The Astrophysical Journal, 509:L53L56, 1998 December 10
1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.
DERIVATION OF SOLAR FLARE CELLULAR AUTOMATA MODELS FROM A SUBSET OF THE
and L. Vlahos2
Received 1998 July 13; accepted 1998 September 28; published 1998 November 10
Cellular automata (CA) models account for the power-law distributions found for solar flare hard X-ray
observations, but their physics has been unclear. We examine four of these models and show that their criteria
and magnetic field distribution rules can be derived by discretizing the MHD diffusion equation as obtained from
a simplified Ohm's law. Identifying the discrete MHD with the CA models leads to an expression for the resistivity
as a function of the current on the flux tube boundary, as may be expected from current-driven instabilities.
Anisotropic CA models correspond to a nonlinear resistivity , while isotropic ones are associated withh(J)
hyperresistivity . The discrete equations satisfy the necessary conditions for self-organized criticality (Lu):2
there is local conservation of a field (magnetic flux), while the nonlinear resistivity provides a rapid dissipation