Alfvén wave filamentation and plasma heating.

*(English)* Zbl 0942.76091
Passot, Thierry (ed.) et al., Nonlinear MHD waves and turbulence. Proceedings of the workshop, Nice, France, December 1-4, 1998. Berlin: Springer. Lect. Notes Phys. 536, 54-82 (1999).

Summary: Alfvén wave filamentation is an important instability as it can lead to wave collapse and thus to the formation of small scales. Here, we derive different asymptotic equations to describe this phenomenon. They apply in different regimes, depending on the level of dispersion with respect to nonlinearity. The (scalar) nonlinear Schrödinger equation, valid when the wave is strongly dispersive, allows the study of the influence of coupling to magneto-sonic waves on the development of instability. We generalize this equation 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 nonlinearities, we use a reductive perturbation expansion to derive long-wave equations that generalize the derivative nonlinear Schrödinger equations and also contain reduced MHD equations for the dynamics in the plane transverse to the direction of wave propagation. For the entire collection see [

Zbl 0930.00079].

##### MSC:

76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |

82D10 | Plasmas (statistical mechanics) |