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Summary form only given, as follows. We have developed a new algorithm, the Darwin direct implicit particle-in-cell (DADIPIC) method, for particle simulation of low frequency, non-neutral phenomena in plasmas. 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. We have chosen to combine two methods, Darwin and direct implicit, to eliminate the constraints c/spl Delta/x//spl Delta/t

The inclusion of a velocity distribution within each Finite Size Particle (FSP) has lead to a decrease in the number of particle required to accurately describe Local Thermodynamic Equilibrium (LTE). Although this is appealing in many instances, systems which are dominated by diffusion and/or pressure gradients suffer from the FSP inability to probe the necessary parameter space. Many methods have been introduced to alleviate this shortcoming, such as deformation and fragmentation of a particle volumes or the generation of virtual particles to effect pressure. We have generated a new algorithm that compares well with selected closed form solutions. Grid and Particle Hydrodynamics (GaPH) works by allowing each FSP to internally undergo local hydrodynamics. The resulting distribution contained within each FSP is then cast into a central and expansion particles. The system is now advanced in time and particles that sufficiently overlap in phase space are merged. By allowing the FSP to aggressively probe the available parameter space through fragmentation, new characteristics to the distribution can emerge. By aggressively merging particles, redundant representations of the distribution tend to be eliminated.