Kinetic description of linear theta-pinch equilibria

Equilibrium properties of linear theta-pinch plasmas are studied within the framework of the steady-state (∂ / ∂ t = 0) Vlasov- Maxwell equations. The analysis is carried out for an infinitely long plasma column aligned parallel to an externally applied axial magnetic field B_z^ext ê ₂. Equilibrium properties are calculated for the class of rigid-rotor Vlasov equilibria, in which the jth component distribution function f _j(H⊥, P_θ, υ ₂) depends on perpendicular energy H⊥ and canonical angular momentum P_θ, exclusively through the linear combination H⊥ - ω _jPθ, where ω _j = const. = angular velocity of mean rotation. General equilibrium relations that pertain to the entire class of rigid-rotor Vlasov equilibria are discussed; and specific examples of sharp- and diffuse-boundary equilibrium configurations are considered. Rigid-rotor density and magnetic field profiles are compared with experimentally observed profiles. A general prescription is given for determining the functional dependence of the equilibrium distribution function on H_⊥-ω_jP_θg in circumstances, where the density profile or magnetic field profile is specified.