Relaxation model for a homogeneous plasma with spherically symmetric velocity space

TL;DR

This paper develops a novel relaxation model for homogeneous plasmas with spherically symmetric velocity space, derived from the Vlasov-Fokker-Planck equation, encompassing classic models as special cases and not relying on near-equilibrium assumptions.

Contribution

A new closed-form relaxation model for homogeneous plasmas using hypergeometric functions, unifying several classical plasma models without near-equilibrium assumptions.

Findings

Model includes two-temperature and thermodynamic equilibrium as special cases

Derivation of the zeroth-order Braginskii heat transfer model

Provides a nonequilibrium plasma modeling framework

Abstract

We derive the transport equations from the Vlasov-Fokker-Planck equation when the velocity space is spherically symmetric. The Shkarofsky's form of Fokker-Planck-Rosenbluth collision operator is employed in the Vlasov-Fokker-Planck equation. A closed-form relaxation model for homogeneous plasmas could be presented in terms of Gauss hypergeometric2F1 functions. This has been accomplished based on the Maxwellian mixture model. Furthermore, we demonstrate that classic models such as two-temperature thermal equilibrium model and thermodynamic equilibrium model are special cases of our relaxation model and the zeroth-order Braginskii heat transfer model can also be derived. The present relaxation model is a nonequilibrium model based on the hypothesis that the plasmas system possesses finitely distinguishable independent features, without relying on the conventional near-equilibrium assumption.