind a macron. They repel each other. If we can only put a certain number of charged particles behind a macron (the current density), we can only deliver so much energy, which limits acceleration.

For a pulse of non-relativistic protons and electrons bouncing off a macron, the maximum current density is given by the Child-Langmuir Law:

Maximum Current Density = (7.7*10^6*BE^1.5*R)/(Pulse Duration* BV)

Current density is in Amperes per square meter (A/m^2)
BE is beam energy in electronvolts (eV)
R is macron radius in meters
Pulse Duration is in seconds
BV is Beam Velocity in meters per second.

For a 500 keV beam of protons composed of 1 nanosecond pulses, pushing on a micrometre-sized particle, we have BE: 500,000 eV, radius 0.5*10^-6 meters, pulse duration 10^-9 seconds and BV is 9,782,000 m/s. The maximum current density becomes 1.39*10^12 A/m^2.

For a 50 eV beam of electrons composed of 1 microsecond pulses, pushing on a millimetre-sized particle, we have BE: 50 eV, radius 0.5*10^-3 meters, pulse duration 10^-6 seconds and BV is 4,193,200 m/s. Maximum current density becomes 3.24*10^6 A/m^2.

To maximize intensity, and therefore acceleration, we want the shortest pulses of the highest energy protons.

We can simplify the process for finding out the acceleration of a spherical macron by working with the power delivered by the pulses:

PA = ((0.375 * Current Density * BE)/(R * Density * PD * W))^0.5

PA is Pulse Acceleration in m/s^2.
Current density is in A/m^2.
BE is beam energy in eV.
R is macron radius in meters.
Density is in m^2
PD is Pulse duration in seconds.
W is the wall thickness ratio.

Following on from the previous examples:

A 500 keV beam pushing a micrometre-sized particle made of diamond (3510 kg/m^3) with nanosecond pulses of protons would provide an acceleration of 3.85 * 10^15 m/s^2. This is a value greater than the maximum the hollowed-out diamond macron could survive mechanically, as calculated above.

A 50 eV electron beam pushing on a sphere of aluminium a millimetre wide achieves an acceleration of 1.75*10^7 m/s^2. This is lower than the maximum the macron can handle.

The macron’s shape could also be improved for use in this type of accelerator. A flat disk catches a larger beam, and so more energy could be transferred with each pulse. A web of fibres, inspired by the designs for electric sails, could have exceedingly high beam capture areas for their mass.

Producing the beam that pushes the macrons is generally not a challenge. Low energy electron beam specifically can be very lightweight, efficient and small. If we base ourselves on the designs of inductive output tubes, 15 kW/kg at over 80% efficiency is to be expected from today’s technology. Proton beams are trickier to produce, but they will still be small and lightweight in absolute terms. Their energy will come from the same RF generators as mentioned previously. See the Particle Beams in Space post for more details.

Since only one particle can be accelerated in a ‘pushrod’ accelerator at a time, it would make sense to also have those generators feed a multitude of accelerator tubes in sequence. 10 generators, each capable of producing 1 GHz of nanosecond pulses, could feed 10 tubes with a continuous supply of pulses each; if each macron clears a tube in 0.1 milliseconds, then ten tubes would have a maximal firing rate of 100,000 projectiles per second.

This might seem like a lot, but each projectile is expected to carry very little energy. A nanogram at 1000 km/s is still only 0.5 joules. A hundred thousand of them per second is just 50 kW. Accelerators in the megawatt range would end up looking like a volley gun or a ‘Metal Storm’ launcher.


Here is a selection of macrons to represent the different approaches to maximizing their performance

     1) A 1 mm diameter sphere of diamond with 1,600 MPa strength and 3510 kg/m^3 density. It is hollowed out to a 1:1000 wall to radius thickness ratio (W:0.001). It masses 1.83*10^-9 kg. When charged negatively, it can support a charge to mass ratio of 1.5 C/kg. Charged positively, it achieves 3 C/kg. 50 keV electrons and 500 keV protons can be deflected. Maximum acceleration is 6.8*10^11 m/s^2.

     2) A micrometre-sized macron made up of carbon fibres with 7000 MPa strength and 1790 kg/m^3 density. It is hollowed out to a 1:100 wall to radius thickness ratio (W:0.01). It masses 9.4*10^-16 kg. When charged negatively, it can support a charge to mass ratio of 296 C/kg. Charged positively, it achieves 2960 C/kg. 50 eV electrons and 500 eV protons can be deflected. Maximum acceleration is 5.8*10^12 m/s^2.

     3) A micrometre-wide, centimetre-long needle of carbon nanotubes with 63,000 MPa strength and 1000 kg/m^3. Wall to thickness ratio is 1:10 (W:0.01). It masses 7.8*10^-14 kg. When charged negatively, it can support a charge to mass ratio of 356 C/kg. With a positive charge, this becomes 3560 C/kg. 50 eV electrons and 500 eV protons can be deflected. Maximum acceleration (vertical axis) is 9.45*10^13 m/s^2.

