Reconnection and scale‐free avalanching in a driven current‐sheet model

Abstract

Uritsky et al. [2002], through a study of Polar UVI auroral image sequences, have produced a set of scale‐free probability distributions for several characteristic properties of the evolving bright emission regions in the nightside auroral oval. These distributions almost certainly reflect the dynamics of the plasma sheet. A scale‐free avalanching process involving reconnection and/or current diversion over an exceptionally broad range of spatiotemporal scales is implied. The most straightforward, and at present sole, explanation for this behavior is that the plasma sheet dynamics is in the neighborhood of self‐organized criticality (SOC). However, the auroral images provide only an indirect measure of the plasma sheet dynamics. Confirmation of this state in the plasma sheet would require multispatiotemporal‐scale in situ plasma sheet studies that, with the advent of multispacecraft missions, are now possible. To suggest specific tests for such studies, a numerical current‐sheet model has been constructed and analyzed to develop the properties and requirements of SOC in a plasma physical setting. The model incorporates the anomalous resistivity of a current‐driven kinetic instability into a two‐dimensional resistive MHD system. The disparate scales of these two systems enable multiscale behavior in the intervening range. Several novel features in the model's behavior are enabled through the assumption of hysteresis in the kinetic instability threshold. Under steady loading of plasma containing a reversed magnetic field topology, an irregular loading‐unloading cycle is established in which unloading is due primarily to annihilation at the field reversal. Following a loading interval during which the current‐sheet supporting the field reversal thins and intensifies, an unloading event originates at a localized reconnection site that then becomes the source of waves of unstable current sheets. These current sheets propagate away from the reconnection site, each leaving a trail of anomalous resistivity behind. An expanding cascade of field line merging results. Some statistical properties of this cascade are examined. It is shown that the diffusive contribution to the Poynting flux in these cascades occurs in bursts, whose duration, integrated size, and total energy content exhibit scale‐free power law probability distributions over large ranges of scales. Although not conclusive, these distributions do provide strong evidence that the model has evolved into SOC.