Self-consistent magnetic field and integrals of plasma motion

Abstract

A general solution of the Vlasov equation for the stationary axisymmetric distribution function of charged particles in plasma, together with a self-consistent solution of the Maxwell equations. is found and physically interpreted.The orthogonal natural system of coordinates of a magnetic field jointly with magnetic induction B and the integrals of motion are first determined. The spatial dependence of the resultant magnetic field is discussed in considerable detail and criteria for the existence of minimum-B are established. It is indicated that currents in plasma itself create configurations with a minimum-B on the axis of symmetry under the following necessary and sufficient exact conditions. (1) There must exist a minimum value of B in the longitudinal direction at r = z = 0 (mirror field): (2) It must be, at r = z = 0, that –(4π/c) (∂iφ/∂r)> ½∂2B/∂z2, where r, φ, z are the cylindrical coordinates, and iφ the electric current in the plasma.