Laser Pistol Laser "bullets" Particle Beam weapons

Colonial laser pistol, Battlestar Galactica (1978). Note recharge plug on side, power gauges on top. I think the cylindrical emitter can move back and forth on the track in order to focus the beam. Click for larger images.

Laser Pistol Last but not least is the old standby: the laser pistol. Dr. Schilling does not think this is as far fetched as most believe. Erik points out that the problem with a man-portable laser pistol would be the power source. Kinetic weapons are probably going to outperform beam weapons for man-portable sidearms for a long time. Luke Campbell has an in depth analysis of laser weapons for science fiction on his website. The key to making a laser do bullet levels of damage is pulsing the laser. The first pulse creates a steam explosion and a shallow crater in the skin of the hapless pirate. By careful timing, the second pulse arrives after the steam from the first pulse has dissipated and creates a second crater at the bottom of the first. If you don't delay the pulses, the cloud of steam interferes with laser beam, protecting the target. By altering the variables one can have a laser beam that will penetrate a human body but only bore a little way into metal. As an added bonus, lasers have no recoil. As an interesting bit of jargon, Luke Cambell calls continuous beam lasers a "heat ray", and pulse beam lasers a "blaster."

Here follows Dr. Schilling's analysis:

I'll assume a 50-year time frame with no particular haste in developing directed-energy small arms and no fundamental breakthroughs. Only technology currently on the drawing board, in however limited a form, is allowed, but in 50 years expect today's crude laboratory demos to be refined, mature technologies. I'll also use a standard military or police service handgun as the baseline - you can easily extrapolate down to a compact pistol or up to a small submachine gun-equivalent if you like, but going up to rifle or heavy-weapon scales is a bit trickier.

Phased Plasma Gun, Babylon 5 (1994).

James Borham notes: It turns out that the future is already here. Lithium-polymer cells are rechargeable, and have an energy density of 1.08 kJ/cm³. This is just shy of half of Dr. Schilling's assumed energy density.

(Ed. Note: for a list of energy densities of various storage devices, refer to the Wikipedia article)

(Ed. Note: using a capacitor will make the laser operate in a similar manner to a camera strobe. You fire, then you have to wait for the little "charged" light to come on before you can fire the next shot.)

Luke Campbell said: Keep in mind that in tissue, the cavity blasted out will collapse back on itself in a few milliseconds (and probably re-expand and collapse again in pulse-like oscillations for a few cycles).

Assault Phaser

In soft materials, vapor expansion will carve out a hole much larger than the original one millimeter - I got four centimeters maximum hole diameter for soft body tissue, so the effect should be at least equal to a modern high-velocity pistol bullet, and perhaps comparable to a small centerfire rifle. Brittle materials are likely to shatter within a similar radius, tough stuff like steel will show little effect beyond the original hole. And no, mirrors will not work as armor. The best finish you can reasonably expect to keep on an exterior surface, will still absorb 10-20% of the incident energy, which will be enough to burn through the outer layer on the first pulse. And the rough and now hot interior will be even less reflective.

I also mentioned earlier that lasers would likely have to have pulse energy and frequency tuned to the specific material being targeted. It might be possible to do this automatically, based on crude spectoanalysis of the material vaporized in each pulse, but if not expect penetration to be roughly halved if a laser weapon is fired at a target it has not been optimized for. Target-shooting lasers won't be optimized for flesh, and certainly not for ceramic armor, so there may be legal implications here. Particle beams are less likely to suffer such inconveniences. Taking into account the inefficiency of the system, the input energy will likely be somewhere between two and five kilojoules per shot. So you could get fifty to a hundred shots from a pistol-sized non rechargeable energy source, or half that with a rechargeable battery. Automatic fire at anywhere up to 20 Hz (1200 rpm) shouldn't be a problem in the short term, though might cause cooling problems if you keep it up.

Phaser Rifle, Star Trek (1966).

You also need to focus the energy on the target, with a spot size of a millimeter or less. With a laser, that gets kind of tricky. A 5-centimeter mirror, about the largest you can really imagine on a pistol, gives an effective range of perhaps sixty meters, beyond which the weapon starts losing penetration quite rapidly. Luke Campbell said: If you are already talking about the laser excavating cavities several centimeters in diameter, sub-millimeter spot sizes do not seem necessary, you just need a moderate fraction of the cavity's maximum size. No, you still need to get down to a millimeter or so to flash-boil water in a layer ~one optical depth in thickness. Once you do that, the steam will expand and spread the damage around, but if you don't hit the threshold for turning water into steam all you do is warm up the target.

