Relaxation model for a homogeneous plasmas with spherically symmetric velocity space

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 hypergeometric ₂F₁ 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.