Equilibrium of finite larmor radius plasma with anisotropic pressure

Abstract

The relations that exist between the pressure tensor, the electric current density in plasma and the selfconsistent magnetic field for equilibrium plasma configurations in magnetic mirror systems are derived and discussed. The analysis starts from the distribution function of equilibrium plasma derived in earlier work. It is found that the pressure tensor (appearing in these relations) is diagonal, with Pξξ ≠ Pφφ ≠ Pηη (Pξξ, Pφφ are the pressure components perpendicular to the lines of force, Pηη that along the lines of force). The plasma pressure in magnetic mirror systems is usually strongly anisotropic also in the plane perpendicular to the lines of force (Pξξ differs considerably from Pφφ) and the approximation Pφφ ≈ Pξξ ≡ P⊥ can no longer be used. This anisotropy is due to the strong dependence of the distribution function on the integral ; the cause of this strong dependence lies in the finite Larmor radius (real plasma consists of spatially bounded beams with Larmor radius of the same order as the plasma radius). Because of the curvature of the magnetic surfaces, the relations between the macroscopic quantities are affected by both longitudinal and perpendicular plasma anisotropy. Equations describing these relations are derived in the paper for finite β = 8πP/B2 and in the approximation β ≪ 1.