The Darwin direct implicit particle-in-cell (DADIPIC) method for simulation of low frequency plasma phenomena

We describe a new algorithm for simulating low frequency, kinetic phenomena in plasma. Darwin direct implicit particle-in-cell (DADIPIC), as its name implies, is a combination of the Darwin and direct implicit methods. Through the Darwin method the hyperbolic Maxwell's equations are reformulated into a set of elliptic equations. Propagating light waves do not exist in the formulation so the Courant constraint on the time step is eliminated. The direct implicit method is applied only to the electrostatic field with the result that electrostatic plasma oscillations do not have to be resolved for stability. With the elimination of these constraints spatial and temporal discretization can be much larger than that possible with explicit, electrodynamic PIC. We discuss the algorithms for pushing the particles and solving the fields in 2D cartesian geometry. We also detail boundary conditions for conductors and dielectrics. Finally, we present two test cases, electron cyclotron waves and collisionless heating in inductively coupled plasmas. For these test cases DADIPIC shows agreement with analytic kinetic theory and good energy conservation characteristics. 33 refs., 7 figs., 2 tabs