Analysis of the Relaxation Process using Non-Relativistic Kinetic Equation

TL;DR

This paper analyzes the relaxation process using the BGK kinetic model, solving the dispersion relation to understand macroscopic and kinetic mode relaxation, providing insights for future relativistic studies.

Contribution

It offers an exact solution to the dispersion relation of the BGK model, enabling accurate analysis of relaxation across all wavelengths without mean free path expansion.

Findings

Solution describes relaxation of initial disturbances at any wavelength

Analysis distinguishes between macroscopic and kinetic mode relaxation

Provides groundwork for future relativistic relaxation analysis

Abstract

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.