By Mathurin-Jacques Brisson
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1993). The intermittency description for plasma turbuIllustrative examples. , 2003). Below, we shall provide two simple phenomenological models, which may have some relevance to the auroral zone or the solar wind (Chang, 2003). Model I. Assuming that the parallel mean magnetic ﬁeld B0 is sufﬁciently strong and the magnetic ﬂuctuations dominate in the transverse directions, we introduce the ﬂux function ψ for the transverse ﬂuctuations as follows, B = ez × ∇ψ + B0 ez (6) The coherent structures for such a system are generally ﬂux tubes approximately aligned in the mean parallel direction (Chang, 2001).
And T. Chang, “Magnetic Field Topology and Criticality in Geotail Dynamics: Relevance to Substorm Phenomena”, Space Science Reviews, 95, 309, 2001. , T. Y. Lui, Complexity and topological disorder in the Earth’s magnetotail dynamics, Chapter 3, this volume, 2004. , and T. Chang, Path-integral formulation of ion heating, Physics of Fluids, 31, 3425, 1988. , Ann. d. Physik, 17, 549, 1905. , Wavelet transforms and their applications to turbulence, Annual Reviews of Fluid Mechanics, 24, 395, 1992.
The authors wish to thank their past and present colleagues, M. Andr´e´ , V. Angelopoulos, R. Bruno, S. C. Chapman, G. Consolini, B. B. Crew, G. Ganguli, M. Goldstein, A. R. Jasperse, S. F. Kennel, P. Kintner, M. Kivelson, A. Y. Lui, E. Marsch, W. Matthaeus, P. F. M. Retterer, C. S. I. E. Stanley, D. Tetreault, V. Uritsky, J. Valdivia, D. Vassiliadis, D. Vvedensky, N. Watkins, J. Weygand, F. E. Young for very useful discussions. Our wavelet analysis employed some of the wavelet software provided by C.