While the first generation of fusion reactors will evidently be d-t fueled, it is expected that subsequent generations of fusion reactors may use pure deuterium and possibly other "advanced" fuels as discussed in Sec. 1.4; one advantage thus gained is the elimination of the need to breed radioactive tritium. However, even though tritium breeding is not necessary, tritium handling will nevertheless still be required because it is one of the reaction products of d-d fusion, Eq.(1.21).

In comparison to d-t fusion, d-d fusion represents reactions among identical particles. The question of interest is therefore the following: given that for distinguishable ions, we have

a + b^() + () (7.29)

with

Rab= NaNb<GV>ab, (7-30)

what is the corresponding reaction rate expression for

a + a^() + () (7.31)

for the case of arbitrary reaction products? That is, what is Raa for this latter case? These considerations are important not only for d-d but also for t-t and h-h fusion.

Some thought suggests that the product NaNb in Eq.(7.29) represents the number of ways that members of the а-type set of particles can combine with members of the b-type set. As suggested in Fig.7.4, any one of the particles from the Na set could combine with any one from Nb and the total number of possible interactions is therefore equal to the number of (x, y) combinations with x and у identifying any one of the Na and Nb particles, respectively. Hence, all binary possibilities between these two sets are included in the product NaNb; that is, this product represents the totality of matrix elements in Fig.7.4.

For the case of particle indistinguishability, however, we have

a = b. (7.32)

Thus, with the total reactant density being Nj and as suggested by the extension of Fig.7.4, it is necessary to exclude the diagonal elements because a particle cannot interact with itself. However, the remaining Nj2 — N; combinations-that is the total number of matrix elements minus the number of diagonal terms — includes also the transposed pairs (x, y) and (y, x) which clearly represent the identical process and event. Hence, the total number of distinct reaction possibilities is only one half of this, giving therefore

N‘^Ni =}Ni(Ni -1)»-^- . (7.33)

The last approximation is, of course, essentially exact because Nj » 1 for all cases of general interest.

We write therefore for the reaction rate density among identical particles

Raa=<^>aaIY (7-34)

where Na is the total number of indistinguishable ions per unit volume; this number differs by a factor of 2 from the case of distinguishable fusing species, Eq.(7.30).