Modelling of solar magnetic fields using cellular automata models

Brockwell, Christopher Peter (2003). Modelling of solar magnetic fields using cellular automata models. PhD thesis The Open University.



Solar activity, including flares, CMEs, sunspots, global fleld reversal and, consequential to these, particle acceleration and X-ray emission result from the complexity of the atmospheric magnetic fields. These fields are driven into complex topologies by the continual stochastic photospheric motions and granulation flows. Significant energy is stored in the magnetic field however magnetic reconnection provides a mechanism for the relaxation and simplification of the field and release of this energy. Reconnection is capable of providing the observed plasma heating, field reorganisation and particle acceleration, although the relationship between reconnection and flaring is not yet understood. It is clear however that the field topology is key. Given fiare-size self-similarity, the short time-scales of hard X-ray emission and the observed apparent self-organisation, flaring models (Lu & Hamilton 1991) have been constructed based upon self-organised criticality (‘SOC’) with minimal physics and have produced plausible fiare-size distributions. The model by MacKinnon, Macpherson & Vlahos (1996) however assumed only local flare-triggering and made no statements regarding flare physics. This model reproduced the broad statistical features of flares yet without any implicit SOC.
We speculate that the observed Solar activity arises from the self-interaction of the magnetic field, flux emergence/submergence and reconnection without the necessity for invoking SOC or power-law distributed convective flows. Our first model was a simple 1-D cellular automata (‘CA’) containing only formalised field connectivity, reconnection and flux emergence/submergence. The model produced self-similarity in fiare-sizes over four orders of magnitude. The following model built upon the first and included more realistic physics with continuous parameter values. The model gave power- law distributions in field density and fiare-sizes (up to seven orders of magnitude) without inclusion of SOC or power-law forcing. The results were robust and insensitive to details of the reconnection mechanism. We derive analytical explanations for the observed rapid decay curves of impulsive-phase X-ray emission and consider that the flares produced represent presently unresolvable reconnection events. It was found that, similar to large Solar flares, large events are rarely concurrent.

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