Luke Campbell said: The problem with particle beams is that scattered radiation from the beam will irradiate the person firing the gun. When you are throwing around kilojoules of ionizing radiation, this will be enough to cause radiation burns, radiation sickness, sterility, and possibly cancer and genetic damage.

(ed note: "Reflex" in this context refers to the viewfinder on a reflex camera. A mirror allows the viewfinder to use the actual camera's optics. The user literally sees the exact image which will be captured on film. When the shutter is tripped, the mirror moves out of the way and allows the image to fall on the film. So in Dr. Schilling's concept, the shooter would aim through the laser pistol's optics, the same optics that will direct the weapon's beam.)

Elsewhere Luke Campbell said: Another interesting thing is that you could use the beam optics for your scope. Just install a switchable mirror that flashes reflective for the millisecond the beam is on, and you could then direct the light from your target that comes into your weapon's optics straight into an eyepiece. You could see exactly where the beam would strike without having to make any allowances for parallax or beam deflection (since the incoming light would be deflected along exactly the same path as the outgoing beam). Thus, no separate lens for a scope, sitting on top of the gun.

I will also note that there currently exists a species of "scope through the gun barrel" piece of gear for conventional slug-throwing rifles, the EOP system.

As it turns out, the Phaser type-I from the classic Star Trek TV show had a reflex aimsight. Turning the dial on the top would raise the acrylic aimsight. This would also work with the type-II pistol phaser, since that incorporates a type-I phaser. You can read about the aimsight here, here, here, here, and here. If you have lots of disposable income, you can purchase a hero movie prop.

James Borham notes: While using the laser's optics as a scope is pretty clever, a quicker type of sight will be needed for close in shots. Iron sights or some type of collimating sight (e.g. red dot sight, holographic sight) strapped to the top will do well. Another clever one would be to use the laser's optics to project a laser sight. Pull the trigger, and the harmless red dot suddenly explodes. BANG! Using the laser optics as a scope would be more useful for long range or high accuracy shots.

From HEALER by F. Paul Wilson

If one is using this information in order to write an SF novel, the question comes up of what will an observer see and hear during a laser pistol battle. Luke Campbell has the information.

What would it sound like?

The actual mechanism of producing the laser beam could sound like anything, from complete silence, to the click of an electrical contact, to a sharp, electric snap, to a gunshot-like thunderclap.

The beam, when incident upon its target, will make a nice bang.

The pistol won't make a "zap" sound, will it?

If the beam is repeated rapidly it might, however, make a buzz. It might end up sounding quite electrical at a few hundred Hertz.

Will it be too quiet to hear or will be loud enough to cause hearing loss? Will it sound like an extended explosion as the series of steam detonations bore a hole? Remember that the temporary cavity caused by the explosions only lasts a few milliseconds, so the beam has to have completed its work of piercing the target at this time. The individual explosions will be too closely spaced (microseconds apart) to be individually audible. Since shocks are always supersonic to the air in their path, and subsonic to the moving air left behind them, multiple subsequent shocks from the same source tend to merge into one stronger shock. Thus, each pulse probably makes one bang. The bang comes from a series of explosions whose total energy is about the same as that of the gunpowder detonating in a firing rifle, so it will probably be about as loud.

Noisy Cricket, Men In Black (1997).

What would the beam look like? This depends on a number of things. If the beam is in the visible part of the spectrum, you get a noticeable path through clean air at indoor lighting intensities. I am not sure if it will be visible out of doors under full sunlight, but you could see it at night. The beam will be widest at the aperture of the gun, probably a few centimeters across to keep the optics from being damaged by the intense light. The beam will converge to a spot a millimeter or so across at the target. In unclean air, the beam will be a lot more visible. This Rayleigh scattering is linear, so the total integrated brightness across the cross section of the beam should be constant, if we neglect the gradual attenuation of the beam due to the light being scattered out of it. Higher frequency light scatters much more than lower frequency light, so a blue beam would be much more visible than a red one. When a visible beam is incident on the target, it creates a very bright flash of the same color as the beam. This may temporarily dazzle those looking at it, and the beam itself may be overlooked because of the bright flash obscuring it.

If the weapon lases in the UV, the intense pulse may cause multi-photon ionization of atoms in the air, causing a fluorescent glow along the path of the beam (possibly red, green, or violet, I'm not quite sure what sparsely ionized air at atmospheric pressure looks like). Since this process is non-linear, it will be dimmest near the aperture where the beam is widest, and most intense nearer the target. Weapon designers will probably try to minimize this effect, since it leads to attenuation of the beam and subsequent loss of effectiveness.

