Atomic Rockets

Lasers

Dr. Schilling does not think the laser pistol 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.

But first a safety note. Pretty much zero science fiction stories, movies, or TV shows mention that laser sidearms have the ability to permanently blind anybody closer to the weapon than the horizon. If the beam is in the frequencies that can penetrate the cornea of the eye, and the beam reflects off a door nob or other mirrored surface, anybody whose eyes get flashed by the beam is going to need a seeing-eye dog. There are more details here.

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 Campbell calls continuous beam lasers a "heat ray", and pulse beam lasers a "blaster."

(ed note: apparently the laser sidearms in the novel are continuous beam)

"But look—the other thing I came to see you about. Notice my new sidearm?"

Monroe-Alpha glanced at Hamilton's holster. In fact, he had not noticed that his friend was bearing anything new in the way of weapons—had he arrived unarmed Monroe-Alpha would have noticed it, naturally, but he was not particularly observant about such matters, and could easily have spent two hours with a man and never noticed whether he was wearing a Stokes coagulator or a common needlebeam.

But, now that his attention was directed to the matter, he saw at once that Hamilton was armed with something novel...and deucedly odd and uncouth. "What is it?" he asked.

"Ah!" Hamilton drew the sidearm clear and handed it to his host. "Woops! Wait a moment. You don't know how to handle it—you'll blow your head off. " He pressed a stud on the side of the grip, and let a long flat container slide out into his palm. "There—I've pulled its teeth. Ever see anything like it?"

Monroe-Alpha examined the machine. "Why, yes, I believe so. It's a museum piece, isn't it? An explosive-type hand weapon?"

"Right and wrong. It's mill new, but it's a facsimile of one in the Smithsonian Institution collection. It's called a point forty-five Colt automatic pistol."

"Point forty-five what?"

"Inches."

"Inches...let me see, what is that in centimeters?"

"Huh? Let's see—three inches make a yard and a yard is about one meter. No, that can't be right. Never mind, it means the size of the slug it throws. Here...look at one." He slid one free of the clip. "Damn near as big as my thumb, isn't it?"

"Explodes on impact, I suppose."

"No. It just drills its way in."

"That doesn't sound very efficient."

"Brother, you'd be amazed. It'll blast a hole in a man big enough to throw a dog through."

Monroe-Alpha handed it back. "And in the meantime your opponent has ended your troubles with a beam that acts a thousand times as fast. Chemical processes are slow, Felix."

"Not that slow. The real loss of time is in the operator. Half the gunfighters running around loose chop into their target with the beam already hot. They haven't the skill to make a fast sight. You can stop 'em with this, if you've a fast wrist.

(ed note: apparently the common technique is to pull the trigger and hold it on while slashing the beam across your target)

From Beyond This Horizon by Robert Heinlein (1942)
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.

There are four basic technological approaches I would consider based on my personal knowledge, all of which would lead to similar end results if they worked at all.

Phase-locked diode laser arrays
Lots of microlasers on a chip, all working together. Extremely efficient, if you can actually get them to work together.
Diode-pumped YAG lasers
Lots of microlasers on a chip, each working alone. They won't produce a good beam that way, but if you tune them to the right absorption band and direct them all into a YAG crystal, you can get the latter to lase quite efficiently.
Pulsed linear induction accelerators
Fairly conventional technology for producing high-energy, high-current electron beams with external magnetic fields. This one will need to be pushed right up to the theoretical limits to work on a handgun scale, and it will need an unconventional electron source such as a pseudospark discharge.
Wake field accelerators
Clever way of producing high-energy electron beams using the internal electric fields of forced plasma waves. Still in it's infancy, potential unknown but may well be adequate in the long run.
Dr. Schilling

Power

You'll also need a power source. Three approaches come to mind, two of which are pretty sure things. Burning a liquid propellant in a pulsed MHD generator or flux compression generator can be done now, and there are thermal primary (i.e. non rechargeable) batteries that are pretty close to what would be needed. Unfortunately, both of these involve high operating temperatures and expendable power sources.

Advanced bipolar designs of conventional secondary batteries might be up to the task, and have the advantage of being fully rechargeable. Besides, it is rather humorous to consider that a 21st-century laser weapon might really be powered by a lead-acid or NiCad battery.

I'll assume non-rechargeable systems at an energy density of 2.5 kilojoules per cubic centimeter, which is quite plausible. You might consider a rechargeable battery pack as an option, with half the capacity of the non-rechargeables.

Dr. Schilling

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.

As for nonrechargable batteries, check out the various molten salt batteries. They're stored as a solid, so they can be stored 'charged' virtually forever. As soon as you bring them up to operating temperature (400 C or more), and as long as you keep them there, you have an incredibly high output battery. The military has used them like this for a very long time, and most current research is focused on making them rechargeable. I can't find any hard numbers on them (apparently the energy density varies widely), but it's clear that they can have very high energy density.

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

James Borham

Either way, the energy will have to be stored in and dumped from a capacitor or (if the switching problem is solved) inductor to meet the peak power requirement. Electrochemical double-layer capacitors ought to do the job if nothing else is available.

(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.)

Dr. Schilling

If you can combine a chemically fueled laser with the type of pulse behavior needed for optimal armor penetration (a rather formidable challenge), a 'laser rifle' might not be too bad; under ideal circumstances a 10 kilojoule laser might be similar in lethality to a rifle, and could even have fuel requirements on a par with the ammunition weight of a rifle. Of course, this requires a very narrow focus beam (a couple millimeters wide) and you'll be limited to optical or near-IR. If we assume a helium-neon laser (634 nm) a 10 cm mirror would have a beam divergence of 15 microradians, giving a useful range of 100 meters or so (3mm spot).

So...this requires massive tech inventions and an expensive, probably delicate weapon to reach the performance of a rifle. This is not exactly worthwhile.

Efficient ultracapacitors might allow around 100J/g, which in combination with an excimiter laser (and probably a fuel cell for recharge) might be enough for a decent sniper weapon and could give a quite large number of shots on a fuel tank, though the number of shots at one time would be quite limited.

On the severe handwavium side, there's gamma-ray lasers powered by nuclei in metastable states. In this case, the energy density is immense (1.2 GJ/g for Hf-178m2, for example) and diffraction limits are unlikely to be relevant (a 1mm diffraction-limited lens could project a constant 1mm beam for 1,000 km or so). However, the technical problems are, to say the least, formidable, and even if resolved, the 'fuel' is highly radioactive; simply avoiding killing the user would require large amounts of shielding.

