Some problems in the kinetic theory of plasmas.

This thesis covers essentially two problems in the kinetic theory of plasmas. The first concerns the investigation of plasma oscillations in a constant electric field - a topic investigated by Akheizer and Sitenko as early as 1956 [1] More recently Stenflo [2] has considered the problem in which he replaces the collision integral of Boltzmann's equation by a Fokker-Planck term and a B.G.K. term. The dispersion relations derived by Stenflo contained a number of parameters the relative importance of which he did not clearly define. We have undertaken here a stability study of longitudinal oscillations of a weakly ionised gas permeated by a uniform electric field. A dispersion relation is formulated in terms of error-type functions and some computational studies are carried out for various plasma parameters of interest. The results are exhibited graphically in the form of Nyquist plots. The conclusions made by Stenflo and others regarding possible instabilities of the plasma needs modification, certainly in the context of a weakly ionised electron-ion gas. The second topic covered here concerns the transport theory of relativistic gases. This has received increasing attention in recent years [3,4]. Much attention has been devoted to calculating the first order relativistic effects on the transport coefficients. Up to now only the 'Maxwellian' model, investigated by Israel [3], has been considered. The method of attack is via the Chapman-Enskog approach. In this second topic we develop a more general approach to the problem by generalising the classical spherical harmonic solution of the Boltzmann equation to the relativistic case. The theory is applied to transport problems of fully ionised plasmas in the Coulomb field.