General relaxation model for a homogeneous plasma with spherically symmetric velocity space

TL;DR

The paper tackles closing the Vlasov-Fokker-Planck moment hierarchy for homogeneous plasmas with general, spherically symmetric velocity space. It develops a kinetic moment-closed model ($KMCM$) by combining the finitely distinguishable independent features (FDIF) hypothesis with King-function expansions (KMM0) and new $R$-function/$R$-integration formalisms to obtain closed-form transport and kinetic-dissipative terms. A temperature-relaxation model is derived, yielding a general relaxation frequency $\nu_T^a$ that captures nonlinear dependence on species parameters and reduces to the Braginskii near-equilibrium limit in shell-less cases. The framework provides a semi-analytical, semi-numerical approach to the VFP equation with potential as a benchmark for fusion and solar plasmas and can be extended to axisymmetric velocity spaces.

Abstract

A kinetic moment-closed model (KMCM), derived from the Vlasov-Fokker-Planck (VFP) equation with spherically symmetric velocity space, is introduced as a general relaxation model for homogeneous plasmas. The closed form of this model is presented by introducing a set new functions called $R$ function and $R$ integration. This nonlinear model, based on the finitely distinguishable independent features (FDIF) hypothesis, enables the capture of the nature of the equilibrium state. From this relaxation model, a general temperature relaxation model is derived when velocity space exhibits spherical symmetry, and the general characteristic frequency of temperature relaxation is presented.

Figures (1)

• Figure 1: Illustration of the amplitude functions multiplied by a factor $(1+\hat{u}_a^2)$ for $N_{K_a} \equiv 1$ and various normalized average velocity $\hat{u}_a$ in KMM0.