Two Cellular Automata for Plasma Computations

Plasma ap plicati ons of comput ational techniques based on cellular auto mat a are inhibited by the long-ran ge nature of electromagnetic forc es . On e of the most promis ing features of cellu lar automata methods has been th e parallelism that becomes possible because of the local natu re of th e interactions , leading (for example) to t he absence of Poisson equat ions to be solved in fluid simulations. Because it is in the nature of a plasma that volume forces originate with distant charges and currents, finding plasma cellular automata becomes largely a search for tricks to circumvent this nonlocality of the forces. We describe automata for two situations whe re th is appears possible: two-dimensional magnetohydrodynamics (2D MHD) and the one-dimensional electrostat ic Vlaso v-Poisson system. Insufficient computational experience has accumulated for either sys tem to argue th at it is a serious alternative to exist ing methods . 1. Two-dimensional magnetohydrodynamics (2D MHD) T he basic equations of two-dimens ional incomp ress ible magne tohydrodynamics are a relatively straightforwa rd generalizat ion of those of two-d imens ional fluid mechanics, and for our purposes can be written as {1-3J : a~;) + 'il . (puu) = 'ilp +j X B + pv'il'u ,