Near IR beams are likely to only be visible if there are relatively large pieces of dust, lint, or pollen floating around, which will glow incandescent as they burn under the irradiation of your beam. I doubt beams in the "thermal" IR range would be used, even though the air is fairly transparent to these wavelengths, because with short, intense pulses you tend to get cascade ionization with these lower frequencies, and this will completely absorb the beam.

Beams at non-visible frequencies will also make a flash and a bang where incident on the target from the expanding plasma of their explosion, but nowhere near as bright as that of a visible beam.

In vacuum, of course, the beam itself is always invisible, but you can still see the flashes at the target.

Will the beam be invisible or bright enough to be blinding? It is quite likely to be both. The beam itself may be invisible or minimally visible, but if even a tiny fraction of the beam is specularly scattered into your eye, near IR and visible and some near UV will be focused to a diffraction limited spot on your retina, causing burns and permanent scarring. This can lead to degradation of vision or total blindness. Interestingly, the brain compensates for blind spots on the retina, so that you might have lost up to 60% of your vision from multiple exposures to beams and you still think you can see just fine. Also interestingly, the fluid in our eyes can cause a small amount of non-linear upconversion of intense coherent light that passes through it, so when directly exposed to a near IR beam, you may actually see it as two IR photons are combined into one visible photon with twice the frequency. Some people who have been blinded by pulsed neodymium lasers (which lase at around 1 micron near IR) have reported that the last thing they ever saw was a green flash (green, at 0.5 micron, has half the wavelength and twice the frequency of the 1 micron neodymium line).

Anyone likely to be using a laser will probably wear protective goggles or contacts. With today's technology, you would probably make them out of an optical band gap material that excludes a very narrow window of light centered on the laser's frequency. This means that the people who fired the lasers would not be able to see the beams or flashes of their own weapons (assuming they used visible light lasers). They would still see the flashes from the plasma explosions, though, plus incandescence of suspended atmospheric particles and fluorescence from multi-photon absorption.

(Luke has more details here)

Johnny1A asked: Suppose our weapon users want to minimize the effect on potential innocent bystanders, or are worried about having to fight without their optical protections. What would be the best way to make such a laser weapon so that bystanders/unshielded users were not blinded? You could use a weapon that emits a beam at frequencies that are mostly absorbed by the lens or vitreous humor. I seem to recall that laser light at 1.5 microns near IR and longer wavelengths are largely absorbed by the eye before any of it can get to the retina. At the other end of the spectrum, many near UV wavelengths are also absorbed by the materials of the eye. (Holger Bjerre points out that while such UV wavelengths do not penetrate the eye, they will abrade the surface of the eye. After all, such UV lasers are used for laser-vision correction surgery. Such abrasion may or may not be correctable, but it is damage.)

What would the Asteroid Pirate look like after they got hit?

The method of subsequent explosions on the back of an expanding cavity driving the cavity through the target will leave a wound much like that of a gunshot, except without fun stuff like the bullet fragmenting or breaking up. A variant where nearly parallel beams a few cm apart literally rip the tissue between them could leave a wound looking more like an ugly gash - add on a few more of these beams on the same plane and you could literally cut someone in half with one millisecond pulse, using only about as much energy as goes into accelerating the bullet of a modern day battle rifle. (ed note: in some SF novels by E.E."Doc" Smith and Robert Heinlein, this is referred to as setting your sidearm to "fan beam")

Will there be a large splash of blood and gore on the wall behind the unlucky pirate?

Quite likely, Note that since you do not have the momentum associated with a projectile, it will be more spread out than you would get from a gunshot wound, and you would get blood and gore coming out the front, too.

I assume that since the beam is one millimeter in diameter but the hole in the pirate is four centimeters, little or no wound cauterization will occur.

Nope, the wound would be ragged and messy. It is created by mechanical, not thermal effects.

What will the laser pistol look like?

The laser weapon will probably end up looking something like a camcorder, with a big lens that the beam goes through, and a fairly compact design. Since mirrors and internal optics can bend the beam inside the weapon, there is no need for the long barrels you see on modern firearms. Cooling, if necessary, would probably not involve fins - I would expect something more like the radiator on modern automobiles. Remember, shedding your heat through contact with the air is much more efficient than radiation.

(ed note: keeping in mind that using contact with the air doesn't work if there is no air, i.e., in vacuum. C. James Huff notes that there is one kind of fin for radiant cooling and another for air cooling. He mentions that the fins on a CPU hot sink is a good example of the latter. For a vacuum rated laser he recommends a compressed or liquified gas cartridge since a radiant cooler would be inconveniently huge.)

