Consider an antimatter propulsion device that uses the
interaction between hydrogen (proton and electron ) and antihydrogen (antiproton and
The electron and positron interact as follows:
The interaction between the proton and antiproton is much
more complicated and energetic:
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
(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
(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
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%.