A hybrid-kinetic model for high-β plasmas

A hybrid-kinetic model (Vlasov ions and drift-kinetic electrons) is developed to describe the equilibrium and stability properties of collisionless high-beta plasmas in arbitrary magnetic field configurations. No ordering of ion properties (such as ω/Ω_i and r_Li/L_⊥) is assumed, so the ions are described by the exact (unexpanded) Vlasov equation. The electrons are assumed to be strongly magnetized with ω/Ω_ɛ ∼r_Le/L_⊥=ɛ≪1, and the electron Vlasov equation is expanded in ɛ to give a drift-kinetic equation for f_e. Examples of linear screw-pinch equilibria are constructed to demonstrate the ease with which equilibrium solutions are found within this formalism. Also, it is shown that the hybrid-kinetic model correct to O (ɛ) includes physical effects which are important during the implosion and immediate post-implosion phases of high-density pinch experiments, where stability behavior is characterized by the fast time scale ω^-1_LH= (Ω_eΩ_i)^-1/2. In particular, a local dispersion relation is derived for the modified-two-stream and lower-hybrid-drift instabilities, which have characteristic growth rates of order (Ω_eΩ_i)^1/2 when ω²_pe/Ω²_e≫1.