Streamlined Darwin simulation of nonneutral plasmas

Abstract

Efficient, new algorithms that require less formal manipulation than previous implementations have been formulated for the numerical solution of the Darwin model. These new procedures reduce the effort required to achieve some of the advantages that the Darwin model offers. Because the Courant-Friedrichs-Lewy stability limit for radiation modes is eliminated, the Darwin model has the advantage of a substantially larger time-step. Further, without radiation modes, simulation results are less sensitive to enhanced particle fluctation noise. We discuss methods for calculating the magnetic field that avoid formal vector decomposition and offer a new procedure for finding the inductive electric field. This procedure avoids vector decomposition of plasma source terms and circumvents some source gradient issues that slow convergence. As a consequence, the numerical effort required for each of the field time-steps is reduced, and more importantly, the need to specify several nonintuitive boundary conditions is eliminated.