Optimizing a relativistic anti-personnel weapon

Question

Let's say you have a technology that lets you build a gun that can accelerate a mass up to 145 grams to a speed of 0.90 C. (Don't worry about the plausibility of this technology) The projectile can be made from any matter with a density between that of a baseball (0.026 lb/in^3) and uranium (0.683 lb/in^3). As is demonstrated by the popular relativistic baseball thought experiment, such a technology cranked all the way to maximum would be great for leveling cities, but not so good for shooting a person standing a few feet away.

What is the ideal mass, shape, and material for the projectile be able to meet the following specifications?

1. It must not significantly risk the life of the shooter or innocent bystanders anywhere within 3 ft of the projectile's path or impact point.
2. It must not significantly risk incapacitating or injuring the shooter or innocent bystanders anywhere within 10 ft of the projectile's path or impact point.
3. It must do maximum damage to the target following the above specifications.

Answer 1

You can shoot a relativistic speed particle at a person. You can do it with intent to cure.

Evolution of Carbon Ion Radiotherapy at the National Institute for Radiological Sciences in Japan

The HIMAC is built on an area of about 120 × 65 m2 and houses the synchrotron which consists of ion sources, a linear accelerator cascade made of a radiofrequency quadrupole (RFQ) and an Alvarez linear accelerator (that can accelerate ions up to 6 MeV/u), dual synchrotron rings (which accelerate ions to 73% the speed of light), and independent horizontal and vertical high-energy transport beam lines which deliver the accelerated carbon ions to three treatment rooms with fixed ports: room A (vertical), room B (vertical and horizontal) and room C (horizontal) (Figure 3). In addition to these vertical and horizontal ports, the patient can be immobilized in the supine or prone positions with additional degrees of freedom provided by up to 20–30° tilt angle of the treatment couch.

How much punch does a carbon ion pack? I used https://www.omnicalculator.com/physics/kinetic-energy

0.72 * speed of light = 215850569 m/s Carbon atom = 12 atomic mass units kinetic energy = 0.000000000464202 joules.

How about a bullet?

4 gram bullet 1000 m/s kinetic energy = 2000 joules

Working backwards, a mass of 0.0000000001 grams at 215850569 m/s = 2329 joules. Close enough for WB stack.

How big is this projectile? Let us keep it made of carbon.
A mole of carbon weighs 12 grams. It contains Avogadros number of carbon atoms = 6.022 X 10^23) atoms. So 1 gram contains 5.0183333e+22 atoms and 0.0000000001 grams contains 5.0183333e+12 carbon atoms.

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So to have the kinetic energy punch of a bullet, your relativistic projectile would be pretty small. It seems like something with that much kinetic energy would keep on going out the other side, yet those 0.72c carbon ions are used to treat tumors. How do they jigger it so the carbon ions deposit their kinetic energy into the tumor and not out the other side? This is the cool thing about particle radiation as used to treat cancer: you can determine the penetration depth by adjusting the charge of the particle. Charge slows the particle down via interactions with the substrate, and most of the energy is deposited when the particle is almost at a standstill.

In my mind, the use of charge on a particle makes particle beams possible in an atmosphere. Obviously they are possible if they are being used to cure people of cancer! I suspect but do not know that the ability of charge to slow a moving particle decreases over a certain mass. For offensive use, a stream of individual ions with known charge and a sum of the desired kinetic energy might make more sense.

Unlike a bullet this kinetic energy will be deposited as heat and radiation and so might not have the stopping power of a lead bullet with the same kinetic energy. I am not up for figuring out how much kinetic energy as heat it will take to incapacitate an opponent. If he survives the encounter, the radiation effect will be tough on him later from a cancer perspective.

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OK. Up for figuring out kinetic energy as heat to incapacitate an opponent. Referencing https://en.wikipedia.org/wiki/Joule. 1 joule will raise 1 gram (=1 ml) water by 0.24 C. So 2000 joules will raise 1 ml of water 480 C. If you could boil 1 ml of water within an opponent I think that would slow down your opponent. The question is precision. You particle will probably not drop off its energy with the precision you would have if you were doing carbon ion radiotherapy with everything fixed in place and close together. If that heat is spread out, the water in a body has a great ability to conduct away heat.

The cool think I was picturing was a particle beam like a hose. You would dial the charge up and down. You could dial the charge so particles would drop off energy 30 meters in front of you, which would cause the air to become incandescent flame. Then dial it forward so the flame beam disappeared into the building of interest. I envision dialing the beam out the other side and back.

I was inspired to write a short thing about such a beam. You can read it here. https://www.fictionpress.com/s/3342628/1/Particle-Beam

Answer 2

Nope - the impact is too strong

The problem with relativistic projectiles is that they're moving fast enough to impact the molecules in the air. And that split the atoms, which generates a wave of plasma and radiation, which spreads out in a sphere. In other words, any projectile moving at relativistic speeds with by nature generate a side effect. Reducing the mass of the projectile doesn't help with reducing the result of the explosion because the generated energy is coming from the split atoms, not the projectile itself.

