Kinetic studies of thermal relaxation in plasma

The Lenard-Balescu equation is generalized for a magnetized plasma from the BBGKY hierarchy equation. The random phase approximation and the two time scale approximation are applied along with the neglect of essential 3-particle correlations. The generalized Lenard-Balescu equation is expressed in terms of binary collisions by the screened Coulomb force and the interaction between the individual particle and the collective mode. Weakly unstable cases which can be handled by quasilinear theory are contained in this treatment. The equation is solved numerically for a two-dimensional charged rod plasma with an external uniform magnetic field whose direction is along the charged rod. The thermal relaxation is measured by calculating the entropy of the system. Results are compared and agree qualitatively with ones from particle simulation. The Fokker-Planck equation is also solved numerically for a three-dimensional unmagnetized plasma. The diffusion and the friction coefficients are obtained. A multi-species plasma is studied. For a two-temperature plasma, the lower-speed portion of the hot plasma distribution overshoots, while the cold plasma is still relaxing to a Maxwellian. In both cases the slowing down of the relaxation rate is due to the relaxation times required for the filling of the high-speed tail