     4) A 10 nanometre diameter sphere of carbon nanolattice with 200 MPa strength and 300 kg/m^3 density. It masses 1.6*10^-22 kg. When charged negatively, it can support a charge to mass ratio of 8850 C/kg. Charged positively, it achieves 39,665 C/kg. 0.5 eV electrons and 5 eV protons can be deflected. Maximum acceleration is 1*10^11 m/s^2.

We select the maximal value for C/kg depending on the accelerator type. All of these particles are field-emission-limited so they could be further optimized to match their strength-limited C/kg values.

The accelerators we will look at are:

A) A single-stage 10 MV electrostatic accelerator.
B) A 100m long multi-stage electrostatic accelerator with an average acceleration gradient of 3 MV/m, for a final energy of 300 MV.
C) A 100m diameter ring of 10 Tesla field strength.
D) A 100m long electron ‘pushrod’ accelerator.
E) A 100m long proton ‘pushrod’ accelerator.

Their performance is as follows:

A1) 7.7 km/s
A2) 243 km/s
A3) 266 km/s
A4) 890 km/s
B1) 42 km/s
B2) 1,332 km/s
B3) 1,461 km/s
B4) 4,877 km/s
C1) 1.5 km/s
C2) 1,480 km/s
C3) 1,780 km/s
C4) 19,827 km/s
D1) 11,661 km/s
D2) 721 km/s
D3) Cannot.
D4) 35.7 km/s
E1) 11,661 km/s
E2) 10,392 km/s
E3) Cannot.
E4) 913 km/s

Some conclusions can be drawn from these values.

Larger macrons are limited mainly by their strength. The identical D1 and E1 values are because the acceleration reaches the maximum the thin-shelled diamond sphere can handle in the ‘blowpipe’ accelerator.

For the smallest macrons, where C/kg is large, circular accelerators become more interesting than linear accelerators (at least if we are not concerned about the weight of the magnets). We can see the progression of velocities from C1 to C4 being much more pronounced than from B1 to B4.

Also of note is the fact that fibre tubes excel in electrostatic accelerators, but cannot be pushed by a ‘blowpipe’ accelerator as they would bend under those stresses.

Fission Enhancement

Millimetre-sized macrons have an interesting property. They can hold a ‘payload’ of a few milligrams within their hollow core. If they are filled with a fissile material, they can bring it up to sufficient velocities to ignite a nuclear reaction upon impact.

Studies for ignition of ‘micro-fission’ have been conducted by researchers such as Winterberg. They worked out that a 0.2 milligram projectile of uranium-235, when covered in a shell of deuterium/tritium ice, could ignite when compressed to about 10*10^12 Pa.

In response to those calculations, another study was performed where the critical mass of uranium enclosed deuterium/tritium (DT) ice was calculated. It then goes on to describe methods of igniting micro-fission by the impact of hypervelocity projectiles. At 20 km/s, the critical mass is just 0.04 grams.

This mass of uranium would fit inside a sphere of 1.6 mm in diameter. Surrounded by a shell of DT ice of equal thickness, and then a 10 micrometer thick shell of carbon fibre, it would have a total diameter of 3.18 mm and a mass of 0.0422 grams. Average density is 2502 kg/m^3 and the C/kg value when positively charged is 0.0067 C/kg.

At an average voltage gradient of 3 MV/m, a linear electrostatic accelerator would have to be 9.9 km long to push this macron to the required 20 km/s velocity. 10 tesla strength magnets would give it a bend radius of 298.5 km. These are impractical options.

With the shell of carbon fibre handling mechanical stresses, an acceleration of 8.29*10^6 m/s^2 is possible. This means a velocity of 20 km/s is achievable within an accelerator length of 24 meters. About 8.44kJ of energy is consumed in 2.4 milliseconds.

Upon impact, the uranium releases a large portion of its 80 TJ/kg nuclear energy. With 100% burnup, this amounts to a kinetic-to-nuclear energy multiplier of 379,149! Even at a low 10%, this is 37,915 times the energy invested.

A 1 MW accelerator shooting nearly 120 of these micro-fission macrons per second would produce between 38 and 380 GW of power at the target.

The paper also suggests a scaling law where increasing the impact velocity reduces the critical mass by a factor Velocity^12/5.

An impact at 200 km/s could be enough to reduce the critical mass to 0.16 milligrams. This quantity of uranium fits inside a spherical volume that is 0.252 mm wide.

Adding the required layer of deuterium/tritium ice brings the diameter to 0.5 mm and the mass to 0.161 milligrams.