(ed note: the handwavium Hf-178m2 is the basis for the infamous Hafnium bomb. Yes, it exists. Yes, it stores incredible amounts of energy in a very tiny package. No, we have not yet figured out how to increase the power output to better than half of the energy discharged every 31 years

Anthony Jackson

(ed note: Noted science fiction author Charles Stross has this deliciously biting analysis of a ridiculous proposed laser weapon called the Stavatti TIS-1 Gasdynamic Laser Infantry Rifle)


The laser itself looks pretty reasonable, in an if-we're-talking-about-laser-weapons way ("laser" and "weapon" belonging in the same sentence in the same way as "automobile" and "rubber-band powered"), but the power supply is what makes this one special. In search of the ultimate in infantry-portable enemy-slaying goodness, Stavatti have one-upped all previous attempts by proposing to use a radioisotope generator containing 750 grams of Polonium-210. This would, of course, provide the necessary 100 kilowatts to power the man-portable death ray. It would also provide 125 petaBecquerels of radiation (as compared with the 100 pB of Cesium-137 spewed out by the B reactor at Chernobyl), and the need to pressurize it to 4000psi leads me to agree with my military informant's summary that "it might actually achieve the near-impossible feat of making Project PLUTO look environmentally benign by comparison."

I will also confess that my suspension of disbelief took a slight knock when I got to the bit about the TIS-1 also sporting a bayonet lug.

Anyway, I'd just like to say that I fervently hope the Pentagon's planning and procurement folks give this proposal the attention it undoubtedly deserves. As Polonium-210 is accounted for (when you can buy it) at a market price of roughly $12 million per gram, this weapon system will cost roughly $54Bn per rifle per year to run — the US Army could afford almost an entire squad, and thus might have to scale back their other projects accordingly.

(PS: 100 kilowatts is, in automobile terms, about 130 horsepower. So if you were to ditch the Dr Strangelove power supply the gadget could plausibly be mounted on a HMMV or Land Rover. But I find that idea somewhat disappointing ... and anyway, what would be the point of sticking a bayonet on a vehicle-mounted laser cannon?)

blog post by Charles Stross

There was discussion about ultracapacitors:

http://www.spectrum.ieee.org/nov07/5636

Apparently they are approaching 50% of the energy capacity of a lithium ion battery. Boost that over 100% and it would make a nifty power source for a man-portable laser weapon.

Winchell Chung

It looks to me like they expect 25% to 50% of the energy of a Li-ion battery. They still haven't made a prototype yet. It is exciting work, and I hope they succeed.

Luke Campbell

Hm. 50% would be 80 Wh/kg (288 kJ/kg). This is approximately 7% of the energy density of a typical chemical propellant and 0.6% of the energy density of gasoline. Incidentally, EEstor is claiming 1330 Wh/kg, but I'm not convinced that I believe them.

Note that thin film lithium and lithium-ion batteries have already pushed significantly beyond the capacity of lithium-ion. For current (if non-commercial) versions, I'm seeing numbers of around 250 Wh/kg and 2500W/kg, which is a bit low power density for a shot from an energy weapon. Theoretical potential is substantially higher.

For amusement: 2nd generation batteries in Ken Burnside's Attack Vector: Tactical game hold 2 gigajoules in a 25 ton structure, which works out to 80 kJ/kg or 22 Wh/kg, and can discharge in 16 seconds (or possibly less), which works out to 5 kW/kg. However, I'm pretty sure that a 1 hullspace component that can provide 1 energy point per game-turn segment for 20 segments (thin-film Li-ion with no tech improvements other than scaling and commercialization) would be gamebreaking. For that matter, 7th gen batteries (extrapolating from high end ultracapacitors) would rather distort the game as well.

Anthony Jackson

The thin film stuff should suffice for electrically powered projectile weapons, if you carried a backpack of batteries. If you figure a modern assault rifle packs something like a 1.5 kJ punch, and if you can get ~50% electrical -> mechanical efficiency, and you want to be able to autofire at 10 round/s, you'll draw 30 kW. This is about a 15 kg pack for modern lithium batteries, 12 kg for your thin film varieties. On the other hand, you could fire off many hundreds of shots if you had enough bullets. If you limit your fire to 3-round bursts, you could cut the power draw perhaps in half (depending on how fast our soldiers pull the trigger), and thus will only have to schlep around half as much weight. Needless to say, the batteries will be used to charge up a capacitor for the intermittent high power pulse used to launch the projectile.

Near future heat-ray style lasers are expected to be practical weapons at about 100 kW. This would require a 40 kg pack using the thin film batteries, but would give you 6 minutes of continuous lasing. Note that 100 kW is for use against rockets and thin skinned aircraft, it might or might not be useful against humans!

If, as I suspect, pulsed lasers are more efficient at causing death and destruction, you could get by with smaller power packs. In my pet future setting, admittedly optimistic "battle lasers" put out lethal 5 kJ beams at full power, and draw 10 kJ. They can sustain 2 shots/second if you want to avoid heat buildup, but can be fired more rapidly for short periods if they have the electrical power available. Lower power beams allow significantly higher rates of fire, although they are not too good against foes with armor. Something like could use an 8 kg pack for 2 full power shots/second if using the thin film lithium batteries, and would give you 720 shots. Combine this with something like a 1 kg ultracapcitor for rapid fire of a limited number of shots when you need them. The ultracapcitor recharges from the battery pack when you are hiding behind cover, switching between targets, crawling through the mud, or whatever else you are doing to avoid being shot. (For what its worth, my setting uses "fast discharge power packs," roughly modeled on ultracapacitors, with specific energies of 200 kJ/kg and specific powers of 40 kW/kg. There are also "high capacity power packs" with three times the specific energy but one third the specific power if you want to tote around a heavy pack that gives you lots of shots, as well as various batteries that give even higher specific energies but even lower specific powers.)

Luke Campbell

Cooling

And you'll need some serious cooling. I'd go with liquid-metal microchannel heat pipes etched into all the hot surfaces, and leading to cooling fins around the "barrel". If you use the chemical-propellant option, regenerative cooling could also work.

Dr. Schilling

Pulsing

Whether you use lasers or particle beams, you'll need a bit over a kilojoule of output energy to reliably incapacitate a human target. In the case of a laser weapon, that energy would be subdivided into ~1 joule pulses at ~5 microsecond intervals, to achieve penetration in the face of a laser's natural tendency to deposit energy at the target's surface. Particle beams don't have that problem; boost the electrons up to a few hundred MeV, and you can dump the whole kilojoule's worth at once.

The plasma clears away easily in that time frame; debris is the real issue, and the driving force between the 5 microsecond pulse rate. That allows roughly 90% of the debris to clear the beam path, assuming a 1mm beam and instantaneous 1J pulses. 1 joule every 5 microseconds is optimal against soft tissue, other materials will want different pulse trains.

I'm assuming a weapon designed to penetrate ~30cm in soft body tissue. This gives about 15cm in bone or plastic, 5cm in brick or concrete, or 2.5cm in steel or most ceramics. Synthetics won't be very good at stopping energy weapons, even tough ones like kevlar, but you might be able to find a ceramic that could stop a laser beam with a centimeter's thickness or so. Particle beams are tougher to stop; it mostly comes down to sticking mass in the way without regard to material properties.

