## 4. Summary and conclusions## 4.1. SummaryWe have introduced a new set-up for classical solar flare CA models which yields, among others, consistency with Maxwell's equations (e.g. divergence-free magnetic field), and availability of secondary variables such as currents and electric fields in accordance with MHD. Both are new for solar flare CA models. The set-up specifies the so far open physical interpretation of the CA models. This specification is to some extent unavoidably arbitrary, and it would definitely be interesting to see what alternative interpretations would yield - if they can be derived consistently. We can claim, however, that the interpretation we chose is reasonable, it is well-behaved in the sense that the derivatives of analytically prescribed vector-potentials are reproduced and that the abstract stress-measure of the CA models is related to the current, due to general properties of spline interpolation. The central problem which was to solve is how to calculate derivatives in a CA model, i.e. how to continue the primary grid-variable in-between the grid sites, since the notion of derivatives is alien in the context of CA models quite in general. In this article, our main aim with the introduced set-up was to demonstrate that the set-up truly extends the classical CA models and makes them richer in the sense that they contain much more information, now. The main features we revealed about the CA models, extended with our set-up, are:
## 4.2. ConclusionsOur set-up is to be contrasted to the recently suggested MHD-derived (not based on the sand-pile analogy) CA models of Einaudi & Velli (1999), MacPherson & MacKinnon (1999), Longcope and Noonan (2000), and Isliker et al. (2000a). They all suggest new evolution rules, derived from MHD, and all in different ways (they actually focus on different processes, namely the microscopic, macroscopic, and mesoscopic physics, respectively, in active regions). Our set-up, on the other hand, uses existing CA models, does not interfere (if not wished) with their evolution rules, does also not change their main results, as shown, but reinterprets them, extends them essentially, and makes them compatible with MHD. The set-up we introduced allows different future applications and
posing questions which could not be asked so far in the frame of CA
models. In preparation is a study (Isliker et al. 2000b) to reveal in
detail what physical flare scenario the extended CA models imply. We
will address the questions: (1) how to interpret the small scale
processes of the models (loading and bursting) in terms of MHD; (2)
what the A different future application we plan with CA models extended with our set-up is the introduction of particles into the models, with the aim to study thermal emission, particle acceleration, and non-thermal emission. This will allow a much deeper comparison of the CA models to observations than was possible so far, and this is actually the most important benefit of the set-up we introduced. Such comparisons will allow a new judgment of the adequateness or not of classical CA models (in their current form) to the problem of solar flares, beyond the three statistical distributions of the primarily released energy. Solar flare CA models which include particle acceleration would represent the first global and complete model for solar flares. © European Southern Observatory (ESO) 2000 Online publication: December 5, 2000 |