MHD consistent cellular automata (CA) models

Abstract

Abstract.In Isliker et al. (2000b), an extended cellular automaton (X-CA) model for solar flares was introduced. In this model, the interpretation of the model's grid-variable is specified, and the magnetic field, the current, and an approximation to the electric field are yielded, all in a way that is consistent with Maxwell's and the MHD equations. The model also reproduces the observed distributions of total energy, peak-flux, and durations. Here, we reveal which relevant plasma physical processes are implemented by the X-CA model and in what form, and what global physical set-up is assumed by this model when it is in its natural state (self-organized criticality, SOC). The basic results are: (1) On large-scales, all variables show characteristic quasi-symmetries: the current has everywhere a preferential direction, the magnetic field exhibits a quasi-cylindrical symmetry. (2) The global magnetic topology forms either (i) closed magnetic field lines around and along a more or less straight neutral line for the model in its standard form, or (ii) an arcade of field lines above the bottom plane and centered along a neutral line, if the model is slightly modified. (3) In case of the magnetic topology (ii), loading can be interpreted as if there were a plasma which flows predominantly upwards, whereas in case of the magnetic topology (i), as if there were a plasma flow expanding from the neutral line. (4) The small-scale physics in the bursting phase represent localized diffusive processes, which are triggered when a quantity which is an approximately linear function of the current exceeds a threshold. (5) The interplay of loading and bursting in the X-CA model can be interpreted as follows: the local diffusivity usually has a value which is effectively zero, and it turns locally to an anomalous value if the mentioned threshold is exceeded, whereby diffusion dominates the quiet evolution (loading), until the critical quantity falls below the threshold again. (6) Flares (avalanches) are accompanied by the appearance of localized, intense electric fields. A typical example of the spatio-temporal evolution of the electric field during a flare is presented. (7) In a variant on the X-CA model, the magnitude of the current is used directly in the instability criterion, instead of the approximately linear function of it. First results indicate that the SOC state persists and is only slightly modified: distributions of the released energy are still power-laws with slopes comparable to the ones of the non-modified X-CA model, and the large scale structures, a characteristic of the SOC state, remain unchanged. (8) The current-dissipation during flares is spatially fragmented into a large number of dissipative current-surfaces of varying sizes, which are spread over a considerably large volume, and which do not exhibit any kind of simple spatial organization as a whole. These current-surfaces do not grow in the course of time, they are very short-lived, but they multiply, giving rise to new dissipative current-surfaces whic...

Magnetic Complexity, Fragmentation, Particle Acceleration and Radio Emission from the Sun

“…of all sizes that follow a well defined statistical law [30,31,32], which agrees remarkably well with the observed flare statistics [33]. We can then conclude, after many years of studies, that a possible model for the dynamic evolution of the AR is the following: The 3D magnetic field is stressed from the photospheric motions, forms continuously UCS which relax, re-arranging the local magnetic field and causing flares of all sizes (Fig.…”

“…A stochastic model for type III bursts was introduced and compared with observations [42]. In this model the AR is assumed inhomogeneous with a very large number of fragmented energy release regions (UCSs) connected to magnetic fibers.…”

Simulating flaring events in complex active regions driven by observed magnetograms

“…The physical reason for selecting this criterion lies in the fact that large magnetic stresses favor magnetic reconnection in three dimensions, even in the absence of null points (Priest et al 2003). Mathematically, it can be shown that the selection of G av as the critical quantity in our model relates to the diffusive term of the induction equation (see Isliker et al 1998, for a detailed discussion). Let us write the induction equation in the form:…”

“…The simulation results presented in the next section have been performed using a 32 × 32 × 32 cubic grid with "open" boundaries in the relaxation events (see Isliker et al 2001, for a detailed discussion on open boundary conditions). Each simulation is driven for 3 × 10 5 iterations, which equals the times that LOAD module is being called during the simulation.…”

“…Although clearly deviating from the initial SOC models, the robust scaling laws in the flares' distribution functions survived. Isliker et al (2000Isliker et al ( , 2001 tried for the first time to associate the classical CA models' components with physical variables. Magnetohydrodynamic (MHD) and CA approaches were connected through the physical interpretation of numerous CA elements, such as the grid variable, the time step, the spatial discreteness, the energy release process, and the role of diffusivity.…”