Transport Coefficients fo r Magnetohydrodynamic Cellular

T his article will p resent some approximate theoretical calculations of transport coefficients for magnet ohydrod ynamic (MHD) cellular automata (CA). Throughou t , the attent ion will be limi ted to two-dime ns ional (2D) models . CA, as possible fluid simu lat ion tools, have recently become an act ive research area [1-4], followi ng several years of basic b ackground investi gat ions on lattice gases [5-8] . A cellular au tomaton for simu lat ing 2D MHD has recently been proposed [9] . As in the fluid case, 2D MHD macroscopic cont inuum equations can b e de rived with some degree of convict ion from the dynam ics represent ed by the microscopi c computer game which the cellular automaton is. In interpreting fu ture result s from MHD CA computations, it will be desirabl e to have theoretical est imates of the kin emat ic viscos ity and magneti c diffus ivity der ived from a microscopic kinetic theory. T he principal purpose of th is art icle is to present such a derivat ion. Sect ion 2 reviews the 2D MHD CA previously put forward [9], and relat es it to its anc estor, the hex agon al lat t ice gas [1]. Section 3 p resents a Markov ian stochastic model of it s dynamics. Section 4 is devoted to t he calculat ion of the kinematic viscosity v and the magnetic diffusiv ity '1, which are expecte d to characterize the magnetoflu id which t he CA is simulating . Sect ion 5 briefly discusses the results an d remarks upon poss ib le gen eralizations. In the development, some familiar ity with the ChapmanEnskog procedure for der iving fluid equat ions and t ransport coe fficients from kinetic equations will be ass umed; the bo oks of Chapman and Cowling