## Laser Cannon

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

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

### Equations

Now for the dull equations.

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

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

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

RT = 0.305 * D * L / RL

where:

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

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

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

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

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

θ = 0.61 L/RL

where:

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

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

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

BPT = BP/(π * (D * tan(θ/2))2)

where:

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

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

BPT = BP/(π * RT2)

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

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

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

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

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

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

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

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

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

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

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

### Efficiency

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

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

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

We = (1.0 - Ce)

where:

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

WP = CP - BP

where:

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

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

Eric Rozier has this analysis of heat sink mass:

#### nLIGHT

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

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

Power Conversion Efficiency
980-nm wavelength
Diode cooled toEfficiency
25°C
(Room Temperature)
70%
10°C76%
-50°C85%

### Attack Vector: Tactical Lasers

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

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

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

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

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

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

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

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

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

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

### Combat Mirror

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

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

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

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

### Mirror Armor

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

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

### Accuracy

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

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

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

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

### Turret

#### Airbourne Laser

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

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

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

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

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

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

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

#### Luke Campbell's Turret

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

### Optics

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

However, Ken Burnside says:

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

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

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

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

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

### Bomb-Pumped Lasers

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

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

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

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

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

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

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

θ = 2 * (w / l)

where:

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

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

1.22*L/l = 2*w/l

where:

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

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

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

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

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

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

#### Footfall

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

#### Impulsively Driven Laser

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

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

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

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

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

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

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

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

### Non-Bomb-Pumped Lasers

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

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

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

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

## Particle Beams

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

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

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

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

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

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

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

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

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

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

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

Dr. Geoffrey A. Landis had this to say:

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

θ = (5e-9 * Sqrt[BT]) * Sqrt[80/Bn]

where:

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

RT = Tan(θ) * D

where:

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

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

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

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

### Electrostatics, Neutrons, and Space Charge

While particles cannot travel at the speed of light, they can get close enough that it is hard to tell the difference. Unfortunately, particle beams do obey the inverse-square law.

Beams of protons or electrons suffer from "electrostatic blooming", meaning as the beam travels its diameter steadily expands which weakens the damage it inflicts on the target. This is because like charges repel and opposite charges attract. A proton beam is composed of like charges so the protons spread out like they all have bad body odor and halitosis.

A beam of neutrons does not suffer from electrostatic bloom since they have no charge, nor could they be deflected by charged fields. However this also means it is difficult to accelerate the neutrons in the first place. Charged particles can be accelerated by using charged fields. And if you discovered a new way to accelerate neutrons, chances are whatever it is could also be used as a defense.

Without electrostatic bloom neutron beams are only limited by "thermal bloom". Brett Evill says this will give a neutron beam an effective range of 10,000 km, but he doesn't mention the details of this estimate. Nelson Navarro is of the opinion that a science fictional heavy neutron beam could be produced by a science fictionally efficient method of breaking up deuterium nuclei.

Another problem is one shared by ion drives, the "space charge." If you keep shooting off electron beams you will build up a strong positive charge on your ship. At some point the charge will become strong enough to bend the beam. And the moment your ship tries to dock with another it will be similar to scuffing your shoes on the rug and touching the doorknob. Except instead of a tiny spark it will be a huge arc that will blow all your circuit breakers and spot-weld the ships together.

Don't try to neutralize the charge by firing off positively charged proton beams. John Schilling warns that space is filled with an extremely low-density, but conductive, plasma. You try to eject charge from your ship, and the ship itself becomes part of a current loop. Not only is the current flowing through the hull (or trying to) likely to cause problems, but all those electrons or protons being sucked in produce deadly X-rays upon hitting the hull.

### Bremsstrahlung

Powering up a particle beam to the point where it can cut armor is difficult. But there is another option: death by "Bremsstrahlung".

Consider the x-ray tube in your dentist's office. It is basically an electron beam striking a metal target. Now, what if the electron beam was a particle beam weapon and the metal target was the hull of the enemy spacecraft? A hypothetical observer on the far side of the ship could make a nifty x-ray photo revealing the skeletons of crew members dying in agony of radiation poisoning.

Please note that Bremsstrahlung only occurs with charged particle beams, it doesn't happen with beams of neutrons.

The particle beam weapons postulated for Star Wars missile defense were to disable missiles by damaging the sensitive electronics via radiation, not by carving the missiles into pieces. An APS directed-energy weapons study written for the Strategic Defense Initiative estimated that in order to disable an ICBM, a particle beam had power requirements between 100 and 1,000 megawatts, depending on range and retargeting rate.

Anthony Jackson says if you crank up your particles to a few GeV per nucleon they will be in the soft end of the spectrum of primary cosmic rays. Each particle will be highly penetrating, and you no longer need to actually focus the beam. Just apply a couple megajoules per square meter and everything dies (unless it's behind a huge amount of shielding or is basically operating at pre-microchip levels of automation. Neither is an option for a surface mounted weapon turret.). We are talking about a surface radiation level of over 500 grays. Such a cosmic ray beam would require armor with a TVT (for radiation purposes) peaking at 200-300 g/cm2.

Also note that if the particles are moving a relativistic velocities higher than, say, 90% c, you will have about the same energy release if the particles are matter or antimatter. In other words, it is pointless for relativistic particle beam weapons to use antimatter, with all the added complexity due to antimatter manufacture and storage.

Ships that expect to be fired upon by particle beam weapons would be well advised to add a layer of paraffin or other particle radiation armor on the outside of their metal hull, to prevent the beam from generating Bremsstrahlung with the hull.

### SDI Neutral Particle Beam

One of the more exotic weapon proposals that came out of the Strategic Defense Initiative was orbital neutral particle beam weapons.

As previously mentioned, charged particle beams suffer from electrostatic bloom, which drastically limits the range. It is possible to neutralize the beam by adding electrons to accelerated nuclei, or subtracting electrons from negative ions. This creates a neutral particle beam.

While this will eliminate electrostatic bloom, the neutralization process will also defocus the beam (to a lesser extent). As a rough guess, maximum particle beam range will be about the same as a very short-ranged laser cannon.

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

Most of the images below are of very poor quality, and many of the details are still classified. The scale of these weapons is unknown, but they are huge. Some are "folded", with a U-shaped section. This is a desperate attempt to cut the length in half. Scott Lowther guesstimates the entire weapon is on the order of 100 meters long or so.

## Atomic Rockets notices

This week's featured addition is SPIN POLARIZATION FOR FUSION PROPULSION

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This week's featured addition is NTR ALTERNATIVES TO LIQUID HYDROGEN