The power in a fusion reactor core is evidently governed by the fusion reaction rate. If only one type of fusion process occurs and if this process occurs at the

rate density Rfo with Q&, units of energy released per reaction then the fusion power generated in a unit volume is given by

With Rft, expressed in units of reacuons-m -s ana i^ft, in iviev per reaction, me units of the power density Рд, are MeV-m’^s"1 which can be converted to the more commonly used unit of Watt (W) by the conversion relationship 1 eV-s"1 = 1.6 X 10"19 W since 1 W = 1 J-s’1. For the case of a uniform power distribution the total

energy released during a time interval T in some volume V follows from Eq.(2.20) as

(2.21b)

That is, energy may be viewed as the area under the power curve while power may be interpreted as an instantaneous energy current.

The energy generated in a given fusion reaction, Qfu in Eq.(2.20), is the "Q — value" of the reaction, Eq.(1.15), and can be experimentally determined or extracted from existing tables; this part of the power expression is simple. However, the determination of the functional form of the reaction rate density Rfu is more difficult but must be specified if the fusion power Рд, is to be computed.

In order to determine an expression for the fusion reaction rate density, consider first the special case of two intersecting beams of monoenergetic particles of type a and type b possessing number densities Na and Nb, respectively, Fig. 2.3.

In a unit volume where the two beams intersect, the number of fusion events in a unit volume between the two types of particles, at a given time, is given by a proportionality relationship of the form

Rfu ж Na Nb Vr

where vr is the relative speed of the two sets of particles at the point of interest. This relation is based on a heuristic plausibility argument for binary interactions. Obviously, some idealizations are contained in Fig.2.3 and Eq.(2.22), such as particles of varying energy and direction of motion as well as the interaction of particles with others of their species not being accounted for, but will be considered in subsequent sections.

The proportionality relationship of Eq.(2.22) can be converted into an explicit equation by the introduction of a proportionality factor represented here by <7ab for a given vr:

The subscript ab and the functional dependence on vr, indicated in Gab(vr), is to emphasize that the magnitude of this parameter is specifically associated with the particular types of interacting particles and their relative speed. The common name for Oab(vr) is "cross section" and, since all the terms of Eq.(2.23) are already dimensionally specified, its units are those of an area. This parameter has been assigned the name "bam", abbreviated b, and defined as

lb = W’24 cm2 = 10’28 m2 • (2.24)

Figure 2.4 illustrates the cross section for a case of deuterium-tritium fusion. Note a maximum of a few bams in the vr = З X 106 ms’1 range in this figure.