A sandpile model with dual scaling regimes for laboratory, space and astrophysical plasmas

There is increasing evidence that the Earth's magnetosphere, like other macroscopic confined plasma systems (magnetic fusion plasmas, astrophysical accretion discs), displays sandpile-type phenomenology so that energy dissipation is by means of avalanches which do not have an intrinsic scale. This may in turn imply that these systems evolve via self-organized criticality (SOC). For example, the power law dependence of the power spectrum of auroral indices, and in situ magnetic field observations in the Earth's geotail, indicate that the coupled solar wind-magnetospheric system can to some extent be described by an avalanche model. However, substorm statistics exhibit probability distributions with characteristic scales. In this paper a simple sandpile model is discussed which yields for energy discharges due to internal reorganization a probability distribution that is a power law, implying SOC, 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 analyzed 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. These are anticipated to correspond regimes accessible to both laboratory and astrophysical plasmas. The relevance of the emergence of distinct self-organized confinement regimes in space, astrophysical, and magnetic fusion plasmas is discussed. Since the energy inflow may be highly variable, the response of the sandpile model is examined under strong or variable loading. (C) 1999 American Institute of Physics. [S1070-664X(99)03011-6].