Derivation of solar flare cellular automata models from a subset of the magnetohydrodynamic equations, Astroph. Journal Letters, 509, L53, 1998


Several cellular automata models have appeared in the literature to account for the power - law distributions found for solar flare HXR observations. Here we examine four of these models and show that their criteria and magnetic field distribution rules can be obtained by discretizing the MHD diffusion equation and using a basic form of Ohm's law. In the process a) we present a numerical method for intergrating the discretized MHD equation, called cellular MHD , and b) we show that the identification of the cellular MHD models with the CA models results in prescribing the resistivity as a function of the currents along the flux tube boundaries. The resistivity can be further modified to balance the physical effects (current - driven instabilities) versus the more accurate representation of observed durations of HXR flare events. The principles of the numerical method are compared to those of the standard intergration of MHD equations and the advantages of each are discussed.

Subject headings : chaos - diffusion - MHD - Sun:flares