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.

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:

laserpower*laserenergy^(1/3)/spotsize^2

or to

laserpower*laserenergy^(1/3)*mirrorsurface^(3/2)

(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.  

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(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.

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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!

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• 

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.

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.

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.

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

http://spectrum.ieee.org/tech-talk/aerospace/military/tactical-laser-weapon-module-can-laserify-almost-anything

(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.

(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.

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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.

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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.

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.

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.

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.

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.

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 E_γ = 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.

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)

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MATTER BEAM
     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.

KERR
     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

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

KERR
     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.

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TROY
     I love gooooooold

KERR
     Troy, The blingiest laser in space

TROY
     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.

KERR
     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.

TROY
     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.

• 

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:

• carbon dioxide
• ³helium-argon
• ³helium-krypton
• ³helium-xenon

Development

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.

Uses

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

Propulsion

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.

Manufacturing

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.

Weapon

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.

      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.

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     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.

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     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.

Performance

     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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

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     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.

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     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.

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     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.

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Volumetric pumping

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

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     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.

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     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.

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     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.

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     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.

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

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     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.

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     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.

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     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

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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     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.

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

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     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.

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     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.

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     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.

4200K:

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     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.

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     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.

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     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.

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     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.

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

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     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.

19,000:

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

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     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.

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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.

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     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.

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     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.

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     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.

Conclusion

     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.

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.

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.

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.

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Comments

ISAAC KUO

     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.

KERR

     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.

ISAAC KUO

     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.

KERR

     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.

SAM

     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.

ADDITIONAL COMMENTS

TROY

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

ISAAC KUO

     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.

KERR

     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.

LUKE CAMPBELL

     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".

KERR

     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.

KERR

     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.

TROY

     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.

ISAAC KUO

     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)

and

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).

ISAAC KUO

     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.

LUKE CAMPBELL

     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.

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 is...it'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.

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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!

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Isaac Kuo:

As for Jupiter's magnetic field...hmm...at 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.

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.