So what if we reduced the surface area? Suppose we made the projectile a mono-atomic arrow projectile, which would reduced the number of split atoms. Well, that might help tone down the plasma and radiation, especially since air isn't exactly dense. Individual atoms don't release that much energy. (Link.) True, the split atoms might lead to a chain reaction, but hopefully the air isn't dense enough for there to be a problem. I don't have a simulator handy (but they exist in labs), so I can't guarantee that it will be able to go through the air without any side effects. (In fact, it probably will, but maybe it'll be survivable 10ft. away.) Not to mention that it'll go through the person and hit the guy behind him.

You can fiddle around with the projectile to make it a bit bigger for more resistance, I guess, and maybe keep it small enough to avoid the air, but then you run into another problem. The problem here is that while air isn't dense, people are dense. People are very dense. (Insert joke here.) Even a monoatomic arrow projectile would impact a very large amount of atoms in a human, and the tight grouping of atoms in human means that the split atoms would lead to chain reactions. In other words, any relativistic projectile that hits a human has the potential to turn said human into a nuclear bomb. Unsurvivable, yes. Not significantly risk the life of bystanders 10ft. away from the impact point, no.

Answer 3

To meet the requirements you need to use very much lower velocities - the interaction with the atmosphere is simply going to be too dramatic (it destructive) at anything like relativistic speed.

Ideally you want a kinetic projectile which will be as aerodynamic as possible in air and not at all aerodynamic in flesh - a hollowpoint. dumdum or whatever which will change shape on impact and dump all its energy in 15cm or so of watery material and not overpenetrate.

I don't think anyone knows what impacts in the 10-100 k m/s regime look like but I suspect this will be the sweep spot - anything faster will be so tiny and will tend to zip through like a needle.

Answer 4

Once the bullet leaves the barrel of your gun, it has to sweep out a cylinder of air between the gun and the target. Air's about a thousand times less dense than lead, but by the time a 1cm long bullet has swept out a 10m cylinder it will have had to pass through approximately its own mass in air. Initially it will, in fact, collide with air particles, because it has a big fat cloud of electrons that will readily interact with air molecules. These will get blown off pretty quickly, hopefully leaving behind the nuclei which will be much more compact and will be able to travel much further before colliding with something

Each collision has so much energy that even nuclear binding forces are kinda negligible so you can easily end up with all sorts of interesting effects like fusion and fission as well as plain old deflection. The projectile has a lot of momentum, but those air atoms are still going to impart a small direction change to the bullet atoms. The bullet will be ablated away from the tip backwards, and the ablation will produce an expanding cone-shaped region of hot, bright plasma. It'll be filled with high-energy electrons, so it'll be a good source of beta radiation and x-rays, neither of which are good for the shooter or bystanders.

The projectile will sweep all the air away from in front of it, but will be travelling so fast that there's not really much time for the air to refill its wake before the bullet hits its target (or is ablated away). It might look a bit like a straight lightning bolt, and be pretty loud into the bargain when than channel collapses. Incidentally, a lightning bolt only carries the energy of a 5-50 microgram projectile travelling at .9c. Pretty weedy, eh?

By the time it reaches its target the projectile will be, at best, a dense blob of plasma, with some proportion of the nucleons it started out with. These particles don't "hit" the target in the sense of two solid objects hitting each other, but instead eventually get around into interacting with the target's atoms. The path lengths of heavy ions at .9c is a complex matter, but it will almost inevitably be longer than the target is thick. Overpenetration is therefore practically guaranteed. If your projectile is so small and light as to (hopefully) reduce the chance of this overpenetration, it will likely have insufficient mass and momentum for enough of it to make it to the target.

As the heavy ions decelerate at the target they'll release their kinetic energy by ionising and displacing atoms of the target, and by bremmstrahlung radiation. If the target is behind, or in front of, or carrying (or contains) dense metal components, this can result in some high-energy xrays being emitted, bad for bystanders and nearby scenery.

It isn't clear quite how much of the energy of the projectile will be left in the target as heat, but even 1-10% of a microgram-scale projectile will be enough to make them go bang with considerable force. The kinetic energy of a mere 20 micrograms at .9c is equivalent to the yield of a tonne of TNT. Your projectile would have to be nanogram scale in order not to produce problematic overkill.

Reducing the size of the projectile to limit overkill and radiation effects means your gun more and more closely approximates a GeV particle beam. Such weapons are a bit rubbish in air as they're too easily attenuated which limits their range and still releases hazardous radiation along their beam track. That's why the SDI program only considered them for use in a vacuum. Just use a laser, railgun or coilgun. You know it makes sense.

So, to recap:

It must not significantly risk the life of the shooter or innocent bystanders anywhere within 3 ft of the projectile's path or impact point.

It must not significantly risk incapacitating or injuring the shooter or innocent bystanders anywhere within 10 ft of the projectile's path or impact point.

The shooter can wear suitable protective gear to protect them from flash burns, x-rays and beta radiation. Bystanders cannot, but I suppose there's a reasonable chance that they'll survive and might not even suffer acute radiation sickness.

Anyone near the "impact point" as much as there can be such a thing, is probably hosed though. They'll end up in a (relatively diffuse, admittedly) plasma fireball and then the target will go bang with probably the force of a hand grenade, if not much more. They have a good chance of receiving a serious dose of x-rays, too. So this probably can't be achieved.

It must do maximum damage to the target following the above specifications.

Looks like damage is easy enough, but a gun which avoids the problems above probably can't actually shoot a target at anything other than point-blank range.