Dr. Schilling

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).

Luke Campbell

Yes, and this is a problem if you want to push the penetration much above the 30cm I specified. If your pulses come fast enough to gouge out a meter-deep path before the surrounding tissue recoils back into the cavity and blocks the beam, they come too fast for the per-shot debris to clear the beam.

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.

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.

Dr. Schilling

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.

Luke Campbell

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.

And the mirror needs to adjust for target range - adaptive optics (flexible mirror with microactuators)coupled to a laser range finder seems to be the way to go here - you've already got the pulsed laser part of the rangefinder.

Pulsed, 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.

Dr. Schilling

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.

Luke Campbell

At kilojoule levels in air the backscatter isn't terribly bad; these would be very high-energy electrons, which tends to collimate the scattered radiation in the forward direction. Particle-beam artillery would be another matter, of course.

Dr. Schilling

Targeting

With penetration, range, and repeatability dealt with, it is time to turn to accuracy. Lack of recoil, automatic fire capability, and line-of-sight accuracy are all major assets here, but there is one more improvement to be made. Both lasers and particle beams can be steered at least a degree or two off-axis, in the case of the laser via the adaptive-optic mirror, for particle beams with a transverse magnetic field at the muzzle.

If we can throw in a chip-mounted laser or acoustic gyro set, we can have a gyrostabilized handgun. The weapon shoots not at where the gun is pointed at the instant of firing, but at a weighted average of where it has been pointing over the past quarter of a second or so. Smoothes out a lot of the jitter inherent in human marksmanship.

You'd probably want to integrate this feature with the weapon's sights. A reflex-type optical sight could have an LED display linked to the gyrostabilizer, rather than a fixed reticule. The dot, or crosshairs, would then indicate the actual shot path and would remain similarly stable under jitter.

(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.)

Dr. Schilling

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.

Luke Campbell

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.

James Borham

In combat, I would expect such a weapon to be used in automatic fire mode at ~10 Hz. With fifty to a hundred pulses to play with, you won't run out of ammunition too soon as is the case with current machine pistols. And recoilless, stabilized automatic fire should allow a moderately capable marksman to walk a burst on target in one or two reaction cycles (say, half a second) in most circumstances. Imperial Stormtroopers (tm) could no doubt still find a way to miss with such a weapon at ten meters, but not competent soldiers. Practical combat range, if you don't mind missing a good part of the time, would be on the order of 50 meters

Dr. Schilling

"Your knowledge of weaponry is impressive."

"A holdover from my game-hunting days. Remember them?"

"I remember disapproving of them."

"Well, combustion (gunpowder) weapons are still in demand by 'sportsmen' who find their sense of masculinity cheated by the lack of recoil in energy weapons."

From HEALER by F. Paul Wilson

Wavelength

BandWavelength (m)
Far Infrared3e-5 to 1e-3 m (30,000 to 1,000,000 nanometers)
Mid Infrared5e-6 to 3e-5 m (5000 to 30,000 nanometers)
Near Infrared7e-7 to 5e-6 m (700 to 5000 nanometers)
Red7.1e-7 m (710 nanometers)
Orange6e-7 m (600 nanometers)
Yellow5.7e-7 m (570 nanometers)
Green5.5e-7 m (550 nanometers)
Blue4.75e-7 m (475 nanometers)
Indigo4.3e-7 m (430 nanometers)
Violet3.8e-7 m (380 nanometers)
Ultraviolet A3.2e-7 to 4e-7 m (320 to 400 nanometers)
Ultraviolet B2.9e-7 to 3.2e-7 m (290 to 320 nanometers)
Ultraviolet C2e-7 to 2.9e-7 m (200 to 290 nanometers)
Extreme Ultraviolet1e-8 to 2e-7 m (10 to 200 nanometers)
X-Ray1e-11 to 1e-8 m (0.01 to 10 nanometers)
Gamma-Ray1e-14 to 1e-11 m (1e-5 to 0.01 nanometer)
Cosmic-Ray1e-17 to 1e-14 m (1e-8 to 1e-5 nanometers)

Note that wavelengths shorter than 200 nanometers are absorbed by Terra's atmosphere (so they are sometimes called "Vacuum frequencies") and anything shorter than 10 nanometers is considered "ionizing radiation" (i.e., what the an average person on the street calls "atomic radiation").

In the chart below, you can see the vulnerability of various parts of the human body to various laser frequencies. Hemoglobin is blood. Melanin is skin and hair. Water is all body tissue. Scatter is the molecular bonds holding proteins together.

As a point of detail: see that blue water line? That shows wavelengths to not use, because it means atmospheric water vapor is opaque at those wavelengths. Also, light that is transmitted through flesh or is scattered internally will still typically wind up being absorbed in the end.

Once you have a reasonably deep hole (fairly high aspect ratio) absorption will be essentially 100% regardless of wavelength — light that is scattered or reflected will often not bounce straight out of the hole, giving it a chance to be absorbed by the sides of the hole. This won't help with penetration, but will make the hole bigger.

Anthony Jackson

So lets take a hypothetical laser sidearm, assume a 10cm lens, 10kW output power, 1ms beam duration, and 0.5 duty cycle. Given these as constant, but varying the wavelength of the laser, we get the following penetration on a carbon target at the listed ranged:

7e-7 m (Near infrared)
RangePenetration
25m6.25mm
50m0.78mm
100m0.10mm
200m0.01mm
5.5e-7 m (Green)
RangePenetration
25m12.88mm
50m1.61mm
100m 0.20mm
200m0.03mm
4.3e-7 m (Indigo)
RangePenetration
25m26.96mm
50m3.37mm
100m 0.42mm
200m0.05mm
3.2e-7 m (UVA)
RangePenetration
25m65.4mm
50m8.18mm
100m 1.02mm
200m0.13mm

It's obvious that as wavelength decreases, neglecting atmospheric effects, damage on the target increases. So the question is, how low can I push my wavelength, and what are the effects? If 90% of the UVA beam is scattered, then it is equivalent to the infrared beam. If only 50%, it is superior.

Seems like an important point to figure out. Does anyone have a good model? I've been digging on scholar.google.com to no avail.

Eric Rozier

Hm. Not sure how you're getting penetration.

Actually, it's penetration that increases, not damage. In any case, the practical limits for laser weapons are as follows: 1) We have very limited ability to generate high power short wave lasers. 2) Beyond a certain energy density, air breaks down and becomes opaque due to nonlinear effects. I'm not sure exactly how this scales with wavelength, but I'm pretty sure shorter wavelength is worse.

Factor (1) tends to produce lasers in the 800-1000 nm range. Factor (2) doesn't generally limit modern lasers, but is a real issue for small arms lasers.

