Particle distribution function in plasma and the self-consistent magnetic field

Abstract

The equilibrium configuration of plasma (the stationary distribution function of charged particles) and of the self-consistent magnetic field is determined on the basis of the first integrals of motion. A detailed analysis is made of the mutual relation between the resultant magnetic field B and the dependence of the distribution function on the integrals of motion; the necessary and sufficient conditions which must be satisfied by the distribution function with a minimum-B field are obtained. For the configuration with a minimum in B on the axis of symmetry, the function F(pφ) must decrease rapidly with increasing pφ in the vicinity of pφ = 0. Accordingly, the number of particles must have a maximum for particles that perform Larmor gyration around the axis (epφ < 0), and the number of particles intersecting the axis (pφ = 0), must be non-zero