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. © 1999 American Institute of Physics. @S1070-664X~99!02611-7#