We had previously noted that d-t fusion involves radioactive tritium as a fuel and high energy neutrons as reaction products; the former poses problems of radiological safety because tritium diffuses readily, while the latter leads to difficulties of first-wall endurance, shielding and induced radioactivity. Similarly d-d fusion produces both tritons and neutrons, e. g. Table 7.1.

From an examination of the temperature dependence of sigma-v, Fig.7.5, we note that of the five most readily attainable fusion reactions, only

d + h —> p + cc, Qdh= 1 MeV (7.48)

does not involve neutrons or tritons. For this reason, d-h is often called an attainable "clean" fusion reaction.

As suggested in Fig.7.5, the maximum <Gv>dh occurs at temperatures higher than the maximum for d-t fusion, requiring therefore higher reaction temperatures. In addition, at higher temperatures-as well as for reasons of a higher proton number in helium than in hydrogen-bremsstrahlung radiation is

d+ —» n (14.1) + a (3.5)

t +1 —» n (5.0) + n (5.0) + a (1.3) Vj: h —> p (5.7) + a (1.3) + n (5.1) d + d —» h (0.8) + n (2.4)

d+*h —> a(3.7) + p (14.6)

hTh -> p (5.7) + p (5.7) + a (1.4)

Table 7.2: Characteristics of the general d-d initiated fusion linkage processes. (Particle

Energies in brackets, in MeV.)

more severe.

Further, there exists the question of an adequate helium-3 supply. It is known that 3He is scarce, occurring with a natural abundance of 3He/(3He + 4He) = 10’6. An existing supply of tritium, however, eventually produces helium-3 by nuclear decay

t —> h + /З’ , tin = 12.3 years. n

with Ti/2 denoting the half-life of tritium. In addition, one may conceive of a d-d fusion reaction so that the helium-3 produced via

d + d —» n + h (j 50)

could serve as a helium-3 fuel source. However, a most significant source of this terrestrially scarce fusion fuel has recently been identified in lunar rock samples. It appears therefore that 3He could be mined in sufficient quantity on the moon’s surface and transported to the earth under energetically favourable conditions of reaction (7.48).

The designation of d-h as a clean reaction needs to be somewhat tempered because of the potential for unclean side reactions. That is, while the principal reaction proceeds according to

d + h—>p+cc, Rdh=<‘<^s/>dh N d N h » (7-51)

the existence of a deuteron population Nd will evidently enable the following triton and neutron producing reactions to occur simultaneously:

In order to emphasize some essential concepts involving multi-stage low temperature reactions, we first consider the following general reaction process involving arbitrary а-type and b-type particles:

cl + b —> ^ c + d. (12.7)

Here, the formation of the intermediate (ab) comes about as a result of a binary collision process and this intermediate is subsequently transformed by a decay process. Thus, though the same straight arrow symbol is used for the formation and decay processes in the reactions of Eq.(12.7), the two constitute distinctly different physical phenomena.

We introduce a reaction parameter каь for the formation of the intermediate species (ab) in reaction (12.7) so that the rate density of formation of the new species (ab) of density Nab is given by

R+ab = KabNaNb ■ (12.8)

Thus, if this formalism is applied to the d-t fusion process, we can equate = <cv>dt.

The decay of (ab) in reaction (12.7) is equivalent to the process of radioactive decay of an (ab) particle of density Nat>- Thus, the decay rate density can be characterized by a mean lifetime 1/А, аь for the intermediate, giving therefore

R-ab = XabNab • (12-9)

By inspection of the reactions in Eq.(12.7), the rate equations for the various particles a, b, ab, c and d in terms of their densities Na, Nb, Nab, Nc and Nd are given by the following:

dNa

dt

dNb

dt

With the imposition of initial conditions for each of the reacting species, the dynamical description of reaction (12.7) is thus fully specified. Note, however, that these equations are nonlinear and also display some redundancy.

The above characterization will now be used to provide a reduced dynamic description of the muon-catalyzed d-t fusion process. As an initial simplified case, if muon decay and its parasitic loss by alpha capture are ignored, then a typical muon-catalyzed chain would be written, with x in the reactions of Eqs. (12.3) replaced by p, as

(12.13)

where is the muon decay constant. The reaction shown here represents the

dominant processes involved in muon-catalyzed d-t fusion. However, a number of additional reactions are possible as we display in Fig. 12.2.