Transverse collapse of low-frequency Alfvén waves

The dynamics of long-wavelength dispersive Alfvén wave trains propagating parallel to an ambient field in a magnetized plasma is investigated by means of a three-dimensional extension of the derivative nonlinear Schrِdinger equation that includes the mean effect of the longitudinal magneto-sonic waves. In the strongly dispersive regime, quasi-monochromatic right-hand polarized plane waves perturbed by a broad-spectrum noise develop a transverse collapse leading to the formation of strong magnetic filaments parallel to the ambient field, as asymptotically predicted by the nonlinear Schrِdinger equation for the wave envelope. In contrast, for left-hand polarized waves filamentation only takes place when the noise is confined to Fourier modes with wavenumbers close enough to that of the pump. In the regime where dispersion and nonlinearity are comparable, the amplitude growth is strongly inhibited but intense gradients are still formed, associated with the creation of pancake-like magnetic structures. The transverse focusing of weakly nonlinear dispersive waves still takes place when the spectrum of the initial conditions is broadened, in spite of the fragmentation of the magnetic filaments into chains of magnetic bubbles and ultimately into randomly distributed three-dimensional structures.