Anti-Matter Costs for Space Travel

References:

Antimatter Production for Near-term Propulsion Applications (Link to PDF)
By G.R. Schmidt, H.P.Gerrish, J.J. Martin, G.A. Smith and K.J. Meyer

Anti-matter Production Efficiency

The conversion of input energy into the rest mass energy of the antimatter can be expressed via the following equation:

η = Eout / Ein

Where:

η: Conversion Efficiency of the process.
Eout: Rest Mass Energy of the collected anti-matter. (1.79 x 1014 Joules for one gram)
Ein: Energy placed into antimatter production plant.

NOTES: A perfectly efficient antimatter production process (which is a practical impossibility, like 100% efficient energy conversion) would have a η of 0.5 due to the fact that in order to create an anti-proton, you have to create its standard particle counterpart.

Anti-matter Production Efficiency Examples

Present Day production facilities with an acceleration energy of 120 GeV and a collection ratio of 1:100,000 exist at such places as Fermilab and CERN. They have a overall η of 4 x 10-8 with a 50% wall plug efficiency factor. Producing one gram of anti-protons would require 4.5 x 1021 Joules – or 1.25 million terawatt hours (1,250 PW/h).

Near-Future production facilities with an acceleration energy of 200 GeV and a collection ratio of 1:20 are thought possible by NASA. They would have a overall η of 10-4 with a 50% wall plug efficiency factor. Producing one gram of anti-protons would require 1.78 x 1018 Joules – or 494 terawatt hours.

Far Future production facilities with an overall η of 10-2 would require only 1.78 x 1016 Joules, which breaks down as 4,944 gigawatt/hours or 4.94 terawatt/hours.

Magi-Tech production facilities with an overall η of 0.49 like Star Trek's antimatter production plants which simply “flip” normal protons into antiprotons via woo-tech would require merely 3.65 x 1014 Joules, which breaks down to merely 101.4~ gigawatt/hours.

Power Requirements in Plain English

To help clarify some of these numbers, here are some real world examples:

2008 World Power Generation (Complete): 19,103~ terawatt-hours.
2009 U.S. Power Generation (Complete):
3,953 terawatt-hours.
2009 U.S. Power Generation (Nuclear Only): 798~ terawatt-hours.

Antimatter Mission Examples (quick and dirty so far)

Slow Interstellar Exploration: (4.5 Light Years in 40 years – 30,000 km/sec delta V)

Single Stage Antimatter Beamed Core Rocket (80,000 km/sec ev): 51 metric tons of dry mass and payload, plus 24 metric tons of antimatter for an all up launch weight of 75 metric tons. 4.27 x 1023 J of energy needed.

Fast Interstellar Exploration: (4.5 Light Years in 10 years – 120,000 km/sec delta V)

Single Stage Antimatter Beamed Core Rocket (80,000 km/sec exhaust velocity): 51 metric tons of dry mass and payload, plus 179 metric tons of antimatter for an all up launch weight of 230 metric tons. 3.19 x 1024 J of energy needed.