An actual fusion reactor will evidently be associated with an external tritium-fuel stockpile, much as a fission reactor needs to have an assured external supply of fissile fuel. We depict such a system in schematic form in Fig. 14.6 where we also show the tritium flows and processes which will affect the inventory of tritium in the external stockpile.

Our preceding discussion involved the description of the tritium destruction rate in the fusion core as well as the tritium production rate and accumulation in the blanket. As suggested in Fig. 14.6, tritium bred in the blanket may decay or it may be extracted for deposit in the external stockpile; once in the stockpile, tritium may also decay, it may also be withdrawn for burning in the fusion core, or it may be lost by transport processes such as diffusion. The dynamical equation for the tritium in the stockpile is therefore

(14.31)

where the F(> terms are the flow rates suggested in Fig. 14.6.

The tritium supply rate to the stockpile may well be taken identical to the tritium extraction rate from the blanket so that according to Eq.( 14.27)

(14.32)

where N, b*(t) is the tritium inventory in the blanket at time t produced by neutron capture in lithium and T,.b is the mean residence of the bred tritium in the blanket.

The prompt removal rate of tritium from the stockpile should-for obvious reasons-be equal to the tritium destruction rate in the core:

f:,,x=r:,. (14.33)

Further, radioactive decay losses from the external stockpile are

(14.34)

Finally, for the present illustration, we assume that the various transport losses from the stockpile are a constant fraction of the inventory such that

= (14.35)

Substituting Eqs.(14.32) to (14.35) into Eq.(14.31) then specifies the dynamical state of the tritium inventory in the external stockpile as

.(a, +ex)N;jt). (изб)

dt Tub

A solution of this equation requires an examination of the various terms and an imposition of some reactor operational modes.

With Єх, C t, and Tt, b as system constants and also taking Rdt* to be constant, the time dependence of the tritium in the blanket Nt, b*(t) is given by Eq.(14.30). Under these conditions, Eq.(14.36) can be specified by the first order differential equation

dNl _ C, R’dtTb dt TtJ>

Here we have also shown an initial condition for the tritium in the stockpile at t = 0. This equation can be cast into the generic form

(14.39c)

While an explicit solution for the time dependence of the amount of tritium in the stockpile, NtjX*(t), can be obtained by solving the above inhomogeneous first — order differential equation, Eq.(14.38), we will find it more instructive to examine the differential equation itself; this will provide for a better understanding of how the various parameters influence the availability of this essential fuel.

Prior to start-up, the tritium in the external stockpile simply decays. Thus, at t=0, when the tritium inventory is Nt, x*(0) = Ntj0, an instantaneous withdrawal from the stockpile to the core takes place and gradual replenishment from the blanket to the stockpile is also initiated; the differential equation thus describes the slope of Nt x (t) at any point in time.

Within a sufficiently short time after startup, e. g. t = 0+, we find from Eq.( 14.38) that

implying that the tritium inventory will initially decrease at a rate dependent upon the magnitude of the initial tritium inventory and fusion reaction rate.

Further, for t sufficiently large, the central term of Eq.( 14.38) will vanish and hence

Slope of Ni(t) =A0-A2N*Joo).

(14.42)

with the general characteristic time variations of tritium suggested in Fig. 14.7. Note that a minimum may exist unless Ct(ib / xtjb) = 1 in which case a zero tritium inventory will be attained.

Time, t Fig. 14.7: Characteristic tritium stockpile inventory as a function of various system parameters.

Problems

14.1 According to Eq.(14.2), an inventory of tritium will become depleted but helium-3 (h) will be produced. This newly bred fuel could supply a fusion reaction based on the d + h —> p + a cycle. If tritium is thus an energy "debit" due to its decay, what is the corresponding energy "credit" for the production of helium-3 as a function of time?

14.2 Compute the Nt = Nd concentration in a fusion core generating 100 kW per litre for various temperatures from 1 keV to 500 keV.

14.3 Determine an explicit solution for Eq. (14.37).

14.4 Examine a self-sufficient tritium breeding fusion reactor such that NtjX—>0 as t—>°°.

14.5 How long, after start-up, until the tritium inventory in the external stocknile attains a minimum?