Also, lasers are getting surprisingly efficient. When each beam pulse contains no more energy than imparted to a rifle bullet, lasers might need cooling no more than a modern rifle.

Buck Rogers in the 25th Century (1938) Artwork by Dick Chalkins

A laptop computer whose batteries suddenly burst into flame

Laser "bullets"

The energy requirements mentioned by Dr. Schilling make it clear that the laser's battery will be carrying plenty of juice. Anything carrying that much energy will be at least slightly unstable. In other words, it wouldn't take much to make a charged battery into a home-made bomb (which might come in handy if one suddenly needed a bomb.). You might have read news reports about laptop computers whose batteries suddenly burst into flame.

And don't even think about sticking a fork into the open contacts.

This has been observed somewhat tongue-in-cheek by John Routledge as Routledge's Law: "Any interesting battery material for a laser gun would be more usefully deployed as an explosive warhead." He also notes the problem with ammunition cook off. If you are holding a fully-charged laser pistol, and some lucky enemy sniper manages to score a direct hit on the pistol's battery, it is going to be just too bad if the resulting explosion vaporizes you and all your friends within a large radius.

Assuming a worst case of 5 kilojoules per shot and a rechargeable magazine containing 50 shots, the magazine is packing 250 kilojoules. This is the equivalent of 250,000 * 2.7778e-4 = 70 watt-hours or 250,000 / 4,500 = 55 grams of TNT (For comparison purposes, a standard 8 inch stick of dynamite is about 208 grams and hand grenades used by the US Army have explosive charges of 56 to 226 grams of TNT). At his specified power density of 2.5 kilojoules per cubic centimeter, this would imply a magazine volume of 100 cm³. this is approximately the same volume as forty-two .45 caliber rounds.

You may remember that in Star Trek, phaser hand weapons could be set to explode like hand grenades, a "forced chamber explosion."

The above is a reasonble energy magazine. At the extreme end, in L. Neil Smith's BRIGHTSUIT MACBEAR, we find the five-megawatt fusion-powered pistol.

Deflagrating gun, Barbarella by Jean-Claude Forest (1964). Note the weapon's power pack strapped to the leg. "Deflagration" means "cause to burn with great heat and intense light". In other words it lies somewhere between "burns quietly" and "explodes"

Before laser bullets are developed, you might find laser pistols with separate power sources. In the role playing game Traveller, laser carbines are powered by a large battery worn in a back pack. In the Barbarella comic, deflagrating guns have their battery strapped to the upper leg. Gene Roddenberry's original conception of the Star Trek phasers had a separate waist belt containing several power units. In William Tedford's Silent Galaxy AKA Battlefields of Silence, the hand laser's battery pack is strapped around the wrist.

There was an amusing scene in a remarkably bad '50s movie called Teenagers from Outer Space. The hero unfortunately broke the power pack on his focused disintegrator ray. He manages to cobble together a solution just in time to save the day. He attaches a cable from a nearby high-tension power line, and convinces the power plant to shove the generator output up to maximum!

Some SF novels have postulated one-shot power modules. "Laser bullets" in other words. In Norman Spinrad's Agents of Chaos, laser pistols were a ruby rod with a magazine full of "electro-crystals". Pulling the trigger caused the next crystal in the magazine to release its charge, that is, it was sort of a super-capacitor. Taking this a step further, one can imagine a "laser revolver", with capacitors taking the place of bullets. Don't throw the spent capacitors away, they can be re-charged. A .45 caliber cartridge is about 11.43 mm x 23 mm, which gives it a volume of about 2.4 cubic centimeters. At a rechargeable 2.5 kj/cm³ this means a battery the size of a .45 round would hold a good 6 kilojoules, enough for an extra-strength laser bolt.

In David Drake's Hammer's Slammers novels, the "powerguns" utilized an as-yet undiscovered scientific principle to instantly convert copper impregnated plastic wafers into a high-temperature bolt of plasma traveling at high velocity. Drake said all he wanted to do was postulate some hand-waving way of putting plasma bolts into bullets so he could write about futuristic soldiers.

