Self-organized criticality, multi-fractal spectra, sporadic localized reconnections and intermittent turbulence in the magnetotail

It has been suggested that the dynamics of the Earth's magnetotail may be described by the stochastic behavior of a nonlinear dynamical system near forced and/or self-organized criticality (SOC). It has been further argued that multiscale intermittent turbulence of overlapping plasma resonances is the underlying physics that can lead to the onset and evolution of substorms. Such a description provides a convenient explanation of the localized and sporadic nature of the reconnection signatures and fractal spectra that are commonly observed in the magnetotail region. These concepts provide a new paradigm for the understanding of the ever-elusive phenomenon of magnetic substorms. In this review, we describe some of the basic physical concepts and mathematical techniques (such as the dynamic merging of coherent structures, nonclassical nonlinear instability, path integrals, the theory of the renormalization-group, low-dimensional chaos, self-similarity and scaling, fractals, coarse-grained helicity and symmetry breaking) that play a central role in the development of these new ideas. (C) 1999 American Institute of Physics. [S1070-664X(99)02611-7].