Numerical Method for Two-Dimensional Vlasov Equilibrium as a Nonlinear Boundary Value Problem

Abstract

A computational method for analyzing axially symmetric Vlasov equilibrium as nonlinear boundary value problem is presented. The method consists of combined use of shooting method and Newton’s method. Equilibrium distribution function is expressed in terms of constants (or quasi-constants) of motion and parameters representing temperature anisotropy and magnetic trapping. Charge and current density calculated are substituted into Maxwell equations which reduce to coupled equations for magnetic flux function and electrostatic potential. These equations are solved by shooting method from two opposite boundaries on which the values are determined by Newton’s iteration scheme such that solution are smoothly connected inside plasma. Some techniques are introduced to remove singularities on symmetry axis and to determine boundary values on vacuum surface. The method is applied to bumpy cylinder with hot electrons and surface plasma and to thermal barrier with sloshing ions, energetic and warm electrons and surface plasma, assuming periodicity along symmetry axis.