This tiny fuel particle can be comfortably help inside the 1mm diameter diamond shell described earlier as projectile 1. The mass of the macron would increase from 0.00183 milligrams empty to 0.162 milligrams loaded. Its C/kg value and maximum acceleration would fall by a factor 89. An electrostatic accelerator with an average voltage gradient of 3 MV/m would have to be 197.8 km long. A 10 Tesla ring of magnets would have to be 1,186 km in diameter. These are again clearly not wise choices.

In a ‘blowpipe’ type accelerator, an acceleration reduced by a factor 89 still permits a velocity of 200km/s to be achieved within a mere 2.2 meters of length.

The advantage of a smaller, faster micro-fission macron is that it can reach targets further away in less time. However, the energy multiplication effect is greatly reduced.

A 200 km/s projectile contains 20 GJ/kg of kinetic energy. Nuclear fission releases only 4x this amount. If we factor in incomplete burn-up of the fuel, it is likely that there won’t be a significant increase in the energy delivered.

Impact Fusion

Greater macron velocities can focus more energy into an impact. These impacts generate incredible temperatures and pressures… conditions under which deuterium-tritium fuel with undergo thermonuclear ignition.

Winterberg once again leads the way in providing the theory and maths behind these exciting high energy physics applications. He states that a macron accelerated to over 100 km/s can generate temperatures of over 300 million K and compress fusion fuel to a density of 1000 kg/m^3 (10x that of DT ice).

Another source mentions 100 km/s ignition being possible only if the fuel is surrounded by a collapsing shell of material, and 50 km/s might only needed if the impactor is shaped into a conical shape.

Igniting fusion using hypervelocity impacts has several major advantages.

There is no minimum ‘critical mass’ of fuel, so the smallest macrons can be used. The confinement and fuel burn time depends on the length of the projectile divided by the velocity. This favours elongated fibres with a tip of fuel; also a great shape for achieving 100 km/s with accelerators of reasonable length.

DT fuel contains about 330 TJ/kg of energy, meaning that there is an energy multiplication effect of 66,000 at 100 km/s (assuming 100% burnup) and the energy gain can be maintained at up to 25,690 km/s!

This is an important fact, as many sources mention ignition velocities instead of at least a few thousand km/s.

We could, for example, fill the millimetre-sized diamond shell described above as projectile 1 with DT ice. It would be able to hold 78 micrograms of fuel, which is 43.8 times the shell’s own mass. The macron’s maximum acceleration is reduced by this extra load, but it still manages to reach 100 km/s in a ‘blowpipe’ accelerator of just 31 cm.

A 1 MW accelerator would be firing off 2,500 of these projectiles per second. Up to 64 GW of fusion energy could then be released at the target.


The first obvious application of hypervelocity macrons in space is in propulsion.

The smallest, lightest macrons can be accelerated to velocities exceeding 10,000 km/s. This translates to an Isp of 1,000,000 seconds. Only the most powerful electric engines or advanced propulsion system are capable of this. In the future, fusion energy can exceed this exhaust velocity.

A hypervelocity macron is an improvement over other types of propulsion that achieve those Isps in that it can be shaped out of any sort of common dust, and does not need to emit radioactive material. The energy source could be solar or a closed-cycle nuclear reactor. Kinetic streams of projectiles have been thoroughly discussed as an efficient propulsion system, even up to interstellar velocities.

Fission enhanced macron projectiles are particularly suited for use as a propulsion system. Lower impact velocity requirements means less drive mass, while the ability to greatly reduce the critical amount of uranium also means a great reduction in the minimum pulse energy. Project Orion, for example, assumed a minimum release of 627 gigajoules with each nuclear pulse; any lower and the uranium fuel would be wasted in incomplete burns. Mag-Orion, a Z-pinched variant with a magnetic nozzle, managed 340 GJ thanks to the use of expensive Curium-245. A macron accelerator with 0.04 grams of uranium would only release 3.2 GJ, a hundred times less.

This reduction in pulse energy means smaller suspension, smaller magnetic nozzles or thrust plates, reduced heat loads and smoother accelerations. Less equipment has to be dedicated to recovering and storing energy in between pulses. Maneuvers can be done more precisely. There is much less risk of damage in case of a misfire.

A fusion rocket that uses macron propulsion enjoys many of these advantages too. A kinetic impactor can concentrate the output of an ignition mechanism like an ion beam from a particle accelerator from several milliseconds to less than a nanosecond. The exceedingly difficult peak power needed to ignite fusion is therefore replaced by a thousand to a million times less demanding accelerator. The ignition event can also feasibly be made to take place far away from the engine’s physical structures too. Macrons retain their velocity while drifting through space, so they are just as capable of igniting fusion a hundred meters from a spaceship as a meter away; this is especially important if drive powers on the order of terawatts are needed for a ‘torch drive’.

But these are minor gains compared to the possibility of remotely-accelerated macron-driven propulsion systems.

