Vlasov-Maxwell system: 2-D equilibria, reversed field pinches

Exact solutions to the Vlasov-Maxwell system in the two dimensional circular cylindrical model are presented. The magnetic surfaces are shifted circles for the m = 1 case, where the shift is determined by a parameter (epsilon); (epsilon) = 0 gives concentric circles and represents 1-D solutions. For m greater than or equal to 2 cases, the solutions are singular at the origin and the magnetic surfaces contain islands and separatrices. An improved one dimensional model with currents in both the axial and azimuthal directions is also presented. It is shown that this simple finite pressure model can yield field reversed equilibria in the presence of appropriate boundary constraints.