Relativistic Droplet Accelerator

In this blogpost, Matter Beam discuss a potential weapon that based of a concept meant for interstellar travel. The concept is that the particles in a particle beam are allowed to cool and condense, which in the concepts case is mercury, into metallic droplets that take longer to diverge that travel at near-light speed's.

The post then goes on to explore the damage and performance of such particles that do not go at relativistic velocities as in the scenario of what Matter Beam was talking about, such a feature was unnecessary.

However, I'm curious on the performance of such a weapon if it retained it's original velocities.

In short, what is the performance of a relativistic droplet weapon?

To narrow things down let's have three relativistic velocities and three particle source's:

Velocities in c

1. 0.500

2. 0.800

3. 0.900

Particle source:

1. Iron

2. Tungsten

3. Osmium

• Huh, that was suppose to be 'reality-check'. Commented Jul 30, 2022 at 7:27
• Reality check recently got turned to [internal-consistency] Commented Jul 30, 2022 at 17:10

2 Answers

TL;DR: don't think of this as a gun that fires bullets. Think of it as a neutral particle cannon that doesn't suffer from electrostatic blooming and has low rates of thermal blooming.

It will act like a beam of 145/625/1214 MeV nucleons, eg. highly penetrating radiation which is difficult to armor against at the low end and impractical at the high end, if you're in a spacecraft that needs to move around under its own steam.

Lets start with the easy bits first.

A droplet weighing 10-16 grams will carry the same kinetic energy regardless of what it was made of. Given the speeds involved, you do need to break out the relativistic kinetic energy equation, because the regular kind gets increasingly inaccurate... at .5c the Lorentz factor is already over 1.15, so the plain kinetic energy equation would be 15% out, and it only gets worse at higher velocities.

At .5c, the kinetic energy of the droplet is a mighty 14mJ (that's little-m milli joules). At .8c is is 60mJ and at .9c it is 116mJ.

That's small beans by itself, but you wouldn't be firing just one blob... you'd want a stream of these things and they'd hammer their way through the target. The firing rate depends on some many different variables I'm not going to even offer an example. It can be as much or as little as your needs, power supply and cooling capacity allow for.

At those speeds though you can't really treat the blobs like tiny bullets any more. At .5c, each proton has 145 MeV of kinetic energy, at .8c it is 625 MeV and at .9c it is 1214 MeV. Compare this to the nuclear binding energies of the nuclei involved: iron-56 has a binding energy of 8.8 MeV per nucleon, and is the highest of any nucleus. Clearly your blobs may as well be dense clouds of neutrons and protons and electrons in close proximity to one another from the point of view of the target. At .9c, your nucleons have more kinetic energy than their own mass... for a proton that's 938 MeV, meaning that they'd not be much more destructive even if they were made of antimatter. This also makes them fast enough to be considered HZE particles.

That in turn means you can look up existing research on effective shielding of galactic cosmic rays, which have a significant number of 1 GeV/nucleon HZE ions. One useful paper I've read in the context of shielding relativistic starships has been Radiation Hazard of Relativistic Interstellar Flight, and it does not have good news.

For velocities up to 0.3c, a titanium ‘windscreen’ of 1 – 2 cm can provide sufficient protection, however it becomes dramatically thicker with acceleration above 0.3c and reaches several meters at β = 0.9

(β here is proportion of lightspeed, eg. a β of 0.9 is the same as saying 0.9c)

Note that this is for the sort of particle flux you expect in interstellar space, eg. rates of nucleons per second per square centimeter, whereas each of your blobs has millions of nucleons.

It goes on.

Below β ~ 0.5, a water tank of several tens of centimeters in thickness would be sufficient to reduce radiation down to a safe level, however cruising speeds closer to the speed of light would require tens of meters of water shielding, i.e. many tons of additional load.

This should tell you that your deadly blob cannon is effectively a neutral particle beam that is neatly immune to electromagnetic countermeasures, and acts as highly penetrating radiation that can reach through several meters of solid material. Ships that aren't armored with many, many tonnes of ice and metal will find that the blobs pass more or less clean through. Many of the particles that make up each blob will interact however, producing a shower of secondary radiation and heating and imparting defects to the crystal structure of metals and semiconductors, and damaging cell components like DNA... your ship might not blow up or melt, but it will be incapacitated by radiation.

The radiation flux is going to be proportional to the firing rate of your gun, which you haven't established and I'm not going to guess, but you can reasonably assume that a beam from your blob cannon will melt or burn a track clean through a spacecraft at high power levels, and at lower levels it will destructively irradiate electronic components and at lower levels still lethally irradiate living things.

It doesn't matter what type of particle it is, and the micro-droplets won't impact like bullets due to their small size. The article describes a droplet weighing 10^-16 grams. Even at 0.9c, this only imparts around 0.003 Joules to the target. The target wouldn't feel the individual impacts.

The only purpose of the droplets, even in combat, would be to reduce beam spread. The weapon will otherwise behave like a normal particle beam: it will deposit a steady stream of energy to the target, as heat. The amount of heat depends not only on the speed of the beam, but also on the mass per second carried by the beam.

Also, note that even the reduction in beam spread is only really significant at very long distances, such as interstellar distances. The reason is that the stream needs time for the atoms to cool and condense into droplets. The article you linked, and the paper the article cites, don't go into details about how long that is expected to take, but it is a result of random motion of atoms in the beam, eventually bumping into each other to chemically bond. The faster the beam, the more widely spread the atoms will initially be, and the longer it will take for them to bump into each other and form droplets.

• By the time an atom of mercury moving at 0.9c cools from plasma, to gas, to liquid it will probably be far away from any like atoms. It will be a lonely atom flying along thru space, On its own trajectory, growing colder, turning to mercury ice. Wasnt there a song about something like that? Commented Jul 30, 2022 at 17:34
• @Willk The paper claims that a beam temperature of 45 Kelvin on exiting from the gun could be possible. It also says that "existing ion accelerators have typical beam temperatures of hundreds to thousands of degrees" which, if accurate, means 45 Kelvin might not be not too far off. So if you buy that, the beam would already be cool enough. The issue would be getting the particles close enough to each other to bond, when they'd initially be moving in random directions, mostly away from the beam line. I think it's safe to say that only a tiny fraction of the particles could ever form droplets. Commented Jul 30, 2022 at 17:43
• @Willk Maybe if you had multiple beams gradually converging on each other like the Death Star laser, that would help get more of the particles close enough to each other to form droplets. Commented Jul 30, 2022 at 17:45
• The whole point of the droplets as I understand is to reduce divergence. If you can reduce divergence with funky beams then just do that. Although the CGI for blobs of mercury appearing might be worth the hassle. Commented Jul 30, 2022 at 17:52
• @Willk The multiple beams wouldn't themselves reduce divergence - in fact they would be partly detrimental to it because they aren't all parallel. The purpose of multiple beams would be so that multiple streams of particles can intersect, giving a greater chance for particle-particle collisions to form droplets. Thinking about this, I believe you would have to have at least 2 beams for this to work, one positively ionized and the other negatively ionized. Otherwise, if there was only one beam of ionized particles, they would never combine due to having the same charges. Commented Jul 30, 2022 at 20:07