Signatures of dual scaling regimes in a simple avalanche model for magnetospheric activity

Recently, the paradigm that the dynamic magnetosphere displays sandpile-typ e phenomenology has been advanced, in which energy dissipation is by means of avalanches which do not have an intrinsic scale. This may in turn imply that the system is in a self-organised critical (SOC) state. Indicators of internal processes are consistent with this, examples are the power-law dep endence of the power spectrum of auroral indices, and in situ magnetic fiel d observations in the earth's geotail. However substorm statistics exhibit probability distributions with characteristic scales. In this paper we disc uss a simple sandpile model which yields for energy discharges due to inter nal reorganisation a probability distribution that is a power-law, whereas systemwide discharges (flow of "sand" out of the system) form a distinct gr oup whose probability distribution has a well defined mean, When the model is analysed over its fall dynamic range, two regimes having different inver se power-law statistics emerge. These correspond to reconfigurations on two distinct length scales: short length scales sensitive to the discrete natu re of the sandpile model, and long length scales up to the system size whic h correspond to the continuous limit of the model. The latter are anticipat ed to correspond to large-scale systems such as the magnetosphere. Since th e energy inflow may be highly variable, the response of the sandpile model is examined under strong or variable loading and it is established that the power-law signature of the large-scale internal events persists. The inter val distribution of these events is also discussed. (C) 2001 Elsevier Scien ce Ltd. All rights reserved.