The use of only deuterium as a fusion fuel introduces several important considerations. For temperatures up to about 200 keV, the d-d reaction parameter sigma-v is substantially smaller (roughly two orders of magnitude) than it is for d-t fusion, Fig.7.5; hence, for equal particle densities and ion temperatures below about 200 keV, a d-d fusion reactor will possess a much smaller power density and hence will require a larger size for a specified total fusion power production. Note additionally that radiation losses tend to increase with higher temperature, thereby further contributing to problems of a viable power balance. Nevertheless, deuterium based fusion possesses some very appealing properties. For example, an important feature of the deuterium fueled reactor is that the products from d-d

fusion may fuse with the deuterium fuel and possibly even among themselves.

The primary d-d fusion reaction proceeds via two (almost) equally likely reaction channels

‘ t + p

h + n

where for notational simplicity, we use h = 3He. The bred tritium and helium-3 nuclei possess significant sigma-v parameters to fuse with the deuterium fuel, Fig.7.5. The reaction

d + t —> a + n (7.36)

will be dominant with

d + h —у (X + p

also taking place. In addition, there also exists the possibility of the reaction products to fuse among themselves to yield

t + t -» 2n + a (7.38a)

p + n + a

t + h^>

d + a.

Reactions involving reaction products are often called side reactions.

A complex system of linked reactions may possibly emerge. The following suggests a classification of d-d sustained reaction systems.

(a) PURE-D Mode

The idealized case of d-d fusion only is given by

d + d —> t + p (channel -1) (7.39a)

d + d —> h + n (channel — h) (7.39b)

which proceed at the rates

Rm = ~L<w >ddl, Qddt = 4.1 MeV (7.40a)

Rcuih = ~<(TV>dd, H. Qddh = 3.2 MeV (7.40b)

where the reaction Q-values are extracted from Table 7.1. Here, it is also essential to introduce the additional t and h subscript notation according to the channel designations of Eq.(7.39); values for <CTv>ddjt and <CTv>ddih are listed in Table C. l of Appendix C.

Further,

< ov >dd = < ov >ddl + < ov >dddl for which, to a very good approximation

< OV >dd, t °V >dd, h = у < OV >dd

at temperatures of common interest.

(b) SCAT-D Mode

The very large <CTv>dt parameter, Fig.7.5, suggests that for most of the temperature range shown, the bred tritium will be consumed almost immediately upon production while the bred helium-3 will not be burned so rapidly due to the smaller <ov>dh at these temperatures. This fusion reaction mode may therefore be represented as

(7.42a)

d + t —^ n + cc

d + d —> h + n (channel — h) .

Here the arrow suggests a reaction link. A summary reaction representation for this cycle is

5d^>2n + h + oc + p, QSCATD = 24.9 MeV (7.43)

providing Eqs.(7.42a) and (7.42b) occur at equal rates, i. e. Rddjt = Rdt so that

Ni

~Y«n>dd,,= NdN,<av>d, ■

This relationship implies

Nt _ 1 < >dd, t _ 1 < ov >dd Nd 2 <aw>dt 4 <ov>dt

and thus provides for triton fusion burn at a rate equal to its production rate. This fusion operation mode is often called the "semi-catalyzed-D cycle" (SCAT-D). By reference to Fig.7.5, the relative tritium concentration in the fusing plasma may therefore be small at low-to-medium temperatures but will increase for higher temperatures.

(c) CAT-D Mode

An examination of Fig.7.5 suggests that the fusing of helium-3 nuclei with deuterons is the next most likely nuclear reaction. This completes the catalysing process, hence the name CAT (catalyzed) cycle:

(channel -1)

d + t —> n + (X

d + d —> h + n (channel — h)

d + /i—>a + p

which is equivalent to

6d^>2n + 2a + 2p, QCATD = 43.2 MeV (7.47)

provided that the four reactions proceed at equal rates.

The exact sustainment of only one of the above specific d-d bum modes may in general be very difficult. The more general case is suggested in Table 7.2 where the connection reaction linkages will evidently vary with temperature and density.