Anthony Jackson

Anthony Jackson: Hm. Not sure how you're getting penetration.

From the equations on the Atomic Rocket website. As I said, assuming a Carbon target.

(ed note: he even made an online calculator)

Anthony Jackson: Actually, it's penetration that increases, not damage.

Not sure how you figure that. At 7e-7m, we vaporize 2.23e-8m^3 of carbon at 25m. At 4.3e-7m, we vaporize 3.61e-8m^3 of carbon at 25m.

Both damage and penetration increase.

Anthony Jackson:

1) We have very limited ability to generate high power short wave lasers.

2) Beyond a certain energy density, air breaks down and becomes opaque > > due to nonlinear effects. I'm not sure exactly how this scales with > > wavelength, but I'm pretty sure shorter wavelength is worse.

Factor 1 disappears with less handwavium than it takes for an MFT, so I'm not terribly concerned with it. While X-rays have some inherent problems, we can and do make cheap UV lasers right now, and there seems to be no reason why we can't up their power significantly.

Factor 2 is definitely an issue for small arms lasers, but at what point does it become a problem? What is the wave length at which we get the most bang for the buck? How bad is it at various wave lengths? Surely a model exists somewhere.

Eric Rozier

A lower limit on wavelength in oxygen atmospheres is somewhere around 150 to 200 nanometers. Below this you get single photon absorption by an electronic transition — this means your beam gets absorbed very fast.

For femptosecond pulses when you get self-focusing, you can get so called supercontinuum light, where the monochromatic light of the laser gets scattered into white light across a range of wavelengths. Self focused filaments can propagate for ten meters at least, and the primary absorption is in the plasma core of abut 0.1 mm across, indicating that air can handle gigawatt power levels across most of the visible spectrum across areas of more than 0.01 mm^2.

Another data point is that 0.193 micron light (193 nanometers) at 50 GW/m^2 will fall off with distance R as approximately exp(-R/100 m) due to two photon absorption.

If I'm not concerned about civilian eye safety and I don't care if the bad guys can see where I am, visible green is probably a pretty good wavelength to use for long distance lasing — it focuses well compared to longer wavelengths but doesn't suffer much from atmospheric Rayleigh scattering like shorter wavelengths. Details on calculating Rayleigh scattering can be found here

http://panoptesv.com/SciFi/LaserDeathRay/LinAbs.html

Since you are describing a pistol, however, you probably don't care about long range targets. In this case you might consider using nanosecond to femptosecond pulses, causing damage by producing power levels high enough to explode a small part of the target, thus causing mechanical damage through the shock wave rather than direct heating. Now the range depends more on your instantaneous intensity. Some rough details can be found at

http://panoptesv.com/SciFi/LaserDeathRay/Blaster.html

http://panoptesv.com/SciFi/LaserDeathRay/DamageInstant.html

In this regime, you can also use self focusing and filamentation to increase your depth of field so you can penetrate your target right through at close range

http://panoptesv.com/SciFi/LaserDeathRay/DepthOfField.html

http://panoptesv.com/SciFi/LaserDeathRay/SelfFocus.html

Luke Campbell

Lasers In Practice

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.

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.

Luke Campbell

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.

Luke Campbell

Laser Blindness

As I already stated, pretty much no science fiction in movies, TV or novels mentions the blindness hazard of laser sidearms (with the possible exception of Jack Williamson's Trapped In Space). On Terra, anybody within about five kilometers (i.e, the horizon) of an operating laser weapon is at risk of loosing their eyesight permanently. If the beam flicks over a window, a shiny automobile, or anything else reflective (reflected or scattered light); an innocent bystander will suddenly require the services of a working dog. People knowingly entering a laser gun battle will be wearing anti-laser goggles (or contact lenses). Laser gunmen who care about innocent bystanders will use lasers of frequencies opaque to the cornea of the eye.

There is a laser safety classification system. Class 1 is safe for eyesight. Class 1M is safe as long as you are not looking at the laser through a magnifying glass or telescope. Class 2 is safe for eyesight due to the human blinking reflex (most laser pointers fall into this catagory). Class 2M is safe with no magnifying glasses or telescopes. Class 3R are mildy dangerous. Class 3B are dangerous but diffuse reflection is not (laser protective goggles required). Class 4 are incredibly dangerous, since it will also burn holes in clothing and skin (laser protective goggles required). Naturally all laser weapons are class 4.

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 Campbell

Luke has more details about laser eye damage here. Below is a sample:

Any death ray worth its name will be sufficiently intense that anyone looking directly into the beam will be instantly blinded (if not killed — it is, after all, a death ray). There are, however, other vision hazards. The cornea, lens, and vitrous humor of the eye are transparent to wavelengths between roughly 0.35×10-6 and 1.4×10-6 meters. If a small fraction of a death ray beam in this wavelength range is specularly reflected off a smooth surface, anyone looking at that surface will focus the reflected light into a tiny spot on their retina. This can heat the retina up enough to cause a third degree burn, leading to a spot of permanent blindness. Very powerful lasers (such as just about any death ray) can still be hazardous after mutliple specular reflections — the fraction of the beam that reflects off the target might bounce off a shiny hubcap, reflect off a window, and then reflect off the shiny paint job of a passing car to blind a bystander.

Luke Campbell

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?

Johnny1A

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.

Luke Campbell

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.

If I'm not concerned about civilian eye safety and I don't care if the bad guys can see where I am, visible green is probably a pretty good wavelength to use for long distance lasing - it focuses well compared to longer wavelengths but doesn't suffer much from atmospheric Rayleigh scattering like shorter wavelengths.

Luke Campbell

Is there even a plausible solution to the eye safety problem? I can see that for missile defense or blowing up IEDs, eye safety might not be too much of a problem...but for small arms it seems implausible to field weapons that tend to leave civilians blind.

Isaac Kuo

You can cut down on it by a lot by using frequencies that don't pass through the eye. That means either greater than 1400nm or less than 400nm. There is still the possibility of indirect blinding caused by the target of the laser being heated white-hot and emitting thermal radiation, and it's possible to actually produce sunburns on the cornea if enough radiation hits them, but these are lesser problems (and the latter effect probably isn't a factor at ranges where the heat won't also start fires).

For that matter, self-focusing lasers may not reflect well and thus have similar advantages.

Anthony Jackson

Other than repeating what Anthony said, let me just expand a bit on the self focusing aspects. A self focused filament will convert the initially coherent laser radiation into incoherent white light directed by the lens that its field creates in air rather than the inherent directionality of the light. Take away the air, or the high field causing the lensing, and the light will spray out in all directions (it is actually mostly forward and backward propagating, but is not tightly collimated). If part of the light is reflected, it will lose this self focusing ability. Even incoherent light can be dangerous if it is intense enough, but less so than a collimated reflected beam. In addition, when the beam interacts with solid matter, it will flash that matter to plasma, and the plasma will absorb much of the beam. Most reflections will be off the plasma-air interface, which is likely to be irregular thus giving diffuse rather than specular reflection.

