A simple avalanche model as an analogue for magnetospheric activity

Abstract

The power law dependence of the power spectrum of auroral indices, and in‐situ magnetic field observations in the earth's geotail, may be evidence that the coupled solar wind‐magnetospheric system exhibits scale free self organised criticality and can to some extent be described by avalanche models. In contrast, the intensity of, and time interval between, substorms both have well defined probability distributions with characteristic scales. We present results from a simple cellular automaton that models avalanches in a one dimensional “sandpile”; here we examine the simplest case of constant inflow. This model generates a probability distribution of energy discharges due to internal reorganization that is a power law implying SOC, whereas systemwide discharges (flow of “sand” out of the system) form a distinct group which do not exhibit SOC. The energy dissipated in a systemwide discharge follows a probability distribution with a well defined mean, as does the time interval between one systemwide discharge and the next. Internal and external avalanches can therefore in principle be identified with distinct processes in the dynamic geotail. If so, the avalanche model places restrictions on the class of physical process that may be invoked to explain the observed geomagnetic dynamics.