Wave collapse in dispersive magnetohydrodynamics: direct simulations and envelope modeling

An example of wave collapse arising in dispersive magnetohydrodynamics is analyzed by means of both direct numerical simulations and envelope formalism. It is shown that in spite of the presence of various types of waves and of purely hydrodynamic effects, the evolution of a longitudinally homogeneous Alfvén-wave beam propagating along an ambient magnetic field is accurately described by a cubic nonlinear Schrِdinger equation with an external potential proportional to the initial wave intensity. In this description, an axisymmetric beam can only collapse on its axis when its transverse extension significantly exceeds the typical scale of the modulational instability of the carrying wave. An axisymmetric configuration is however unstable with respect to azimuthal perturbations, leading to off-center collapse, even in situations that are smooth when axisymmetry is preserved. In the case of a wave packet with a finite longitudinal extension, a minimum size is required for blowup, associated with the formation of strongly anisotropic magnetic structures.