Ion extraction and optics in three dimensions

An algorithm is described for a solution to the three-dimensional (3-D) Poisson-Vlasov equations for ions extracted from a plasma. A variational formulation of Poisson's equation using isoparametric finite elements leads to a band matrix, which is solved by a modified Gauss-Cholesky method. A semi-implicit method is described for the inclusion of nonlinear plasma electrons, allowing an explicit solution of the extraction sheath. An intrinsically 3-D example is shown.