Antimatter Propulsion

Consider an antimatter propulsion device that uses the interaction between hydrogen (proton and electron ) and antihydrogen (antiproton  and antielectron=positron ).

The electron and positron interact as follows:

The interaction between the proton and antiproton is much more complicated and energetic:

(1046 Mev kinetic energy released due to masses difference) on the average, sometimes more and sometimes less pions. Assume that, on average, each pion carries 1/6 of the kinetic energy released or 173 MeV.

Then the pions decay as follows:

(135 MeV from the pion rest mass and 173 MeV from the proton-antiproton interaction for a total of 308 MeV; decay time at rest=sec);

(34 MeV kinetic energy from rest masses difference and 173 MeV kinetic energy from proton-antiproton interaction; decay time at rest=sec).  The muon on average only gets about 10% of this total available kinetic energy of about 207 Mev, or about 21 MeV. The rest (about 186 MeV) is carried out of the reaction chamber by the neutrino; see below.

So now we have:

(The muons and gamma rays carry about 700 MeV kinetic energy. About 744 MeV kinetic energy is carried away by the neutrinos; see below).

Then the muons decay as follows:

(About 105 MeV from rest masses difference and about 21 MeV from the pion decay; decay time at rest=sec). The electron/positron on average only gets about 40% of this total available kinetic energy of  about 126 MeV, or about 50 MeV. The rest is carried out of the reaction chamber by the neutrinos; see below.

So now we have:

(The electrons and gamma rays carry about 816 MeV kinetic energy; about 1048 MeV kinetic energy is carried away by the neutrinos).

If we assume that the  created in the last reaction do not escape the reaction chamber, and that they eventually find each other and annihilate:   .

So now we have:

(The gamma rays carry about 818 MeV kinetic energy; about 1048 MeV kinetic energy is carried away by the neutrinos).

So the total effect of the proton-antiproton interaction is, on average:

(About 818 MeV kinetic energy; 1048 MeV kinetic energy is carried away by the neutrinos).

The 12 neutrinos interact very little with each other or any other matter, so they escape out of the reaction chamber with about 55% of the available kinetic energy.

So the sum of the kinetic energies of the original electron-positron interaction (about 1 MeV) and the proton-antiproton interaction (about 818 MeV) is about 819 MeV.  About 55 % of the available kinetic energy is carried off by the neutrinos.  So, contrary to what one often reads in science fiction stories, antimatter propulsion devices do not have 200% conversion efficiencies (counting only the antimatter as the fuel since matter is assumed readily available). The efficiency is only about 90% according to this method of accounting; still a large amount of energy.

However, all of the above assumes that the pions and muons all decay inside the reaction chamber.  Some of them will have rather high velocities, which will increase their decay time and give them more time to escape the reaction chamber.  So surely no chamber can be designed to capture all of them. Also, not all final electron-positron pairs will interact in the chamber, but this is a small amount of energy.  Finally, not all gamma rays can be expected to transfer their energy to the reaction chamber before escaping.  So the efficiency will certainly be less than 90%; I would guess more like 75%.

However, on a trip in “empty” space, one would have to carry the propulsion matter as well as the antimatter, so the matter should rightfully be counted as fuel.  So my final guess for the real fuel efficiency is about 35-40%.