Analysis of the Relaxation Process using Non-Relativistic Kinetic Equation

We study the linearized kinetic equation of relaxation model which was proposed by Bhatnagar, Gross and Krook (also called BGK model) and solve the dispersion relation. Using the solution of the dispersion relation, we analyze the relaxation of the macroscopic mode and kinetic mode. Since BGK model is not based on the expansion in the mean free path in contrast to the Chapman-Enskog expansion, the solution can describe accurate relaxation of initial disturbance with any wavelength. This non-relativistic analysis gives suggestions for our next work of relativistic analysis of relaxation.Comment: 18 pages, 14 figures, accepted for publication in Prog. Theor. Phys

Evolutionary Conditions in the Dissipative MHD System Revisited

The evolutionary conditions for the dissipative continuous magnetohydrodynamic (MHD) shocks are studied. We modify Hada's approach in the stability analysis of the MHD shock waves. The matching conditions between perturbed shock structure and asymptotic wave modes shows that all types of the MHD shocks, including the intermediate shocks, are evolutionary and perturbed solutions are uniquely defined. We also adopt our formalism to the MHD shocks in the system with resistivity without viscosity, which is often used in numerical simulation, and show that all types of shocks that are found in the system satisfy the evolutionary condition and perturbed solutions are uniquely defined. These results suggest that the intermediate shocks may appear in reality.Comment: 13 pages, 4 figures, accepted for publication in Prog. Theor. Phy