Effect of the Spatial Distribution of Plasma Parameters on the Operation of a Fusion Reactor

Abstract

The operation of a fusion reactor on a fuel alternative to the D–T (D–D, Cat–DD, D–³He, p–¹¹B, and p–⁶Li) requires a higher fuel mixture temperature and a longer energy confinement time in the plasma. It is shown that for a fixed fusion reaction power, an increase in the plasma parameters peaking reduces the power required for additional plasma heating. In addition, the peaking of the plasma parameters reduces the radiation loss in the plasma. All this softens the requirements to the operation conditions of fusion reactors.

APPENDIX

For the main five fusion reactions (D–T, D–D, Cat–DD, D–³He, and ³He–³He), the rate coefficient of the reaction with an error that does not exceed 10% as a rule for temperatures 0.086 keV < T < 862 keV can be written in form

$$\langle \sigma \nu \rangle {{10}^{{18}}} = {{10}^{u}}\,\,{\text{c}}{{{\text{m}}}^{3}}{\text{/s}}{\text{,}}$$

(A.1)

where

$$u = \sum\limits_{i = 1}^3 {{{a}_{i}}{{\theta }^{i}},} $$

(A.2)

θ = log₁₀T, temperature T is expressed in kiloelectronvolts, and log₁₀ is the decimal logarithm. Angle brackets indicate averaging over the Maxwell distribution. For the D–T reaction, formula (A.1) holds up to energy of 500 keV.

The values of coefficients a_i are given in Table 1.

Table 1. Values of coefficients a_i for formula (A.2)

The approximation was performed using the results from [31].

The power density released in the aforementioned reactions can be written in form

$$W = \alpha n_{e}^{2}\langle \sigma \nu \rangle \,\,{\text{W/c}}{{{\text{m}}}^{3}}.$$

(A.3)

Here, electron concentration n_e is expressed in the units of 10¹⁴ cm^–3, and the rate coefficient is given in the units of 10¹⁸ cm³/s. The values of coefficient α are given in Table 2.

Table 2. Values of coefficient α for formula (A.3)