From HAMMER'S SLAMMERS by David Drake. Needless to say, this is all hand waving with absolutely no basis in scientific fact. The problem with lasers was the power source. Guns store energy in the powder charge. A machinegun with one cartridge is just as effective — once — as it is with a thousand round belt, so the ammunition load can be tailored to circumstances. Man-killing lasers required a 400-kilo fusion unit to drive them. Hooking a laser on line with any less bulky energy source was of zero military effectiveness rather than lesser effectiveness. Science lent Death a hand in this impasse — as Science has always done, since the day the first wedge became the first knife. Thirty thousand residents of St. Pierre, Martinique, had been killed on May 8, 1902. The agent of their destruction was a “burning cloud” released during an eruption of Mt. Pelée. Popular myth had attributed the deaths to normal volcanic phenomena, hot gases or ash like that which buried Pompeii; but even the most cursory examination of the evidence indicated that direct energy release had done the lethal damage. In 2073, Dr. Marie Weygand, heading a team under contract to Olin-America, managed to duplicate the phenomenon.

In the original Star Trek episode "The Galileo Seven", Mr. Scott drains the energy out of a bunch of phaser pistols into the engines of the shuttlecraft. Doing some pointless calculations based on a very unscientific script we can hazard a guess at the energy content of a phaser pistol.

Some website I found claimed that a shuttlecraft was 17 metric tons. Assume that each crewmember is 68 kilos (150 pounds), this adds another 476 kilos for the seven crewmembers. The shuttle doesn't quite make orbit. As an upper limit, to make orbit would require a deltaV of around 8 km/s. Plugging this into the equation for kinetic energy gives us an energy requirement of about 5.6e11 joules. There appears to be six phaser pistols drained, so each phaser contains 5.6e11 / 6 = 9.3e10 joules.

How much is 9.3e10 joules? Well, it is 9.3e10 * 2.7778e-7 = 26,000 kilowatt-hours or 9.3e10 / 4,500,000 = 21,000 kilograms of TNT. Well, let's face it, it takes lots of energy to vaporize an human being with one zap.

From Star Rangers (aka The Last Planet) by Andre Norton (1953).

From Ron Turner's Space Ace pop up book (1953). This is hysterically out of date. A. This is the Hydramatic Mark 4 Flame gun, which you see me toting with the space suit above. It was developed by Professor Maklin Devonport of the Interplanetary Research Institute in 1995. The Hyramatic takes its name frmo the fact that it operates on a liquid hydro-ammonal compound, which is contained in a cylinder and fed to the gun via a feed line, which couples onto the gun at (a). Its lethal range in space is 2,000 yards - a useful weapon. B. This is the Atomatic. It is rather bulkier than the "Hydra" but it has the great advantage of being self-contained. It fires .20-calibre atomic bullets; of course a .20 bullet in the old days would have been just about useless, but these, having atomic heads, produce spectacular results. I once saw a pirate ship (which was attacking transports on the Earth-Mars run) torn completely apart by a burst from one of these atom guns. The burst had penetrated the hull and hit the power plant; the pirates never knew waht hit them!

Particle Beam weapons

What about particle-beam sidearms? Well, their minor draw-back is the fact that each shot you fired would have the side effect of exposing you to a lethal dose of radiation. But other than that they would be quite spectacular weapons.

Luke Campbell said: The problem with particle beams is that scattered radiation from the beam will irradiate the person firing the gun. When you are throwing around kilojoules of ionizing radiation, this will be enough to cause radiation burns, radiation sickness, sterility, and possibly cancer and genetic damage.

Dr. Schilling mentions above that the conventional way to generate particle beams are with pulsed linear induction accelerators, but these will be difficult to reduce to pistol size. A more radical method of creating particle beams is with wake field accelerators, which produce electron beams on the electric fields of forced plasma waves.

He also mentions that high-current electron beams tend to be self-focusing in air, which simplifies things if you take that route. For ranges much over a hundred meters you have to start worrying about energy loss, which can probably be dealt with. For handguns, it isn't a problem.

You'll need a bit over a kilojoule of output energy to reliably incapacitate a human target, just like lasers. Unlike lasers, you won't have to pulse the beam, just pour it on in one big bolt.

Luke Campbell and Anthony Jackson got into a discussion of this. Alas it is over my head like a cirrus cloud.

Luke Campbell:Semantically, "particle beam" usually means the things being shot out the end can be treated as individual particles, without too much interaction. "Plasma" usually has significant inter-particle interactions. Practically, particle beams fire a stream of relativistic atoms or sub-atomic particles. These are beams of ionizing radiation - you know, the stuff the anti-nuke crowd gets so worked up about. If you get a particle beam intense enough to burn someone, it will also deliver a lethal dose of radiation from a hit anywhere on the body while it is at it. Radiation will scatter from the beam "impact" site, irradiating things around it. In an atmosphere, radiation will scatter off air molecules to irradiate things near the beam. Some of it will backscatter, irradiating whatever fires the gun. Forget about a sci-fi hero using a particle beam "blaster" - after blasting a hoard of bug eyed space aliens, he'd be sick or dying from radiation poisoning. In real life, particle beam weapons were considered for their ability to use radiation to disable things (mostly ICBMs) without necessarily blowing holes in them.