All this assumes that the self focusing works as advertised. If your gun tries to self focus the beam half a meter in front of the target, but it misjudges the distance to the target, the beam could still be monochromatic and coherent, and might reflect off shiny bits. Is this more of a worry than bullet ricochets from modern firearms? I don't actually know.

Luke Campbell

This filamenting ability seems to require a very high power level, so diffuse reflection would seem to be dangerous. I'm thinking of close quarters situations, like a hostage rescue, where the civilians in question might be less than a meter from the bad guys you're shooting at.

But let's suppose we're not using filamenting. A "death ray" laser weapon is going to need to be somewhat powerful in order to take down the bad guy. Even if we're using a wavelength that is blocked by the eye, diffuse radiation from the hot target spot might be a problem. Is it?

Or maybe the diffuse radiation is only as much of a threat to eyesight as the muzzle flash of a pistol?

Isaac Kuo

Isaac Kuo: This filamenting ability seems to require a very high power level, so diffuse reflection would seem to be dangerous.

Luke Campbell: While the power can be mind bogglingly high, the total energy can be fairly moderate. To cause eye injury (of the sort normally discussed with lasers) you need to deposit enough energy onto a point on the retina to cause third degree burns, fast enough that heat conduction can't take the energy away. Filamented beams clearly have the fast part down, but an uncollimated reflection may not deposit enough energy to burn (or it might — we really don't have the experience with this yet).

Isaac Kuo: Even if we're using a wavelength that is blocked by the eye, diffuse radiation from the hot target spot might be a problem. Is it?

Luke Campbell: I expect it is more like the threat of the arc of an arc welder. Glancing at the flashes, or watching from a distance is pretty safe, but the welder himself better be wearing protective eyewear.

Luke Campbell

Looking at laser safety (http://en.wikipedia.org/wiki/Laser_safety), a typical weapons laser will probably take somewhere between a microsecond and a millisecond to drill into a target, split into multiple pulses.

Each pulse will be something like 10J and 10^-9 seconds. That time gives a safe level of 5e-7 J/cm^2 or 5e-3J/m^2. At 1 meter, the reflected light will probably be 0.1 to 0.5J/m^2, so each pulse will be a hazard out to 5-10 meters.

In addition, we're delivering 1+ kilojoules over maybe a millisecond. That increases our maximum dose to 1e-5J/cm^2, but we're delivering 100+ times as much energy, so this will give a hazard at 10-20 meters. Note that the safe level is 10% of the 50% damage threshold, so the 50% damage distance is 3-6 meters for a 1 kilojoule laser.

Anthony Jackson

Oh! Blink reflex!

If you use a visible laser, like a green laser, then you can maybe flash a weak "safety" pulse to induce endangered civilian eyes to blink before the main weapon pulses.

Put maybe 0.1 seconds between the safety pulse and the main pulse. That's enough time for civilians to blink but not enough time for a bad guy to dodge the "bullet". That's similar to the time delay of a pistol bullet traveling 30m.

Isaac Kuo

It's not like the safety pulse has to be the same wavelength as the main pulse. However, I suspect a better option is to use a wavelength that doesn't penetrate the eye, and then operate at a power level low enough that plasma formation is not a major factor (relying on regular vaporization). This means that the reflected primary beam is not directly dangerous unless it actually hits someone at near full power, and emitted radiation is (a) fairly long wave, and (b) a small minority of the energy release.

Unfortunately, this still requires bringing the surface up to the sublimation temperature of the material. This is not a problem for humans or for soft armors, but refractory ceramics will require temperatures in excess of 3,000K, which will give an emissions peak in the near IR.

Anthony Jackson

Also note that Protocol IV of the 1980 Convention on Certain Conventional Weapons (issued by the United Nations on 13 October 1995) states:

Article 1: It is prohibited to employ laser weapons specifically designed, as their sole combat function or as one of their combat functions, to cause permanent blindness to unenhanced vision, that is to the naked eye or to the eye with corrective eyesight devices. The High Contracting Parties shall not transfer such weapons to any State or non-State entity.

Article 2: In the employment of laser systems, the High Contracting Parties shall take all feasible precautions to avoid the incidence of permanent blindness to unenhanced vision. Such precautions shall include training of their armed forces and other practical measures.

Article 3: Blinding as an incidental or collateral effect of the legitimate military employment of laser systems, including laser systems used against optical equipment, is not covered by the prohibition of this Protocol.

Article 4: For the purpose of this protocol "permanent blindness" means irreversible and uncorrectable loss of vision which is seriously disabling with no prospect of recovery. Serious disability is equivalent to visual acuity of less than 20/200 Snellen measured using both eyes.

Of course the U.S. Department of Defense is working on the Personnel Halting and Stimulation Response rifle, which is a laser-blinding weapon intended for crowd control. It is intended to skirt the 1995 UN Protocol on Blinding Laser Weapons by not blinding the target permanently (they hope).

Design

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.

Luke Campbell

Luke Campbell

The aperture is a 6 cm window protecting a 6 cm lens. Below the main lens is a secondary beam path for close focus attacks (close than ~1m). My conception when designing this thing was that the laser was a phase locked semiconductor laser near the butt of the stock, the large opening in the rear is for the cooling fan to force air past the cooling fins of the laser block (the model actually has all the fan blades, but they don't show up in the renders). And just because we all want to be able to "set lasers to stun," there is a pair of alternate beam paths on either side of the secondary beam path that can emit paired self-focused light filaments that will conduct a taser-like current.

Luke Campbell
Battle Laser

...The side vents blow hot air (hot, not red hot)... I was illustrating some equipment from a role-playing setting I've been developing...

These are pulsed lasers of the "blaster" variety, which emit rapid bursts of ultra-short pulses to drill through their targets. They primarily emit in the near infrared at around 1 micron wavelength, but can frequency double their beam color to green if desired. All these lasers are 50% efficient at turning electric energy into beam energy. The beam parameters are fairly flexible - they can emit lower energy beams for a higher sustained rate of fire, for example.

The battle laser is a heavy hitting weapon designed as an infantry longarm to emit high energy beams for light anti-armor and anti-personnel roles, although it is also popular with sportsmen hunting large game. The beam energy is 10 kJ per shot, made up of 50 pulses of 200 J each, spaced 10 microsecond apart. This puts each pulse in the range of a big firecracker. The total beam energy is about the same as a .460 Weatherby magnum bullet - a bullet for the Weatherby elephant gun and the most powerful sporting cartridge in existence.

