Low Frequency, Electrodynamic Simulation of Kinetic Plasmas with the DARWIN Direct Implicit Particle-In (dadipic) Method.

This dissertation describes a new algorithm for simulating low frequency, kinetic phenomena in plasmas. DArwin Direct Implicit Particle-in-Cell (DADIPIC), as its name implies, is a combination of the Darwin and direct implicit methods. One of the difficulties in simulating plasmas lies in the enormous disparity between the fundamental scale lengths of a plasma and the scale lengths of the phenomena of interest. The objective is to create models which can ignore the fundamental constraints without eliminating relevant plasma properties. Over the past twenty years several PIC methods have been investigated for overcoming the constraints on explicit electrodynamic PIC. These models eliminate selected high frequency plasma phenomena while retaining kinetic phenomena at low frequency. This dissertation shows that the combination of Darwin and Direct Implicit allows them to operate better than they have been shown to operate in the past. 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. The code functions in a two dimensional Cartesian region and has been implemented with all components of the particle velocities, the E-field, and the B-field. Internal structures, conductors or dielectrics, may be placed in the simulation region, can be set at desired potentials, and driven with specified currents. The linear dispersion and other properties of the DADIPIC method are investigated in order to deduce guidelines for its use. 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. The separation of the fields has made the task of predicting algorithm behavior easier and produced a robust method without restrictive constraints. Finally, the code is used to simulate Inductively Coupled Plasmas similar to those used for plasma processing in the microelectronics industry. Collisionless heating in these low frequency systems is one of the important kinetic effects for which DADIPIC is well suited. Agreement with 1-D linear, analytic theory is shown. The utility of DADIPIC is shown in simulation results for 2-D and nonlinear effects which are not amenable to analytic solution.