I. Heating of Magnetized Plasmas by Large-Amplitude Electric Field. I. Reduction of the Grid Effects in Simulation Plasmas.

The electromagnetic field grids in fine-resolution two-dimensional or medium-resolution three-dimensional plasma simulation are very large. We propose a method whereby only a fraction of the grid need be in fast core at any given time. The basic idea is to do several consecutive field solutions with coarse grids displaced relative to one another. The separate solutions may pertain to different time steps (“jiggling”) or the same time step (“interlacing”). The combination of these separate solutions can provide some aspects of the accuracy improvement obtainable with the fine grid which is the superposition of the separate grids. These techniques may be useful when one is strongly limited by the size of random-access memory but can afford to place greater demands on serial-access memory and processor speed. Their effect is to reduce “aliasing” errors, in which plasma perturbations are unphysically coupled when their wave numbers differ by wave vectors characteristic of the grid. Resolution may then be improved by methods described elsewhere. In order to evaluate these methods quantitatively, dispersion relations for plasma oscillations are examined. Aliasing effects, such as grid-induced instability, can be greatly reduced. However, depending on the smoothness of the velocity distribution, “jiggling” can introduce new troublesome modes with frequencies ∼Δt−1; “interlacing” has no known ill side effects. Simulation results are in agreement with theory. In two and three dimensions, there is also a decrease in computation time compared to using a finer gride with similar reduction in grid effects.