On alfa-particle heating of a thermonuclear plasma

The theory of the slowing down and thermalization of alfa-partides created in and slowed down by a plasma considered as an undisturbed thermal bath is re-examined. The considerations are limited to a homogeneous, isotropic plasma. Also the alfaparticles are considered as a density-wise negligible component of the plasma. Under these circumstances, all essential parts of the theory can be studied analytically. Thus all standard approximations can be studied with precision. However, the conclusions do not differ from numerical results earlier obtained by numerous authors. In this sense the present paper must be considered as a review based on analytical methods.

The standard approximations referred to are such as the neglect of the variation of the Coulomb logarithm with velocity, the influence of quantum-mechanical effects, the significance of the impact parameter cut-off (the Debye length), and the assumption of a Maxwellian plasma. Some of these effects have been examined analytically by other authors. However, the present work shows that the Fokker-Planck equation can be solved without the aid of computers for the simplest set of standard approximations. The result thereof is a determination of slowing down rates and rate of growth of energy spread and thereby thermalization of the alfa-particles.