Abstract
The process of Alfvén wave filamentation, by which the energy of a quasi-monochromatic wave packet concentrates into thin field-aligned tubes, is reviewed. Most of the properties of this phenomenon are captured by envelope equations where it is associated with transverse wave collapse. Saturation and possible instability of the resulting structures are analyzed by means of three-dimensional simulations of Hall-MHD equations. To address the case of a collisionless plasma, a long-wave (KDNLS) equation is first obtained from the Vlasov-Maxwell system by a reductive perturbative expansion, thus allowing one to easily derive a dissipative non-linear Schrödinger equation that accounts for the effect of Landau damping of the ion acoustic waves. Filamentation criteria are then obtained, showing that the instability is in particular favored by a large electron-ion temperature ratio. The nonlinear regime displays a complex dynamics of focusing and defocusing magnetic filaments.
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