Hysteresis-controlled instability waves in a scale-free driven current sheet model

Magnetospheric dynamics is a complex multiscale process whose statistical features can be successfully reproduced using high-dimensional numerical transport models exhibiting the phenomenon of self-organized criticality (SOC). Along this line of research, a 2-dimensional driven current sheet (DCS) model has recently been developed that incorporates an idealized current-driven instability with a resistive MHD plasma system (Klimas et al., 2004a, b). The dynamics of the DCS model is dominated by the scale-free diffusive energy transport characterized by a set of broadband power-law distribution functions similar to those governing the evolution of multiscale precipitation regions of energetic particles in the nighttime sector of aurora (Uritsky et al., 2002b). The scale-free DCS behavior is supported by localized current-driven instabilities that can communicate in an avalanche fashion over arbitrarily long distances thus producing current sheet waves (CSW). In this paper, we derive the analytical expression for CSW speed as a function of plasma parameters controlling local anomalous resistivity dynamics. The obtained relation indicates that the CSW propagation requires sufficiently high initial current densities, and predicts a deceleration of CSWs moving from inner plasma sheet regions toward its northern and southern boundaries. We also show that the shape of time-averaged current density profile in the DCS model is in agreement with steady-state spatial configuration of critical avalanching models as described by the singular diffusion theory of the SOC. Over shorter time scales, SOC dynamics is associated with rather complex spatial patterns and, in particular, can produce bifurcated current sheets often seen in multi-satellite observations.