## B26 Fusion power density

In order to understand which values of specific power can be expected from a fusion reactor and how they are related to plasma parameters, it is convenient to assume that the operating temperature is close to the optimal temperature Topt (i.e., the temperature corresponding to the minimum of the nO vs. T curve). The optimal temperature depends on the reaction chosen, on the gain Q, and on radial profile factors. Then electron density can be expressed in terms of the parameter beta ft (E{2^0 f\neT/B2}, with f{1 + E;n;/ne}, a factor of order unity depending on the fuel composition)

The values of ft achievable depend on the stability properties of the specific magnetic configuration considered and will be discussed in Section B.2.7. Note that expressing plasma density in terms of ft is correct as long as no additional stringent limits on plasma density are discovered (e.g., in tokamak operation, density is experimentally observed to reach a maximum proportional to average plasma current density).

From the above conditions, it is possible to determine fusion power per unit volume that can be produced in the form of neutrons and charged particles:

Pspec = n 2f2M£fuS = (ft£2/(2Mofi Topt))2f2<™>£fuS (B.26)

where f2{(n,/ne)(nj/ne)} is a coefficient related to fuel composition; and Efus the energy released in a fusion reaction. It is apparent that in order to maximize fusion power density, for a given reaction plasma density must achieve the largest possible value. From Equation (B.8) this can be accomplished both by maximizing the value of ft and by operating at large B.

For the sake of illustration, in Table B.3 the values of Pspec achievable by D-T and D-3He reactions are shown for three different values of ft and for B = 10 T.

If we compare the D-T and the D-3He reactions at the same value of (ftB2), it follows that the D-3He reaction has a specific power about two orders of magnitude

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