Characterization of the Darwin Direct Implicit Particle-in-Cell Method and Resulting Guidelines for Operation

We investigate the linear dispersion and other properties of the Darwin Direct Implicit Particle-in-cell (DADIPIC) method in order to deduce guidelines for its use in the simulation of long time-scale, kinetic phenomena in plasmas. The Darwin part of this algorithm eliminates the Courant constraint for light propagation across a grid cell in a time step and divides the field solution into several elliptic equations. The direct implicit method is only applied to the electrostatic field relieving the need to resolve plasma oscillations. Linear theory and simulations verifying the theory are used to generate the desired guidelines as well as show the utility of DADIPIC for a wide range of low frequency, electromagnetic phenomena. We find that separation of the fields has made the task of predicting algorithm behavior easier and produced a robust method without restrictive constraints.