Extended relativistic kinetic model composed of the scalar and two vector distribution functions: Application to the spin-electron-acoustic waves

Abstract

Detailed deterministic derivation of kinetic equations for relativistic plasmas is given. Focus is made on the dynamic of one-coordinate distribution functions of various tensor dimensions, but the closed set of kinetic equations is constructed of three functions: the scalar distribution function, the vector distribution function of dipole moment, and the vector distribution function of velocity (or the dipole moment in the momentum space). All two-coordinate distribution functions are discussed as well. They are presented together with their limits existing in the self-consistent field approximation. The dynamics of the small amplitude spin-electron-acoustic waves in the dense degenerate plasmas is studied within the kinetic model. This work presents the deterministic approach to the derivation and interpretation of the kinetic equations. So, no probability is introduced during the transition from the level of individual particles to the collective functions. The problem of thermalization is not considered, but we can see that the structure of kinetic equations is kept for the system before and after thermalization. Hence, the kinetic equations can be used to approach this item.