After reading about the Semyonov Antimatter Starship on Atomic Rockets, I was interested to see if KSPIE antimatter beam core-powered magnetic nozzles followed the .22 ΔV multiplication caused by the proportions of charged pions to uncharged pions and gamma rays in the annihilation products. When I tested it, I found that not only was the ΔV reduction not implemented, but also that the rocket produced too large a ΔV at too low a mass ratio for any antimatter rocket.

The test ship had a dry mass of 4427 kg and a wet mass of 4453. The fuel was equal parts hydrogen and anti-hydrogen. With the engine's stated ISP of 20200000, the ΔV should be 255,203 m/s (lower than a normal Tsiolkovsky rocket equation calculation, because only 22% of the annihilation products are usable in the magnetic nozzle). But the ship accelerated to 3,756,555 m/s. I calculated that to get this final velocity, the charged pions would need to have an exhaust velocity of 2,915,918,907 m/s, which is about 9.72 times the speed of light. Obviously, it is beyond the capability of a beam core antimatter magnetic rocket, or any antimatter rocket, to achieve FTL exhaust velocities, so it is obviously a bug.

I have done another one of these tests on a different KSP install, with similar results.

AntaresMC on Discord said that "The BC gives 100% power as CP instead of 1/4, So the mag nozzle gets 4x pions, YEEEEEY" and also suggested that the engine's anomalous use of LH2 could be to blame as well. I believe this should be fixed as soon as possible, both because it's impossible, and because it makes the AM Radiant drive pointless because the magnetic rocket that precedes it has 9.72 times the ISP.

Read my conversation with AntaresMC on Discord in #bugs on July 8, 2020 for more detailed information and screenshots.

The Beam Core Isp is based on this news article https://newatlas.com/beamed-core-antimatter-propulsion/22654/ which is based on this paper https://arxiv.org/abs/1205.2281

The main finding is that effective exhaust speeds Ve ~ 0.69c (where c is the speed of light) are feasible for charged pions in beamed core propulsion, a major improvement over the Ve ~ 0.33c estimate based on prior simulations.

That increased Ve of .69c was already accounted for in my calculations as the stated ISP of 20200000. The problem is that the engine outperforms its stated Ve by about 11 times. I'm not very knowledgeable on special relativity, but based on some very basic calculations, I found that reletivistic effects (assuming .69c was a "real" value and not a classical one like I used) only boosted the Ve to the equivalent of .87c, not enough to account for the final ΔV of my test ships.

I'm not contesting the .69c Ve, only that the engine is getting 11 times more than that in practice. And that's not even accounting for the fact that only 22% of the annihilation products are usable as propellant. There is still definitely a bug with how the magnetic nozzle uses fuel.

From Discord on July 10, 2020:

Caliperstorm: Following up on my tests that found that the beam core magnetic nozzle had an effective ISP greater than the speed of light, I decided to do some comparative testing against the AM radiant drive
[4:58 PM] Caliperstorm: It seems that the beam core magnetic nozzle does indeed outperform the radiant drive
[4:59 PM] Caliperstorm: Which makes no sense, considering it's only supposed to have an exhaust velocity of .69c and a propellant use efficiency of 22%
[5:01 PM] Caliperstorm: A beam core magnetic ship with a mass ratio of 1.005873052 gets a ΔV of 3,756,555 m/s
[5:02 PM] Caliperstorm: And a radiant drive ship with a greater mass ratio of 1.006004562 preformed worse, only reaching a ΔV of 3,673,823 m/s
[5:03 PM] Caliperstorm: Even though the AM radiant drive is supposed to be literally the best rocket engine possible