The history of tritium accumulation in the breeding blanket and its eventual extraction for recycle to the fusion reactor core is of paramount importance. Consider then a unit volume in the blanket in which tritium gains and losses occur:

(14.23)

The gain-rate is clearly proportional to the rate of neutron production in the core so that, in view of the preceding section, we write

R+t = Rne., = Ct Rdt • (14.24)

Tritium removal in a unit volume of the breeding blanket occurs by radioactive decay and extraction:

• (14’25)

Here, the radioactive decay component is

and the extraction rate is taken to be a constant fraction of the tritium in the blanket:

Here xlb is the mean residence time of the tritium in the blanket. Hence, the dynamical equation for the tritium inventory in the blanket, Eq.( 14.23), is therefore

where an equivalent time constant for tritium in the blanket xb had been defined as

— = A,+ — . (14.29)

With Rdt, C, and xb as constant, Eq.( 14.28) is in a standard form amenable to solution given an initial tritium density in the blanket. Suppose that start-up of a fusion reactor is of interest so that N, ib(0) = 0, then the solution of Eq. (14.28) is

NtM(t)=CtRdtzb(l-eM. (14.30)

The substitution Rd, = Pdt/Q dt renders the tritium accumulation in the unit volume of the blanket particularly evident.

The mean residence time of the tritium bred in the blanket, x, b of Eq.( 14.27), now appears as an important operational parameter. For cases where T,,b is short relative to the inverse tritium decay constant, i. e., x, b « 1/A,, or, alternatively, very long, i. e., x, ib » 1/?ц, a most distinct tritium accumulation and equilibrium concentration in the blanket results, Fig. 14.5. The asymptotic quantity of accumulated tritium is thus directly proportional to the power and the time constant xb.

Some numerical experimentation with Eq.( 14.30) will show that it may take decades for the bred tritium to approach the equilibrium value Nt b(°°). It may also be desirable to introduce either continuous or periodic removal of the tritium while its accumulation is still small; we also illustrate this periodic batch removal of the tritium in Fig. 14.5.

Fast Tritium Extraction (xt b «1/XJ