A stream of macrons can be accelerated a long distance away from a spaceship. They can cross large distances relatively quickly, and then deliver their kinetic energy without any losses. Multiple macrons be fired with a small velocity difference so that over time they bunch together and all simultaneously, providing much higher peak power. All the receiving ship has to do is place an obstacle into the path of the macrons so that the impact creates a plasma explosion. This plasma can be redirected by a magnetic nozzle for thrust. At 100 km/s, the energy needed to vaporize a carbon macron is about 83 times lower than the kinetic energy is contains, so we can expect 1 kg of onboard obstacle material to vaporize 83 kg of incoming carbon macrons.

This sort of propulsion system is similar to beamed propulsion concepts. Propulsive power is delivered without the need for heavy on-board reactors, so high accelerations are possible. The ratio of obstacle material to macron stream mass means that the effective Isp of propellant onboard the spaceship is greatly multiplied too.

Compared to other mass-stream designs for propulsion, each macron carries a tiny amount of energy. It is unlikely that they will do significant damage if a few of them do not hit the intended target.

There is also the possibility to have fission or fusion-enhanced macrons act as propellant for a spaceship. Now we can have small accelerators delivering huge amount of propulsive energy to lightweight spacecraft, to achieve great accelerations and impressive levels of deltaV.

For example, a fission-enhanced stream of macrons could produce a series of nuclear detonations by impacting an obstacle placed inside a magnetic nozzle. The exhaust would be fission fragments with a velocity of 10,000 km/s. A stream of 10 kg/s would release perhaps 80 TW of power. If it takes 1 kg of obstacle material to receive 100 kg of macrons, then a 1000 ton craft with 200 tons of obstacle material would accelerate on average at 1.81g and achieve a total deltaV of 35.7 thousand km/s.

In other words, a 50 GW accelerator can do the work of an 80 TW drive and reduce trip times from Earth to Jupiter to 9.8-14.5 hours for 1000 ton spacecraft.

A laser or particle beam can be used to vaporize incoming macrons. This removes the need for onboard obstacle material to serve as propellant (so deltaV becomes unlimited), but also destroys the structures needed for fission or fusion enhancement, so the energy multiplication effect is also lost. Those lasers or particle beams can also be used to ‘guide’ the macrons down a specific path. The beams can effectively create an electrical field gradient that holds the macrons in the beam’s centre, or can even be bent by uneven gradients. More details in the Cold Laser-Coupled Particle Beams post.


Another application for hypervelocity projectiles is as weapons.We have discussed the need for faster projectiles to compensate for the combat ranges imposed by powerful lasers. The ‘solution’ to this need was described as a ‘pellet’ or ‘dust’ gun. Its features accurately describe the properties of a macron accelerator.At first glance, a macron accelerator produces less watts of output for the same mass of equipment when compared to a laser or a particle beam accelerator. It might also be very bulky as it has many hollow spaces. Worst of all, it does not deliver its energy at or near lightspeed.A deeper look reveals its advantages.The macrons have a chance to hit determined by:

     Chance to hit = (TR/(0.5*TA * (Distance/MV)^2))^2

Chance to hit is a fraction.
TR is the target’s radius in metres.
TA is the target’s acceleration in m/s^2
Distance is the distance to cross in meters.
MV is the velocity of the macron in m/s.

The chance to hit equation basically compared the cross-section of the target to the area the target could potentially cover in the time it takes for a projectile to arrive.

We can see that a 1000 km/s macron targeting a 5 meter radius spaceship that accelerates at 0.5 g (4.5 m/s^2) from a distance of 2,000 km will hit about 30% of the time.

The equation can be rearranged to determine the effective range of a macron for a certain hit chance:

     Effective range = MV * TR^0.5 / (Chance to hit^0.25 * (0.5 * TA)^0.5))

Effective range is in meters.
M is the velocity of the macron in m/s.
TR is the target’s radius in metres.
Chance to hit is a fraction.
TA is the target’s acceleration in m/s^2

If we accept a chance to hit of 10% with a 1000 km/s macron, a 5 meter radius target accelerating at 0.5 g can be engaged at a distance of 2650 km. Note how the range is directly proportional to the macron’s velocity and that increasing acceleration has a much lower effect. Quadrupling the acceleration cuts the target’s deltaV by a factor 4 but only increases the range by a factor 2. This would have to be compensated for by exponentially more propellant.

At the upper end of macron velocities, we can expect effective ranges in the hundreds of thousands of kilometres with good hit chances.

The projectiles deliver their kinetic energy as small plasma explosions that form craters in a target’s armor. An approximation suggested by Luke Campbell is that a hypervelocity impactor excavate a volume of material equal to the kinetic energy divided by three times the yield strength of that material. For something relatively weak, like graphite, this means that the kinetic energy is divided by 2.4*10^8 J/m^3. Vaporizing graphite requires about 500 times more energy per m^3; in other words, a macron accelerator can be 500 times more efficient at removing armor than a continuous beamed weapon, and even better than a pulsed laser.

