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

Abstract

Recently, the paradigm that the dynamic magnetosphere displays sandpile-type 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 dependence of the power spectrum of auroral indices, and in situ magnetic field observations in the earth's geotail. However substorm statistics exhibit probability distributions with characteristic scales. In this paper we discuss a simple sandpile model which yields for energy discharges due to internal reorganisation a probability distribution that is a power-law, whereas systemwide discharges (flow of “sand” out of the system) form a distinct group whose probability distribution has a well defined mean. When the model is analysed over its full dynamic range, two regimes having different inverse power-law statistics emerge. These correspond to reconfigurations on two distinct length scales: short length scales sensitive to the discrete nature of the sandpile model, and long length scales up to the system size which correspond to the continuous limit of the model. The latter are anticipated to correspond to large-scale systems such as the magnetosphere. Since the 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 interval distribution of these events is also discussed.