of the Darwin and direct implicit methods. The Darwin method is a reduction of Maxwell's equations to a radiation
We investigate the linear dispersion and other properties of the Darwin Direct Implicit Particle-in-cell (DADIPIC) method in order to free limit thus removing the light propagation Courant deduce guidelines for its use in the simulation of long time-scale, condition. The direct implicit method works with the finite kinetic phenomena in plasmas. The Darwin part of this algorithm difference equations in an implicit form and is used to eliminates the Courant constraint for light propagation across a grid solve for a time-advanced electrostatic field. In this way cell in a time step and divides the field solution into several elliptic the unresolved plasma oscillations are numerically damped equations. The direct implicit method is only applied to the electrostatic field relieving the need to resolve plasma oscillations. Linear out and are no longer a source of instability.
theory and simulations verifying the theory are used to generate DADIPIC is characterized in this paper by answering the desired guidelines as well as show the utility of DADIPIC for a the following questions. Are spatially and temporally rewide range of low frequency, electromagnetic phenomena. We find solved plasma phenomena simulated accurately? What is that separation of the fields has made the task of predicting algothe response of the method when the above Courant and rithm behavior easier and produced a robust method without restrictive constraints. แฎ 1997 Academic Press plasma frequency conditions are not met? Are there numerical constraints on the algorithm as presently implemented? What improvements can be made to the method?
II. IMPLEMENTATION OF DARWIN DIRECT IMPLICIT
Government nor the University of California nor any of their employees,
PARTICLE-IN-CELL
makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any Our implementation of DADIPIC results in an algoinformation, apparatus, product, or process disclosed, or represents that rithm in which the implicit electrostatic field and the Darits use would not infringe privately owned rights. Reference herein to any specific commercial products, process, or service by trade name, win magnetoinductive fields are found separately. We will trademark, manufacturer, or otherwise, does not necessarily constitute describe the calculation of the fields and then present the or imply its endorsement, recommendation, or favoring by the United algorithm which combines Darwin fields with the implicit States Government or the University of California. The views and opinparticle advance. ions of authors expressed herein do not necessarily state or reflect those of the United States Government or the University of California and shall not be used for advertising or product endorsement purposes. The A. Implicit Electrostatic Method U.S. Government's right to retain a nonexclusive royalty-free license in Implicit methods achieve stability by including informaand to the copyright covering this paper, for governmental purposes, is acknowledged. tion from the next time step in the equations for the time 54