It can sustain a rate of fire of up to 2 full energy pulses per second, or safely handle overheating by up to 8 full energy shots. It has a mass of 4.5 kg and a 6 cm primary aperture. The beam causes full damage out to about 350 meters. It is commonly powered by a 1.7 kg high capacity power pack, with enough energy for 100 full energy shots and enough power to supply 2 full energy shots per second, although the laser can be hooked to a power backpack via a power cable to allow higher rates of fire and ammunition capacity. 6 cm lens.

Luke Campbell
Assault Laser

The assault laser is designed as a rapid fire anti-personnel infantry weapon. It emits lower energy beams than the battle laser, but has beefed up cooling and power supply systems to allow a greater time averaged power. The beam energy is 4.8 kJ per shot, with a sustained fire rate of 5 full energy beams per second, and can safely handle up to an additional 14 full energy beams worth of overheating. Its mass is 4.5 kg and it has a 6 cm aperture. It has an effective range out to about 250 meters. It is commonly equipped with a 2 kg high capacity power pack, with enough energy for 250 full energy shots and a power sufficient to supply 5 full energy shots per second, although again it can hook into a power cord to attach to a larger power pack for greater ammunition capacity and rate of fire. 6 cm lens.

Luke Campbell
Heavy Laser Pistol

The heavy laser pistol is a bulky handgun for heavy hitting stopping power. The beam energy is 3.2 kJ, with a sustained fire rate of 2 shots per second and a safe overheating reserve of up to 8 shots. It masses 1.25 kg and has a 3 cm aperture. It can keep a tight focus for full beam effect out to about 100 meters. It is commonly powered by a 0.24 kg fast discharge power pack fit into the grip. This can supply the laser with 15 full energy shots and 3 full energy shots per second. Alternately, the laser can be attached to a larger power pack worn on the belt or as a backpack for greater ammunition capacity. 3 cm lens.

(looks like a common civil camera) It's a case of convergent evolution. Both are designed to direct and focus light.

Luke Campbell
Medium Laser Pistol

The medium laser pistol is a common self-defense and law enforcement sidearm. It has a beam energy of 1.6 kJ, with a sustained rate of fire of 2 shots per second and a safe overheating reserve of up to 8 shots. The mass is 0.65 kg and it has a 2 cm primary aperture. The effective focus range is around 50 meters. A 0.2 kg fast discharge power pack fits into the grip, which can supply the pistol with 25 shots at up to 5 shots per second. 2 cm lens.

Luke Campbell
Light Laser Pistol

The light laser pistol is a compact sidearm for concealed carry. Its beam energy is 1.2 kJ, consisting of 60 pulses of 20 J each spaced 4 microseconds apart. It has a sustained rate of fire of 2 shots per second and a safe overheating margin of 8 shots. It masses 0.45 kg and has a 1.5 cm primary aperture. The effective focal range is around 30 meters. It is commonly powered by a 0.15 kg power pack in the grip, which gives 25 full power shots at up to 5 per second. 1.5 cm lens.

Luke Campbell

{amount of damage caused by battle laser shot: 10 kJ per shot, made up of 50 pulses of 200 J each, spaced 10 microsecond apart} I use my damage calculator here which lays out all of my physical assumptions and approximations, but which I think captures the basic physical processes of crater gouging. Since stress is concentrated at the tips of cracks, you may get individual cracks propagating beyond the distances listed below in brittle materials, but severe pulverization should be limited to approximately the distances given (as observed in impact and explosive craters).

Incident on meat, the aforementioned pulse train will blast out a hole 53 cm deep and 2.2 cm across (this is probably reported to one more significant figure than is justified). The diameter of the temporary cavity will be about 10 cm, but since muscle is highly elastic this will probably cause only bruising beyond the 2.2 cm permanent hole. Adding gristle and bone doesn't change this much - you get the same permanent cavity and depth in gristle, while bone will be drilled through to a depth of 29 cm, a permanent cavity diameter of 1.2 cm, and shattering and fracturing out to 1.45 cm diameter. Note that a typical person will be about 20 cm to 30 cm through the torso (depending on orientation), so this pulse would not only shoot through a person, but through the guy behind him as well.

Incident on plastic - in this case high density polyethylene - the pulse train will blast out a 32 cm deep and 1.3 cm across hole, with possible plastic flow out to 2.43 cm diameter.

Incident on sandstone, you get a 25 cm deep hole, 1.1 cm across, with shattering and cracking out to 2.1 cm. On granite, the hole is essentially the same except that shattering and fracturing is limited to 1.5 cm diameter. On concrete, the hole is again about the same depth and width, but now you can expect shattering out to about 3 cm.

Against structural steel, you get a 16 cm deep hole that is 0.65 cm across, and possible cracks or permanent deformation out to 1.1 cm. The very strongest maraging steels have the same size hole, but will lack any permanent deformations in the vicinity of the hole.

A representative titanium alloy might get an 18 cm deep hole 0.74 cm across, with possible permanent damage out to 0.84 cm diameter. Aluminum alloys will get drilled to 19 cm and 0.79 cm across, with possible permanent deformation out to 1.5 cm diameter.

High tech armor is likely to be some sort of carbon, perhaps diamondoid, fullerite, or nanotube weave. Against diamond I get a hole depth of 6.1 cm and a 0.26 cm hole diameter. Expect permanent damage out to 4 cm in the form of shattering and cracks. Against fullerite and nanotubes, the hole will be 7.7 cm deep and 0.32 cm in diameter, with possible permanent damage out to 0.41 cm.

Luke Campbell

(Luke Campbell: 10 kJ per shot, made up of 50 pulses of 200 J each, spaced 10 microsecond apart)

Why that level of overkill? You should get the same penetration out of 100 pulses of 25J each, spaced 5 microseconds apart. You'll just have a hole that's half as wide, and you've just dramatically cut the energy requirements.

Anthony Jackson

Two reasons, all relating to the fact that the hole is half as wide.

First, very large aspect ratio holes may be problematic to drill, based on issues of the ejecta interacting with the beam and the hole. With the pulse parameters I used, I'm looking at a 25:1 aspect ratio - which is probably doable although the hole will likely have constricted significantly near the end. At half the width, the aspect ratio will be more like 50:1, which is pretty extreme and may be unachievable. Also, if the hole is constricted, each subsequent pulse will produce a smaller bang, which will gouge out a smaller crater, which will in turn reduce the penetration from this optimistic assessment. In the limit of lots of small pulses, this should give a penetration that depends on the logarithm of the number of pulses, which quickly reaches a point of diminishing return.

Second, your range for maximum effect is cut in half, since you need to focus the pulses to within half the width to efficiently blast out the crater. Against diamondoid armor, the 200 J pulses require a 0.26 cm spot size for maximum effect and a 1 micron wavelength, 6 cm aperture laser will be able to be effective out to about 120 meters with a perfect Gaussian beam. If the craters are only half as wide, you would need to be twice as close.