Lightning gun from the game QuakeWars

Using real tech, there are only two types of particle beams to worry about: electron beams and neutral particle beams. Electron beams are nice because relativistic electrons can get through about half a kilometer to a kilometer of air before either being brought to a stop by collisions with air molecules or (for higher energies) colliding with an air molecule and disintegrating both into an uncollimated shower of radiation. They also exhibit a self focusing effect in air - their interaction with the air concentrates the beam to prevent it from spreading out (this is quite important - since electrons are so much lighter than air molecules, they tend to bounce all over the place if shot out in low quantities - hit a molecules and your electron can end up going in any direction). Note that just because the beam is self focusing, it does not necessarily keep going in the same direction - I've heard humerous stories by observers of atmospheric high power particle beam tests of the beams wandering off in random directions. Some sort of beam guiding mechanism would be necessary (perhaps use one of those self focusing ultrashort laser pulses to ionize a path).

Electron beams don't work at all well in space, since the like charge of the electrons tends to blow the beam apart. Also, the charged electrons tend to interact in wonky ways with the earth's magnetic field, leading to unpredictable beam paths. Hence the neutral particle beams. Here, you accelerate an atom stripped of one or more electrons, and then neutralize the atom before shooting it off into space. Since all the particles are uncharged, they ignore magnetic fields and each other, and just merrily drift along until they slam into their target at relativistic velocities. They are pretty useless in air - the collisions with air molecules either stop the beam within a few meters or disintegrate it into an unfocused shower of radiation.

Plasma guns have a significant problem. If the plasma is at higher pressure than the surrounding air, it expands and pushes the air out of the way, becoming a cloud rather than a beam or pulse. Clouds of lightweight gas (a plasma is essentially a gas with wierd interactions with electric and magentic fields) are quickly stopped by air pressure, and will cool quickly as well. If it is at really high pressure, it will expand violently - this is what we call an explosion. Trying to confine the plasma with electric or magnetic fields just makes things worse. In order to get the fields to travel with the plasma and contain it, they need to be generated by sources within the plasma (generally electric currents generating magnetic fields). The forces exerted by the fields on the sources either helps to explode the plasma (for magnetic fields and electric currents) or squishes the plasma in one direction while helping it to explode in another (for electric fields and macroscopic electric charges).

So, we need to keep the pressure down. Ignoring electric and magnetic fields, we find that the pressure is given by a constant times the temperature times the density. The temperature is necessarily high (there are cold plasmas, but what's the point as a weapon?), so we need low density. Unfortunately, low density means low energy per volume (it turns out that the energy per unit volume is given by the pressure - you can't win by playing with combinations of higher temp and lower density or vice versa). As a result, you need to squirt out a large volume of hot, low density plasma to deliver much energy to your target. You can do this by squirting out a stream of it really fast. You don't have a "pulse" or "beam" of plasma this way, you have a plume (or, equivalently, a jet). You train your jet on your target and hold it there for long enough to burn through. This is sort of a very energy intensive flame thrower with the disadvantage that your target is not covered with sticky, burning chemicals after you take the jet off him (as an idea of how energy intensive, if you can direct the beam only onto the person's skin, about half a megajoule is needed to cause lethal burn injuries involving third degree burns to exposed skin, second degree burns under light clothes, and ignition of hair and clothes. In practice, more energy will be required because the jet will not all impact your target. Compare this to the energy of an assault rifle bullet [500 times less] or an arrow [10,000 times less] for an idea of why plasma guns will not be used - the same energy could propell 500 coilgun projectiles, each highly lethal and much more penetrating).

Somebody suggested that an electron particle beam would resemble a lightning bolt.

Anthony Jackson: Not exactly, but close, unless you have some sort of beamguide. If you create an ionized path with a laser, the electron beam will tend to follow that path.

Actually, that's true of lightning as well. this shows images of an electric discharge done normally and with a beam path created by a femtosecond-terawatt laser.