Stronger materials like carbon fibres require only 5 times more energy to vaporize than to excavate, but this is a still major boost to the destructive efficiency of kinetic weapons.

We can expect a 100 MW stream of macrons impacting hypervelocity to excavate about 0.41 m^3 of graphite or 0.03 m^3 of carbon fibres per second. Using a 100x nuclear energy multiplier upon impact, these volumes can be multiplied to 40 and 3 m^3/s. The actual penetration rate through armor depends on the spacing of the impacts. Closely space impacts, such as within a spot 1 meter wide, would mean a penetration rate of 50.9 m/s through graphite! A wildly maneuvering target might have this potential damage spread out over their entire cross section and then reduced further by the hit chance. Using previous numbers, a 5 meter radius target with a 10% hit chance would find its exposed surfaces ablated at a rate of 5 cm/s if protected by graphite, and 0.38 cm/s using carbon fibres.

Whipple shields could be used to defend against kinetic projectiles. As mentioned in the Propulsion section, very little material is required to destroy an incoming macron. However, the gap created in a whipple shield by the impact of one macron can let through thousands more unimpeded.

It is much harder to add one more layer of shielding material than to fire one more macron to get through it…

The macron accelerator’s offensive performance is also improved by fission or fusion enhancement. It is the only weapon system described so far that output more energy at the target than originally spent. A 1 MW macron accelerator might heavier and bulkier than a 1 MW laser or particle beam, but its actual output can be multiplied a hundred to a thousand times at the target. However much worse the macron accelerator is in a direct comparison, it is more than made up for by the addition of nuclear energy.

To top this all off, macrons are expected to be completely undetectable until they hit their target. Their small size means that they cool down very quickly to temperatures hard to distinguish from background radiation. At the smallest scales (sub-micrometers), even LIDAR cannot interact with them properly, and even if specialized short-wavelength sensors are used, the resolution would be severely limited. If the detection and targeting problems are somehow overcome, the macrons are difficult to destroy en-route. Defensive lasers have very little time to act (seconds at most) and must face the fact that the surface area to mass ratio of the macrons makes them very good at radiating away heat.

For example, a micrometre-sized sphere of carbon fibres could survive a beam intensity of 58 MW/m^2. A micrometre-wide, centimetre-long carbon needle survives 579 GW/m^2. We can therefore expect macrons shaped to handle high laser intensities to defeat even the most power defences (although DT ice is unlikely to remain solid!).

SDI-era research has been done on macron accelerators for space defense. It is now up to you to decide how to make use of hypervelocity macrons.

Thanks for the help of GerritB, Kerr and other ToughSF members for help with researching this topic.

Electrostatics, Neutrons, and Space Charge

While particles cannot travel at the speed of light, they can get close enough that it is hard to tell the difference. Unfortunately, particle beams do obey the inverse-square law.

Beams of protons or electrons suffer from "electrostatic blooming", meaning as the beam travels its diameter steadily expands which weakens the damage it inflicts on the target. This is because like charges repel and opposite charges attract. A proton beam is composed of like charges so the protons spread out like they all have bad body odor and halitosis.

A beam of neutrons does not suffer from electrostatic bloom since they have no charge, nor could they be deflected by charged fields. However this also means it is difficult to accelerate the neutrons in the first place. Charged particles can be accelerated by using charged fields. And if you discovered a new way to accelerate neutrons, chances are whatever it is could also be used as a defense.

Without electrostatic bloom neutron beams are only limited by "thermal bloom". Brett Evill says this will give a neutron beam an effective range of 10,000 km, but he doesn't mention the details of this estimate. Nelson Navarro is of the opinion that a science fictional heavy neutron beam could be produced by a science fictionally efficient method of breaking up deuterium nuclei.

Another problem is one shared by ion drives, the "space charge." If you keep shooting off electron beams you will build up a strong positive charge on your ship. At some point the charge will become strong enough to bend the beam. And the moment your ship tries to dock with another it will be similar to scuffing your shoes on the rug and touching the doorknob. Except instead of a tiny spark it will be a huge arc that will blow all your circuit breakers and spot-weld the ships together.

Don't try to neutralize the charge by firing off positively charged proton beams. John Schilling warns that space is filled with an extremely low-density, but conductive, plasma. You try to eject charge from your ship, and the ship itself becomes part of a current loop. Not only is the current flowing through the hull (or trying to) likely to cause problems, but all those electrons or protons being sucked in produce deadly X-rays upon hitting the hull.

Isaac Kuo:

Anyway, getting back to your original article...I understand the motivation for wanting missiles and lasers to have an uneasy balance. I tried for years for this to be a guiding principle, for the same reason you have.

