|MadSci Network: Physics|
In order to generate antimatter with an accelerator, you have to be able to produce photons with at least 1.022 MeV, which gives 511 keV for each particle in an electron-positron pair. Even then, the probability of pair production with such a low-energy photon is very small. Currently, the most effective antimatter producing accelerators generate something like 10^10 slow, trap-able positrons per second using a 100 MeV electron beam.
There are proposed accelerator schemes that hope to get 100 MeV or more acceleration in a meter or so. Let's be generous and assume new technology will allow not only a table-top system but a factor of one thousand improvement in the production rate over our current, building-sized machines - 10^13 positrons per second. Let's also be incredibly generous and assume you could trap and accumulate the positrons with perfect efficiency and hold them indefinitely.
If you start your antimatter engine when you are in free space, and you want to accelerate at 1 g so the occupants feel earth-normal gravity, my back-of-the envelope calculation suggests that you would have to annihilate about 2x10^22 positron-electron pairs per second per kilogram of mass in your ship, even assuming you could efficiently convert all of the energy into thrust. So, for every second of accelerating one kilogram, you would have to accumulate positrons for 2x10^22/10^13 = 2 billion seconds, just over 230 years (or one year with 230 table-top accelerators).
The nice thing is that IF you were able to get the positrons, that one second of acceleration would come from only a few micrograms of "fuel." Problem is, we are a long way from getting a few micrograms of antimatter in one place, or from holding even a small quantity for more than a few days. There were alot of generous assumptions and big IFs up in those last few paragraphs.
Antiprotons are heavier than positrons by a factor of two thousand, so in principle you would have to accumulate many fewer of them, but as a result of their mass they are also harder to create, needing at minimum a 2 GeV accelerator, and probably 200 GeV to do it at all efficiently.
I haven't even addressed the issue of the energy it takes to run all those accelerators (kilowatts of power at least for each machine), or to run the magnets that provide the fields for confining the positrons, or how you get thrust out of the gamma radiation in an annihilation. In the end, although antimatter is a highly efficient way of storing energy as far as mass is concerned, there are many, many, MANY orders of magnitude in improvements that will have to be made regarding antimatter production before it becomes a reasonable spaceship propulsion mechanism.
Keep trying. It was a long time after Leonardo da Vinci made his drawings of a flying machine before the Wright Brothers made one work.
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