Multidimensional Particle Codes: Their Capabilities and Limitations for Modeling Space and Laboratory Plasmas

Increasing the number of dimensions calls for significant changes in simulation techniques. Demand on computer time and space increases by orders of magnitude, and hardware development affects the feasibility. Gridless and Fokker-Planck codes are possible in one dimension but one needs grids and PIC codes in two and three dimensions. This imposes limits on Debye lengths, particle size and spacing, and resolution. Nonspectral (local) electromagnetic (EM) codes also suffer a Courant restriction on ?t, in addition to the usual ?p?t restriction. Spectral methods therefore have an advantage: they also permit convenient filtering, particle shaping, and control of resolution. Two-dimensional and 2?D codes are well advanced and documented [4], [5]. Three-dimensional codes are in their infancy. Data management, rather than physics or numerical analysis, becomes the major problem [10]. Machine-independent 3D codes are too limited in resolution and speed. Parallelism helps greatly but makes the 3D codes machine dependent. A present-day limit is attempted in a 2*128**3 grid code for CRAY's which processes ~5 million particles in ~2 min per time step. Layering is employed to break up the 3D problem into many 2D problems. Fields and particles are packed and buffered in and out of core. Diagnostics are limited by the large volume of information accumulated in a run. Results of runs with 3D codes have tended to show that the third dimension, treated as "ignorable" in 2D simulations, should not have been ignored.