But I've pretty much given up on the idea. The fundamental problem is that missiles aren't fun. They are a pain to keep track of, in any numbers, and missile combat basically just boils down to numbers.

If you want things to be tactically fun, it may be a better idea to look at different sorts of weapon systems instead. In particular, electron beams can be an interesting weapon system in your setting. Electron beams can be interesting complements to laser weapons, because they can share hardware with a free electron laser.

A couple years ago, I came up with this interesting way to use a planet's ambient magnetic field to focus electron beams over long distances. But the beam spot size is smallest when shooting perpendicular to the magnetic field. The further the target is from this, the larger the beam spot size. Interestingly, the beam spot size does NOT directly depend on range to target--only direction to target, and strength of the ambient magnetic field. (This strength diminishes quickly with distance from the planet, so there is in fact a practical range limit.)

The bottom line is that if you're setting involves mainly space combat near planets, an electron beam is an interesting complement to laser armament. There are some directions and ranges where the electron beam is superior, and others where the laser is superior.

Furthermore, different sized vehicles have different defensive abilities. A relatively large vehicle can completely defend itself from an electron beam with a strong large magnetic field. Small vehicles are vulnerable, though, and an electron beam could be an order of magnitude more efficient at delivering beam energy. (Free electron laser will only convert a fraction of the electron beam's energy into photons, and then the target material may be reflective enough to only absorb a fraction of the laser's energy.)

So, even though the electron beam may be useless against large warships, it's so much more effective against small warships that it's still a useful secondary weapons mode.

Also, the firing port of an electron beam weapon is tiny. The example I calculated out was a weapon with a 4mm spot size and a 4mm firing port. The beam can actually be aimed with electromagnets even after the firing port. Anyway, it's a lot less bulky than a laser turret.

And then there's space weather. Besides the fact that different planets have magnetic fields of different strengths, these magnetic fields are constantly shifting. This results in "windiness" that throws off your electron beam's aim. Earth's magnetic field shifts in the timeframe of around a second, so it's going to be impossible to stay on target at .5 light seconds away. Your practical range is likely much lower than that. Space weather can result in large variations in magnetic field strength--affecting beam spot size--as well as how "windy" it is. The effect on beam spot size effectively changes how wide your firing arc is against a particular target (a smaller spot can penetrate deeper). The effect on windiness changes the effective range of the weapon.

My point's an interesting weapons system that can make tactical maneuvers an interesting puzzle. It's not just about numbers, you've got firing arcs that matter. You've got formations to cover each other's blind spots. You've got situations where a polar orbit is radically different, tactically, than an equatorial orbit, even when neither side has any relevant surface assets.

And from a playability perspective, a really nice thing about these firing arcs is that they don't depend upon dealing with complex 3D rotations. They depend purely upon a spacecraft's position, not its orientation.

Ray McVay:

My god...Jupiter's magnetic field is the largest thing in the entire system. The Jovians will have a weapon that can vape every KKV and Patrol Rocket that's thrown against them. You've figured out how they can wipe out the UN forces stationed in the Jovian system fast enough to put the Trans-Titanian Convoys at risk. Brilliant!

Isaac Kuo:

As for Jupiter's magnetic low Jupiter orbit, it's about 10 times stronger than Earth's at LEO, but there's no compelling reason to be hanging out in low Jupiter orbit.

I'm not sure how strong Jupiter's magnetic field is at Io, but magnetic field strength drops of roughly with 1/r^3. That implies a field strength drop of around 6 cubed at Io, or around 1/20th the strength of Earth's magnetic field at LEO.

So basically...usable, but only about as potent as they are at medium Earth orbit. I'm actually surprised at this. They should have very long range, however, compared to small diameter laser weapons. Practical range depends on how "windy" the magnetosphere is, and I really don't know that.

Isaac Kuo in a Google+ thread

Long Range Electron Beams using Earth's Magnetic Field for Focusing

TL;DR: A novel concept for 100kW to 10MW electron beams can be used for ballistic missile defense, space junk sweeping, and cheap access to space.

This is a weird idea I had a couple years ago, which is basically an unusual alternative to lasers for a long range beam. Normally, electron beams are not considered suitable for long range due to self repulsion. A beam that starts off narrow will bloom outward because the electrons repel each other. You can counter this by starting with a wide beam that focuses inward, but...I've done numbers on that idea; it's not very good.

But using the ambient magnetic field, it's possible to do something completely different. The ambient magnetic field will bend the trajectories of electrons into circular arcs. It's possible to let the beam fan out wide, and then have the ambient magnetic field refocus the electrons back together into tight focus by the time they reach the target.

The beam is fanned out in a rainbow spectrum, with the fastest ions on the inner edge and the slowest ions on the outer edge. Fanning the beam out results in a wide plane of low charge density, greatly reducing self repulsion. The ambient magnetic field deflects the slower ions more than the faster ions. This causes the beam to straighten out parallel and then converge back inward.

