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

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