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

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 of 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 and non-equilibrium state. From this relaxation model, a general temperature relaxation model is derived when the velocity space exhibits spherical symmetry, and the general characteristic frequency of temperature relaxation is presented.