Although now that I think about it, all my previous figures on the beam power were from the figures on power consumption, not beam power. Since I assumed by lasers were 50% efficient, all the previously stated beam powers are too large by a factor of 2 (and the details on the pulse trains which I retro-fitted to give the right beam power will be off as well). Ah well, I plead that I was distracted (I had just learned that I was going to be a daddy).

Luke Campbell

(Luke Campbell: First, very large aspect ratio holes may be problematic to drill...)

Hm. On reflection, this suggests that the ideal number of pulses in a blast may be fixed (probably somewhere in the 20-100 range), since the aspect ratio is basically about half of the number of pulses.

(Luke Campbell: In the limit of lots of small pulses, this should give a penetration that depends on the logarithm of the number of pulses...)

Pretty sure it's order 1/3, since the lost energy tends to go towards making the hole wider.

(Luke Campbell: Second, your range for maximum effect is cut in half, since you need to focus the pulses to within half the width to efficiently blast out the crater...)

On reflection, this may be problematic for unrelated reasons. Air breakdown in clean air occurs at upwards of 1010W/cm2, but in dirty air it can drop down to 108W/cm2 or so. Your 0.26 cm spot size is 0.05 cm2, so the dirty air limit is around 107W or 10J/microsecond. For clean air, the 200J pulses are likely not a problem.

Anthony Jackson

(Anthony Jackson: Hm. On reflection, this suggests that the ideal number of pulses in a blast may be fixed, probably somewhere in the 20-100 range)

Yeah, that's the conclusion I've been coming to.

(Anthony Jackson: Pretty sure it's order 1/3, since the lost energy tends to go towards making the hole wider)

I can see this is true if you are mainly working via melting or evaporation of the material. If the pulses are blasting out a void, however, the energy deposited on the sides of the hole may not be sufficiently intense to deform the material. Of course, the hypersonic jet of ejecta may be able to strip material from the sides of the hole. So we are looking at penetration scaling at somewhere between the 1/3 power and logarithmically for large numbers of pulses. For small numbers of pulses we should, of course, be in a linear regime.

Looking at pictures of various aspect ratio laser drilled holes, the opening to the hole looks to have about the same radius regardless of aspect ratio, which is about the same as the width of the beam. As the aspect ratio of the hole increases, the hole constricts with depth, eventually becoming significantly narrower than the beam.

I am not sure if the same mechanisms that operate in close focus laser drilling necessarily take place in holes drilled as part of an attack by a laser weapon. For example, in laser machining the walls of the hole are often used as a waveguide to extend the depth of field of the laser beam. For weapons, this will be irrelevant at significant ranges. If loss due to multiple reflections down the waveguide is responsible for much of the constriction, then this will not be as much of an issue for laser weapons.

For pulse lasers, as long as you can get most of the energy of the pulse into a given area of the target material, you will blast out a full sized crater. So suppose the crater is 1 cm across (and thus you have a maximum spot size of 1 cm in which to focus your beam for maximum effect), and also suppose your beam is focused to 1 mm. You will continue to blast out full sized craters until ejecta deposition constricts some part of the hole to less than 1 mm. This will result in a much deeper hole than if your beam started out close to the threshold limit of 1 cm.

(Anthony Jackson: On reflection, this may be problematic for unrelated reasons. Air breakdown in clean air occurs at upwards of 1010W/cm2, but in dirty air it can drop down to 108W/cm2 or so. Your 0.26 cm spot size is 0.05 cm2, so the dirty air limit is around 107W or 10J/microsecond. For clean air, the 200J pulses are likely not a problem.)

This is a very interesting observation. It may be that in air we can never be able to reliably penetrate carbon-armor materials.

Luke Campbell

Beam divergence for a near-IR laser (such as Nd:YaG) can be estimated as on the order of 1mm per (aperture in mm) meters, and focus tighter than 1-2mm is probably not useful due to issues of hole aspect ratio, so the range at which these weapons would retain full penetration is reasonable for their apparent roles (as assault rifle, SMG, pistol), though rather sharply capped as compared to conventional rifles (which, while not very effective beyond a few hundred meters, don't drop to irrelevance).

Anthony Jackson

I was envisioning these as pulsed lasers. With a pulse, so long as the light is delivered into a smaller spot than the crater which is excavated, the crater will explode to full effect. Since higher energy pulses explode to give bigger craters, higher energy beams will have longer range for the same primary aperture.

So take the battle laser, with a 6 cm aperture and 200 J pulses (fired in bursts of 50 pulses spaced a few microseconds apart). At 200 J, the crater blown out of a good structural steel is about 6.5 mm. So suppose we want the beam to focus into a 6 mm spot. If the beam wavelength is around 1 micron, we get a range of about 275 meters. As the materials get less strong, the crater gets bigger and the range of the laser gets longer - about 470 meters in concrete, or about 940 meters for meat. Stronger materials need you to be closer - for sooper carbon nano stuff, you will want to be closer than about 140 meters.

Luke Campbell

(If you have droplets of water/ oil / mud on the lens and your first pulse hits it could the resulting steam eventually degrade the lens?)

An interesting question. For the parameters I assumed for these devices, a single shot is about 5 kJ in 0.5 milliseconds, or 10 MW of power time averaged over the pulse. At the lens it is spread out over a 6 cm diameter spot (since the lens is 6 cm in diameter). Since 100 J distributed over a 6 cm spot is not likely to give an impulsive shock wave, I'll treat this as if a 10 MW beam was incident on the lens debris.

I turn to the calculator and look at what 10 MW in 6 cm will do to granite - assume a piece of dust is equivalent to a tiny granite fleck. I find that the vapor pressure is 242 kPa - a bit less than two and a half atmospheres. This is much less than the structural strength of any reasonable lens material, so the evaporating dust fleck will not blast a hole in the lens (material strength of strong refractory materials are measured in tens of GPa or more - hundreds of thousands or millions of atmospheres). The temperature is 2584 K. This will burn unprotected diamond, so we will have to assume that the surface of the lens is not diamond. Zirconia has a melting point of 2986 K, so we can make a thin film covering out of that, with diamond underneath (diamond has excellent thermal conductivity and transparency). Silicon carbide is another possibility for a lens coating. In the half a millisecond of laser irradiation, the dust will evaporate to a depth of 0.06 mm.

So what looks like will happen to a bit of dust on the lens is that a thin layer of the dust will be heated to vapor. The vapor will expand, acting like a rocket to launch the dust off the lens. With a proper selection of materials, the lens will be undamaged.

Repeating the calculation with perfectly absorbing water (a model for mud), I find a pressure of about 6 atmospheres (615 kPa), a temperature of 433 K (a bit over boiling), and vaporization to a depth of 0.6 mm. This comes nowhere near harming the lens, and blasts the water off the lens with a puff of steam. In practice, the water is likely to be mostly transparent, and might boil throughout its volume or even transmit the beam without significant heating for very pure water rather than having a bottom layer evaporating.

