5. Discussion: the context of solar flares
We have shown that the CA of LH (Sect. 2) can be interpreted as the solution to a diffusion equation plus a source term. Here now, we will give some examples to demonstrate the benefit gained through this alternative description: the somewhat neutral rules of the CA can be interpreted (or modified) on the basis of our understanding of MHD equations, as related to solar flares.
Generally, flares are considered to be made up by a large number of reconnection events distributed somehow over an active region (Parker 1988; Parker 1989). In MHD, the processes in the active region are described by the induction equation
plus a momentum equation for the evolution of the velocity field (the currents and the electric field can be considered as secondary quantities). In general then, the evolution of the magnetic field is governed by the convective term (2nd term on the r.h.s. of Eq. 39), since is very small, mostly. Accidentally, this convective evolution may create small scale structures where is not small anymore, and the diffusive term dominates the evolution of the magnetic field (1st term on the r.h.s. of Eq. 39). This diffusive regime is characterized by its spatial scale and its temporal scale . Both scales are bigger than the respective ones of the current sheet and the reconnection process, they characterize the volume and the time in which the magnetic field has been reconnected and the free magnetic energy has been released (for details see Biskamp 1994, and references therein).
Having the described picture of the flare scenario in mind, we can interpret the CA of LH (Sect. 2), not by considering the CA rules, however, but by looking at the continuous version of the CA model (Sect. 4):
© European Southern Observatory (ESO) 1998
Online publication: June 26, 1998