I'm not sure how well it will penetrate flesh; electrons will go a couple inches in, and secondary X-rays (and, most likely, gamma rays from positron annihilation -- very high voltages are required, meaning you get pair production of electrons and positrons) will go a bit forward of that, further penetration is dependent on the ability to open a hole in tissue and/or fully ionize the flesh. Luke Campbell: The CSDA (continuous slowing down approximation) range of a 1 GeV electron in skeletal muscle tissue is close to one meter - lower energy electrons will travel less far. This means it is quite possible for the burn path to completely transfix the target. It is also useful to note that the energy deposited per unit length (or volume) is highest near the end of the track when the electrons are moving slower. For a beam that penetrated, say, 10 cm into tissue, this would mean that you could have a narrow burn entrance wound without a visible hole but get significant flash vaporization of tissue inside the victim. That same 1 GeV electron will travel over 800 meters through dry air at sea level in the CSDA. If you are shooting at distant targets, however, keep in mind that the electrons in the beam will have lower energy the more air they have to punch through, and thus will have lower penetration at the target. Data is taken from ESTAR

Anthony Jackson: We're talking a pistol here. It's probably 10-100 MeV, for a penetration of a couple of inches.

Luke Campbell: With realistic breakdown voltages around 10 to 20 MV/m, a 10 MeV pistol would be half a meter to a meter long. Given additional engineering considerations, for realistic electron beam pistols I wouldn't expect more than 1 to 2 MeV, maybe 5 MeV at the limit. The ranges in skeletal muscle: 1 MeV - 0.5 cm, 2 MeV - 1 cm, 5 MeV - 2.5 cm. Multiply by 800 for the range in air. Unless you consider non-linear beam-matter interactions (such as heating a tunnel to a partial vacuum) this gives very short ranges in air (4 to 20 m), and you would need to use multiple pulses to blast a deep enough hole to reach vital organs.

If you want better performance out of a pistol sized device for a sci-fi setting, you need to postulate a Sufficiently Clever method to get around the breakdown voltage limit. Once you do this, there's no obvious upper limit on the available electron energy.

Anthony Jackson: It's a problem, though I'm not sure how many MeV you really need (my research-fu is failing me). As a practical issue, going above 10 MeV is of limited value for penetrating armor, but may have value for enhancing range.

I found some interesting studies, that were above my head, last time I looked into this. I can't find any of them right now, but I recall a need for a fairly high voltage, a very high current, and a very clean beam, to maximize atmospheric propagation. Key terms might be Nordsieck length and hose instabilities.

Some things I found that seem vaguely promising/related, though they're generally abstracts and often aren't articles I can get at or really understand if I did read them.

This PDF seems to contain useful information that I'm not particularly good at parsing; see section 12.9 in particular.

Two other links, more historical: link1 link2

Luke Campbell: This looks useful. It indicates there are two range-limiting effects. The first is the loss of energy of the beam electrons due to ionization of the air molecules. The other is the spread of the beam due to collisions of the electrons with air molecules causing random changes in direction to the electrons. Magnetic self pinching allows the beam to recover somewhat from the scattering beam spread, but not entirely. One necessary value for analyzing electron beam range due to scattering is the Alfven current, denoted I_A. This is the current at which the magnetic self focusing overcompensates and causes some of the beam electrons to turn around and move in the opposite direction. It is the upper limit on the current of an electron beam (with the caveat that the limit is for the net current - for rapid rise times, magnetic induction can cause plasma electrons to move backwards along the beam, partially canceling the beam current and allowing more beam electrons to pass by before the limit is reached).

For electrons, this limiting current is

I_A = 17E3 amperes * β * γ

where β = velocity / (speed of light) and γ = 1 / sqrt(1 - β²) is the usual relativistic parameter.

The other necessary value is the increase to the spread of the beam due to scattering per unit length traveled, neglecting magnetic self focusing. For dry nitrogen with at atom density (in particles per cubic meter) of N this value is

d(θ²) / dz = 1.04 meters² * N / (γ² * β⁴)

At STP this becomes

d(θ²) / dz = 2.8 / (γ² * β⁴) m^-1

If we neglect energy loss of the electrons, the beam spread can be determined analytically. For a beam of current I and initial radius R_0, the Nordsiek equation gives the spread of the beam with distance

R(z) = R_0 exp[(d(θ²) / dz) * z / (2(I/I_A))] = R_0 exp[ z / z_0]

In other words, we get an exponential increase in beam radius over a characteristic range equal to

z_0 = 2I / (I_A * d(θ²) / dz))

As an example, let us look at a beam of 10 MeV electrons with a current of 5000 amperes in dry nitrogen at STP.

I_A = 34E4 amperes

d(θ²) / dz = 0.007 m^-1

z_0 = 4.2 meters

For the electron energy loss range in dry nitrogen, I get 44 meters from this reference. This indicates that our original assumption of neglecting the energy loss in finding the beam expansion is probably fine for a a multiple of z_0 or two.

