Analytical determination of power-law index for the Chapman et al. sandpile (FSOC) analog for magnetospheric activity - a renormalization-group analysis

Recent suggestion and experimental indications that the magnetotail dynamic s exhibit self-organized critical behavior have re-motivated interest in sa ndpile (avalanche) models. Some examples of specific interest for geomagnet ic activity have the property that internal avalanches exhibit inverse powe r law statistics whereas systemwide avalanches have a well-defined mean. He re, we apply the concept of renormalization group to such a model. We demon strate that invariant analysis based on the renormalization-group theory ca n explain the power law distribution of energy release by internal avalanch es in the large-scale regime of these systems.