From above, the beam looks like a crescent shape. One tip of the crescent is at the firing spacecraft; the other tip of the crescent is at the target.

From the side, the beam looks narrow in the middle. It's thicker at the firing end and the target end. How much thicker?

I'll start with a baseline example of a 100kW beam of 100MeV protons from a 5m long linac. We'll leave the ambient magnetic field a variable, "B". Some sample values:

  • B = 3e-5T : somewhere in LEO
  • B = 1e-7T : somewhere in GEO
  • B = 1e-9T : interplanetary

I'll assume a beam spectrum of 10% velocity (or 20% energy). With non-relativistic calculations for simplicity, the angular deflection rate is constant with time:

radians/s = charge/mass * B

The beam is parallel when it's halfway to the target, so the angular width of the beam at the tips is equal to:

  • angular beamwidth = charge/mass * B * (t1 - t2)
  • = charge/mass * B * (0.5*dist/(1.05*v) - 0.5*dist/(0.95*v))
  • = charge/mass * B * dist/v * 0.5 * 0.1
  • = charge/mass * B * dist/v * 0.05

The rate at which the width of the beam converges/diverges at the tips is:

  • v*angular beamwidth = charge/mass * B * dist * 0.05
  • = 1.60e-19C / 1.67e-27kg * B * dist * 0.05
  • = 0.958e8C/kg * B * dist * 0.05
  • = 4.79e6 C/kg * B * dist

Okay, now let's switch to looking at charge density.

100kW/100MeV is 1 milliamp, and beam velocity is about 138000km/s, so linear charge density is:

lcd = 1e-3A / (1.38e8m/s) = 7.25e-12C/m

Electric field strength will always be less than or equal to the strength if the charge were an infinite plane, or:

lcd/w /e0 = 0.818V/w

We now have the basics required to estimate vertical beam spread. The remaining input variables are:

  • dist = distance to target
  • B = ambient magnetic field

We use the infinite plane field strength to get a vertical acceleration of:

  • acc = (0.958e8C/kg)*0.818V/w
  • = (0.958e8C/kg) * 0.818V / (4.79e6 C/kg * B * dist * t)
  • = 16.4V / (B*dist*t)

Integrating to get vertical velocity, we have

v = 16.4V/B/dist * ln(t) + C1

Integrating to get vertical position, we have

  • h = 16.4V/B/dist * [ (tln(t)-t) + C1*t + C2 ]
  • = 16.4V/B/dist * [ t * (ln(t)-1+C1) + C2 ]

To simplify the math, I'll use this formula all the way from the muzzle to the halfway point. This overestimates the early acceleration, but underestimates the late acceleration. It will get in the right ballpark, though, since it never underestimates by more than a factor of 1:2.

If we want a local minima at |t| = T, we use C1 = -ln(T) and C2 = T for

h = 16.4V/B/dist * [ t * (ln(t)-1-ln(T)) + T ]

(Derivation left as exercise for the reader. "Mathematica says it's so.")

At t=0, we have:

h = 16.4V/B/dist * T

Since T is halfway there, it's 0.5*dist/v, so

h = 0.5*16.4V/B/(1.38e8m/s) = 5.94e-8Tm/B

Aha! What a surprise! The vertical spread doesn't depend on range! It makes intuitive sense, though. On the one hand, greater range gives more time to spread. On the other hand, the beam can be wider, reducing the charge density. It turns out the two factors cancel each other out. Wunderbar!

The vertical diameter of the beam is twice h, so it's:

2h = 1.19e-7Tm/B

With v = 138000km/s, we have:

  • B = 3e-5T : somewhere in LEO
  • 2h = 0.004m = 4mm
  • B = 1e-7T : somewhere in GEO
  • 2h = 1.2m
  • B = 1e-9T : interplanetary
  • 2h = 120m

So, at LEO, this electron beam can focus onto a 4mm x 0mm spot on the target (obviously, the actual width is limited by diffraction limits). But at the other locations, spots size is excessive.

This might be addressed by placing the minimum height closer to the target rather than at the midway point, but the math gets a lot uglier.

So how do things scale if we change things? If we keep the beam energy the same, but the spot height is inversely proportional to the amperage. In other words, if we keep the beam velocity the same but change the power, spot height is inversely proportional to power. If we increase the beam energy (increasing the length of the linac), but keep the power the same, amperage is reduced but fanning width is also reduced by the square root of the beam energy. The overall effect that spot height is inversely proportional to the square root of the beam energy (or length of the linac).

