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Originally Posted by Anthony
To get a lightsail up to 0.1c requires 4.5e+15 J/kg (of spaceship mass), divided by the efficiency of your photon source; for an antimatter-pion drive, at the quoted Isp of 0.69c, requires 7e+15 J/kg, divided by the efficiency of your antimatter production.
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I trust you meant to say exhaust velocity, and the rest of the figures are correct.
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The efficiency of light sources can plausibly exceed 10% (90% for a klystron, though that forces use of long wavelengths and extremely large focusing elements), even extremely optimistic assumptions on antimatter production are on the order of 0.01%, so we're dealing with 3-4 higher orders of magnitude.
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Energy, yes, but what about power? The energy to drive the lightsail has to be delivered continuously at full power and at a single point while the ship is accelerating. The energy required to produce antimatter can be spread over as long a time and as many sources as the storage technology permits and delivered to the ship in packages.
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In addition, the above AM-pion rocket requires storing 0.078 kg of antimatter per kg of ship mass, which is a storage efficiency we have no reason to think is possible.
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This argues for a lower final velocity, but doesn't invalidate the design altogether. What is the effective storage density implied by
Spaceships?
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These are some pretty challenging numbers, but compared to the AM-pion they're trivial.
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A primary advantage of the antimatter pion rocket over lightsails is that once launched it is self-contained. Both technologies require a strong social organization to build and maintain the supporting infrastructure. The rocket needs an enormous investment up front, but carries all that investment with it (in the form of reactants) when it departs. The lightsail, however, needs constant attention throughout the acceleration phase: if there is a breakdown in the supporting social network or simply a loss of interest, the project fails.
Moreover, investing in the infrastructure to produce the required quantities of antimatter pays immediate benefits, in the form of less-energetic antimatter reaction drive options. A network of lasers or masers to drive a lightsail is less flexible overall, and again will be tied up throughout the acceleration phase rather than becoming fully available immediately upon departure.
Social engineering requirements may favor an antimatter rocket over a lightsail, even given the differences in efficiency.