One consequence of this is that electron beams in air will tend to have very short pulses of high current to maximize the self focusing in order to cancel collisional spreading. Unfortunately, this can hinder heating an evacuated tunnel through the air, since for very rapid pulses the air atoms will not have time to move out of the way of the electron beam.

Anthony Jackson: 17e3 = 17,000, correct? For relativistic electrons we can probably safely approximate β as 1 and γ as 2 * energy in MeV. θ is what here? Rate of expansion? It appears we want a current fairly close to I_A; go up to 50,000 amperes and z_0 is now 42 meters. I suspect this range will change as ionization occurs, assuming the electron beam energy is adequate to cause substantial ionization. Let's assume a pulse with an initial diameter of 2mm and a current of 50,000 amperes. That's a peak magnetic field of 5 tesla, which is high but not completely out of the believable range, at least as compared to everything else involved. We have a peak current here of 5e11W, putting us just shy of a terawatt. Now, sustain the pulse for 1 nanosecond, thus depositing 500J in the channel.

The channel has a base cross-section of 3.14e-6 m² and a maximum cross-section of four times that, and a length of 40 meters, so figure total volume is about 4e-4 cubic meters, resulting in heating up about half a gram of matter. 500J / 0.5g = 1 MJ/kg, which is less than the ionization energy of the gas, but is sufficient to heat it up to around 1300K (assuming temperature stabilized) and give an average velocity to the gas of 1400 m/s. It will take about one microsecond for gas to evacuate the channel.

Now, the evacuated channel is maybe 1/4 the density. That will increase the range of electrons by a factor of 4, and also reduces N (and thus d(θ²) / dz) by a factor of 4, which will also increase the nordsieck length. This means the initial 40 meters are only as costly as 10 meters normally, and thus we can tunnel another 30 meters. Rinse and repeat; the theoretical limit is 160 meters.

This, of course, ignores problems with the channel formation: much of the deposited energy may be radiated away rather than turning into thermal movement of molecules, and the shockwave from the initial pulse is going to bounce back as it hits nearby molecules.

Now, lets say our beam hits a human, with a cross section of 5 square millimeters when it hits, and we'll assume a penetration depth of 5 cm², for a total affected volume of 0.25 cubic centimeters, or 2,000J/cm³. Assuming the volume is mostly water, water has a specific heat of 4.18J/cm³, so we flash-heat the water from 37C to 515C. This puts it well above vaporization temperature, and in fact well above its triple point, so it starts to expand, cooling as it does so. In theory, up to 77% of the liquid could turn to vapor; in practice, I suspect the actual amount is somewhat less, due to energy being lost from breaking chemical bonds, secondary X-rays spreading beyond the impact area, and energy loss on contact with nearby flesh.

Interestingly enough, if the cross section reaches 38 square millimeters (about a 7mm wide beam) it will no longer vaporize flesh at all, which means it would produce a charred spot and little other visual effect, though anything in the beam path is dead. Of course, the direct damage may not mean much; 5 cm penetration isn't really enough to kill anything (I'm not sure how the secondary X-rays will be distributed, or what energy level they're at, but the secondary radiation may be quite adequate to disrupt the nervous system). Again, secondary pulses on a microsecond time scale may allow tunneling through matter, as long as the power density of the initial pulse was adequate to cause vaporization.

(Anthony Jackson) I suspect this range will change as ionization occurs, assuming the electron beam energy is adequate to cause substantial ionization.

Luke Campbell: I suspect you are correct. At 10 MeV collisional losses dominate, and if you don't lose energy to ionizing the air molecules the energy loss drops by quite a lot. At higher energies you get radiative losses beginning to dominate, and this will not change with increasing ionization. Note that for a beam burning away an evacuated tunnel for it to travel through, we want to have mainly collisional losses - radiative losses take the form of x-rays which can travel several mm or cm through air and thus do not contribute to heating up the volume of air the beam will travel through.

(Anthony Jackson) Let's assume a pulse with an initial diameter of 2mm and a current of 50,000 amperes.

Luke Campbell: I don't see any real reason not to make the beam very narrow, say a micron in width or so. We seem to be able to generate micron width beams with modern accelerators.

(Anthony Jackson) We have a peak current here of 5e11W, putting us just shy of a terawatt. Now, sustain the pulse for 1 nanosecond, thus depositing 500J in the channel.

Luke Campbell: Complicating this analysis is that the energy deposited increases as the electron energy decreases. However, the energy loss per unit length is roughly constant from 10 MeV to 1 MeV, so this is probably not too significant in this energy range.