We next consider a pulsed d-t fusion reactor for which, as for the previous case, tritium is supplied externally and ideal confinement in the fusion core exists. This pulsed bum mode can well be characterized by three stages of tritium injection, tritium bum, and tritium purging, Fig. 14.2. During injection and purging, some of the tritium will be lost by particle transport into the containment components while during the bum, tritium is destroyed by the fusion process. It is the bum stage that is of most interest to us.

As for the preceding continuous-bum model, we begin with a dynamical description during the bum time Ть — A rapid pulse implies a rapid change in plasma temperature so that sigma-v during the bum cannot be taken to be a constant and we will therefore represent this time dependence by <crv(t)>dt. The consequence of this is that the fuel inventory will vary similarly with time during the bum so that the time dependent reaction rate density Rdt is

R*(t) = Ndc(t)Ntc(t)<av(t)>dt. (14.15)

The dynamical equations for the fuel density in the core are simply

dNdc

-j^ = — Rds(t), (14.16)

at

and

dN

~-^- = — Rd,(t). (14.17)

dt

Note, here, the absence of any inflow-outflow terms during the bum time. The instantaneous d-t power in a unit volume at any time in the bum interval is

Р*(Ч = Ялтл = Nd c(t)Nt c(t)< ov(t) >dt Qdt. (14.18)

We cannot proceed further without a knowledge of the time dependence of <crv(t)>dt. Recalling the definition of this sigma-v parameter, Eq.(2.29) implies that <crv(t)>dt could be determined if the time variation of the deuterium and tritium velocity distributions were known. This may, in principle, be obtained from a detailed time dependent analysis of how the pulse-injection energy is transformed into fuel kinetic energy together with other concurrent energy

transformation processes. However, this analysis is both difficult and tedious, and falls outside the scope of our objectives here.

Still, even without a detailed knowledge of the pulse energetics, we can outline the dominant time variations of the tritium fuel. Consider then, at the beginning of a typical bum cycle, an injected energy pulse spread over a short time period relative to the fusion power pulse. Ionization occurs promptly and the kinetic energy of the fuel ions rises rapidly to initiate fusion reactions and thus triton destmction by fusion. The alpha particle fusion products may thereupon continue to heat the ions to sustain fusion power production. Eventually, a variety of power losses-leakage, radiation etc.-will cool the plasma until the power pulse can be considered terminated. We suggest some of the time variations for a typical pulse in Fig. 14.3.