where the mass defect is 0.048 x 10 kg per each He atom formed, converting about 0.38% into energy with a yield J = 3.45 x 1014J/kg. Note that only about 0.38% of the mass is converted into energy (the actual number depends on the specific fusion reaction, see Figure 8.3). Only in matter-antimatter annihilation does 100% of mass, for instance, that of a proton, p, and of an anti-proton, p", converts into energy. Accordingly, in this extreme case of fusion, the energy release is c2 per each kg, or J = 9 x 1016 J/kg if the value for c is simplified as 3 x 10 m/s. Even not going to such an extreme, on a per-mass basis, fusion yields more than 108 times the energy of gasoline burning with air (the reader is referred to [Chen, 1985] for a comprehensive textbook on fusion and its issues).
These striking numbers, and the relative abundance of hydrogen and deuterium on Earth (deuterium atoms constitute 2 x 10 ~4 of all terrestrial hydrogen atoms [Harwit, 1973, p. 257]) have motivated fusion research since the US Matterhorn Project of the 1950s. The mass defect in fusing hydrogen is still minuscule, but greater by a factor of 4-5 than fissioning uranium or plutonium. The half-century funding of fusion for power generation rides on the hope to extract this energy, starting from the deuterium already present in a small but significant percentage in seawater.
The ultimate energy source is clearly total, 100%, conversion of mass via annihilation, not just a percentage of order 0.3 or 0.4 [Morgan, 1982; Forward, 1985]. Of course this energy would not be necessarily released in the most convenient form for propulsion or power. It may consist mostly of energetic particles, including gamma-rays, for instance. Direct thrust from the momenta of these particles would be very
small; the alternative, thermalizing the energy of mass particles or photons in a useable device would certainly be a major technology problem; however, the experience gained in fusion physics could help.
Based on the considerations made, the large energy density of fusion suggests Isp could be large as well, in particular when no inert propellant is added to the fuel injected inside the fusion reactor, and this is indeed what Figure 8.4 predicts. Assuming the numbers shown are realistic in a conceivable future, it is worth estimating their effect on length of stellar or QI missions. In doing such estimates the trade-off between Isp, F and the overall power and mass demand of the propulsion system are central issues. Just as important is the impact of Isp on the duration of QI and stellar missions.
8.5.1 Mission length with Isp possible with fusion propulsion
An instructive exercise is to see what might be the effect on stellar trips of performance enabled by fusion energy. In [Borowski, 1987] missions at constant thrust F are examined to gauge these effects. A constant thrust mission is different from a mission at constant acceleration, because the mass of the ship decreases with time; its convenience as a yardstick lies in the fact that solutions are analytical. In fact, using this strategy, the round-trip time tES to go from Earth to a star, e.g., Proxima Centauri, turns out to be
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