Oops - SiC also burns when it gets too hot. It looks like zirconia will need to be the lens coating material.

Or rather than zirconia, cubic boron nitride could be used as a coating, since it is just about as hard as diamond, has extraordinary chemical stability, thermal conductivity, and thermal stability. Maybe you could make the entire lens out of cubic boron nitride rather than diamond.

Luke Campbell

Power Supply

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.

John Routledge

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.

External

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!

"Bullets"

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.

Lasers, though they had air-defense applications, were not the infantryman's answer either. 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 four-hundred-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-Amerika, managed to duplicate the phenomenon.

The key had come from spectroscopic examination of pre-1902 lavas from Pelee's crater. The older rocks had shown inexplicable gaps among the metallic elements expected there. A year and a half of empirical research followed, guided more by Dr. Weygand's intuition than by the battery of scientific instrumentation her employers had rushed out at the first signs of success. The principle ultimately discovered was of little utility as a general power source—but then, Olin-Amerika had not been looking for a way to heat homes.

Weygand determined that metallic atoms of a fixed magnetic orientation could be converted directly into energy by the proper combination of heat, pressure, and intersecting magnetic fields. Old lava locks its rich metallic burden in a pattern dictated by the magnetic ambiance at the time the flow cools. At Pelee in 1902, the heavy Gauss loads of the new eruption made a chance alignment with the restressed lava of the crater's rim. Matter flashed into energy in a line dictated by the intersection, ripping other atoms free of the basalt matrix and converting them in turn. Below in St. Pierre, humans burned.

When the principle had been discovered, it remained only to refine its destructiveness. Experiments were held with different fuel elements and matrix materials. A copper-cobalt charge in a wafer of microporous polyurethane became the standard, since it appeared to give maximum energy release with the least tendency to scatter. Because the discharge was linear, there was no need of a tube to channel the force as a rifle's barrel does; but some immediate protection from air-induced scatter was necessary for a hand-held weapon. The best barrel material was iridium. Tungsten and osmium were even more refractory, but those elements absorbed a large component of the discharge instead of reflecting it as the iridium did.

To function in service, the new weapons needed to be cooled. Even if a white-hot barrel did not melt, the next charge certainly would vaporize before it could be fired. Liquified gas, generally nitrogen or one of the noble gases which would not themselves erode the metal, was therefore released into the bore after every shot.

From HAMMER'S SLAMMERS by David Drake.

Gun as Power Supply

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.

...Jaksan got wearily to his feet again. "I don't know. We can keep that in mind. It could be a lead, but I don't know." He lapsed into a deep study as they moved on but at the next halt he spoke with some of his old fire. "Dalgre, what was that process you told me about - the one for adapting disruptor shells for power?"

His assistant armsman looked up eagerly.

"It is." Within three words he had plunged into a flood of technicalities which left the rangers as far behind as if he were speaking some tongue from another galaxy. The Starfire might have lacked a mech-techneer, but Jaksan was an expert in his field and he had seen that his juniors knew more than just the bare essentials of their craft. ...

..."What do you propose to do?" Jaksan asked after a long moment.

"This process you were discussing with Dalgre, can you use disruptor charges in the sled? We must keep the extra fuel for emergencies."

"We can try to do it. It was done once and Dalgre read the report. Suppose we can, what then?"

"I'll take the sled and investigate that."...

...Jaksan was as good as his word. The next morning Dalgre, Snyn and the arms officer dismantled the largest of the disruptors and gingerly worked loose its power unit. Because they were handling sudden and violent death they worked slowly, testing each relay and installation over and over again. It took a full day of painful work on the sled before they were through, and even then they could not be sure it would really rise.

Just before sunset Fylh took the pilot;s seat, getting in as if he didn;t altogether care for his place just over those tinkered-with power units. But he had insisted upon playing test pilot.

The sled went up with a lurch, too strong a surge. Then it straightened out neatly, as Fylh learned how to make adjustments, and sped across the river, to circle and return, alighting with unusual care considering who had the controls. Fylh spoke to Jaksan before he was off his seat.

"She has a lot more power than she had before. How long is it going to last?"

Jaksan rubbed a grimy hand across his forehead. "We have no way of telling. What did that report say, Dalgre?"...

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

Something Different

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!

C. Another type of atomic weapon, but working on the controlled-fission principle, the Radiumatic projects a concentrated radiation beam. Another "brain child" of our brilliant Professor Devonport, it is a much heavier weapon than the previous two, but proportionally more effective.

There is no recoil with this weapon or the flame gun and therefore great accuracy is obtainable.

The Radiumatic, when the front hand grip is removed and the tripod screwed into its place, is converted into an idea weapon for ground use - in positions of defense, for instance.

From Ron Turner's Space Ace pop up book (1953).

Particle Beam

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.

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.

At kilojoule levels in air the backscatter isn't terribly bad; these would be very high-energy electrons, which tends to collimate the scattered radiation in the forward direction. Particle-beam artillery would be another matter, of course.

Dr. Schilling

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.

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.

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).

Apparently an electron particle beam would resemble a lightning bolt.

(Jason: "For an idea of an electron beam path... Look at lightning, which If I'm reading right sounds about the same")

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.

The shot will basically look like a straight lightning bolt (blue-white flash with extremely short duration), and will produce a snap of sound, though at the power levels proposed it won't be very loud; probably rifle bullet level.

The wound won't be all that visible, but will seem peculiar as compared to a bullet wound, since the skin will not be pushed inwards and may actually be pushed outward. It's possible that the skin will not even be visibly punctured, just blackened in a spot (depends how focused the beam actually is, which is unclear). Any tissue near the impact site will be dead or dying, and nervous system operation will be disrupted (stuff near the beam may absorb 100,000 rads or more).

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.

Anthony Jackson

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

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

Anthony Jackson

Mr. Andrew Broeker has some issues with Mr. Campbell's approximations:

My first concern regards Luke Campbell's use of the CSDA approximation to calculate electron penetration depth. This approximation should only be used for very thin targets where only a small fraction of incident particles' energy will be lost traveling through the sample. Since the discussion regard's the loss of all energy, more math gets involved. I've done similar calculations in my lab work and would be happy to do so again if Luke could provide me with the ESTAR data he used to do this.

My second concern is Luke's suggestion that weaponized electron beams should be a micron in width. While he is correct that modern accelerators can achieve such narrow beams, they can do so only via collimation. To achieve such beam diameters, up to 99% of your beam ends up getting dumped on your collimators. This has two consequences. First, drastically reduced beam current. Second, the operator gets irradiated far worse than his target.

Andrew J. Broeker

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.

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

Anthony Jackson

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.

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.

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

Anthony Jackson

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.

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

Anthony Jackson

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.

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.

Anthony Jackson

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.