Kinetic Studies of Thermal Relaxation in Plasma.

Thermal relaxation of plasma is investigated in two cases: two dimensional magnetized plasma and three dimensional unmagnetized plasma. The generalized Lenard -Balescu equation and the Fokker-Planck equation are solved respectively. During the numerical calculation, forward time integration is used in both cases. 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. An initial waterbag distribution relaxes in time to its final Maxwellian in such a way that the change of the entropy becomes e^{-(t/t_ {o})^{2/3}} after the entropy reaches 60% of its final value for omega_{c} < omega_{p }. The relaxation time varies with the magnetic field strength as B^{-1/2} for omega_{c} < omega _{p} and as B^{2 } for omega_{c} > omega_{p}. An initial distribution which is a double Maxwellian distribution which has a high speed tail is found to relax as e ^{-t/t_{o}}. The 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. An initial waterbag distribution relaxes in time in such a way that the entropy changes as e ^{-(t/t_{o})^{0.7 }} after 0.2 Spitzer collision time. 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, which can be more or less described by a truncated Maxwellian distribution. In most cases the density and the energy of a system are conserved in the calculation to within 0.2%.