Abstract
Alfvén wave filamentation is an important instability as it can lead to wave collapse and thus to the formation of small scales. Different asymptotic equations are here derived to describe this phenomenon. They apply in different regimes, depending on the level of the dispersion with respect to the nonlinearity. The (scalar) nonlinear Schrödinger equation, valid when the wave is strongly dispersive, allows the study of the influence of the coupling to magneto-sonic waves on the development of the instability. This equation generalizes to a vector nonlinear Schrödinger equation when the dispersion is decreased. The amount of dissipated energy that results from the wave collapse when damping processes are retained, is also estimated in these two cases. When the dispersion is weak and comparable to the effects of the nonlinearities, a reductive perturbation expansion can be used to derive long-wave equations that generalize the DNLS equations and also contain the reduced MHD for the dynamics in the plane transverse to the propagation.
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Champeaux, S., Gazol, A., Passot, T., Sulem, P. (1999). Alfvén Wave Filamentation and Plasma Heating. In: Passot, T., Sulem, PL. (eds) Nonlinear MHD Waves and Turbulence. Lecture Notes in Physics, vol 536. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47038-7_3
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DOI: https://doi.org/10.1007/3-540-47038-7_3
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