Equilibrium of field reversed configurations with rotation. I. One space dimension and one type of ion

Abstract

Self-consistent solutions of the Vlasov–Maxwell equations are obtained. They involve rigid rotor distributions. This selection is justified on physical grounds. For this selection the Vlasov equation can be replaced by moment equations which terminate without any additional assumptions. For one-dimensional equilibria with one type of ion these equations have exact solutions. A complete equilibrium solution appropriate to a field reversed configuration with rotation can be obtained by solving a generalized Grad–Shafranov equation for the flux function. From this solution all other physical quantities can be determined. A Green’s function method is developed to solve this equation, which provides a basis for an iterative solution. This method has the advantage that at every iteration the boundary conditions are satisfied. In this paper cylindrical geometry with one space dimension and one type of ion is considered, where analytic solutions are available. The convergence of the Green’s function method is established. For this nonlinear problem there is usually more than one solution for completely specified boundary conditions (bifurcation). The present method selects one solution. It is applicable to equilibria with many ion species and to two dimensions.