Now, this math assumes that the beam is being aimed perpendicular to the magnetic field lines. If it's being aimed at an angle to the magnetic field lines, only the component perpendicular to the beam helps fan/focus it. In other words, the spot size is inversely proportional to the sin of the aiming angle (with respect to the magnetic field). Aim perpendicular to the magnetic field, and the spot size is small. Aim vaguely along the magnetic field, and the spot size is big.

So what can we do with this electron beam?

  1. Global Ballistic Missile Defense
  2. Space Junk Sweeping
  3. Cheap Access to Space

1) Global Ballistic Missile Defense

The obvious thing is a weapons laser. A 100kW beam aimed onto a 4mm spot is actually superior to the 1000kW laser beam of Airborne Laser, because it's concentrated onto a much smaller spot--much better penetration. It also has superior range...basically, it can hit anything it can see out to the horizon. It would only take three of them to provide full coverage to the entire world, whereas ABL could only cover a small region a few hundred miles across.

The "bad" news is that this electron beam can only hit ballistic missiles. It can't penetrate Earth's atmosphere, so there's no way to use it to replace drone strikes. (This may be seen as either a feature or a flaw.)

2) Space Junk Sweeping

The small spot size and long range means that it could be used for eliminating small pieces of space debris. Electron impacts would sputter ions, producing reaction thrust directly and/or inducing temporary charge sufficient to deflect the orbits into Earth crossing orbits (where it burns up in Earth's upper atmosphere).

3) Cheap Access to Space

With a 10MW version, the spot size is 40cm. If the target is a cooperative, it can include a 40cm diameter magnet to focus the beam into a small point. The target might be little more than a block of ice, boosted up to orbital speeds by the electron beam vaporizing a conical crater/nozzle into the block. A small jet could sling two suborbital rockets under its wings, repeatedly launching a couple payloads per flight.

Isaac Kuo in a Google+ thread


Powering up a particle beam to the point where it can cut armor is difficult. But there is another option: death by "Bremsstrahlung".

Consider the x-ray tube in your dentist's office. It is basically an electron beam striking a metal target. Now, what if the electron beam was a particle beam weapon and the metal target was the hull of the enemy spacecraft? A hypothetical observer on the far side of the ship could make a nifty x-ray photo revealing the skeletons of crew members dying in agony of radiation poisoning.

Please note that Bremsstrahlung only occurs with charged particle beams, it doesn't happen with beams of neutrons.

The particle beam weapons postulated for Star Wars missile defense were to disable missiles by damaging the sensitive electronics via radiation, not by carving the missiles into pieces. An APS directed-energy weapons study written for the Strategic Defense Initiative estimated that in order to disable an ICBM, a particle beam had power requirements between 100 and 1,000 megawatts, depending on range and retargeting rate.

Anthony Jackson says if you crank up your particles to a few GeV per nucleon they will be in the soft end of the spectrum of primary cosmic rays. Each particle will be highly penetrating, and you no longer need to actually focus the beam. Just apply a couple megajoules per square meter and everything dies (unless it's behind a huge amount of shielding or is basically operating at pre-microchip levels of automation. Neither is an option for a surface mounted weapon turret.). We are talking about a surface radiation level of over 500 grays. Such a cosmic ray beam would require armor with a TVT (for radiation purposes) peaking at 200-300 g/cm2.

Also note that if the particles are moving a relativistic velocities higher than, say, 90% c, you will have about the same energy release if the particles are matter or antimatter. In other words, it is pointless for relativistic particle beam weapons to use antimatter, with all the added complexity due to antimatter manufacture and storage.

Ships that expect to be fired upon by particle beam weapons would be well advised to add a layer of paraffin or other particle radiation armor on the outside of their metal hull, to prevent the beam from generating Bremsstrahlung with the hull.

SDI Neutral Particle Beam

One of the more exotic weapon proposals that came out of the Strategic Defense Initiative was orbital neutral particle beam weapons.

As previously mentioned, charged particle beams suffer from electrostatic bloom, which drastically limits the range. It is possible to neutralize the beam by adding electrons to accelerated nuclei, or subtracting electrons from negative ions. This creates a neutral particle beam.

While this will eliminate electrostatic bloom, the neutralization process will also defocus the beam (to a lesser extent). As a rough guess, maximum particle beam range will be about the same as a very short-ranged laser cannon.

For a neutral particle beam, the divergence angle is influenced by: traverse motion induced by accelerator, focusing magnets operating differently on particles of different energies, and glancing collision occurring during the neutralization process. The first two can be controlled, the last cannot (due to Heisenberg's Uncertainty Principle). The divergence angle will be from one to four microradians, compared to 0.2 for conventional lasers and 20 for bomb-pumped lasers.

Most of the images below are of very poor quality, and many of the details are still classified. The scale of these weapons is unknown, but they are huge. Some are "folded", with a U-shaped section. This is a desperate attempt to cut the length in half. Scott Lowther guesstimates the entire weapon is on the order of 100 meters long or so.

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