as shown by the complete solution for V

V2 2 2a2

This solution is plotted in Figure 7.6 for three different Mp/m ratios (1,000, 10,000 and 100,000) and also for the special case Mp = 0. For clarity, the three curves for nonzero Mp have been plotted after scaling them by 10. Note that V may become comparable to c only for a close to 1. Conventional fission processes occur with much lower mass conversion, of order 10- : a typical value of a for 235U fission is 9.1 x 10-4. Adding propellant, that is, adding Mp, the velocity (and Isp) drops rapidly. However, if the reactor must work at reasonable temperature and produce significant thrust, propellant must be added, and one must accept lower Isp, a necessary compromise. The Mp constraint explains why NTR tested in the past never reached Isp > 900 s or so. Fusion may occur at slightly higher a, of order 0.003 or 0.004 (see Chapter 8). Only complete matter-antimatter annihilation proceeds with a = 1, and the theoretical limit speed becomes c.

The special case of Mp = 0 means that all the energy developed by fission ends as kinetic energy of the fragments: the work point of the engine is on the upper curve and V (or Isp) is maximum for a given a. Conceptually this means fission products themselves are the propellant, ejected "as they are'', with all their kinetic energy, and perfectly collimated. Such ultimate propulsion strategy has been proposed at the Lawrence Livermore National Laboratories to maximize Isp. Thrust is modest in this strategy: the mass of fuel fissioning per unit time is naturally low, of order of

(1)kg/h for large power reactors; a 1-GW rocket with Isp = 105s would produce thrust of order 1,000 N.


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