Transverse collapse of low-frequency Alfven waves

The dynamics of long-wavelength dispersive Alfven wave trains propagating p arallel to an ambient field in a magnetized plasma is investigated by means of a three-dimensional extension of the derivative nonlinear Schrodinger e quation that includes the mean effect of the longitudinal magneto-sonic wav es. In the strongly dispersive regime, quasi-monochromatic right-hand polar ized plane waves perturbed by a broad-spectrum noise develop a transverse c ollapse leading to the formation of strong magnetic filaments parallel to t he ambient field, as asymptotically predicted by the nonlinear Schrodinger 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 disp ersion and nonlinearity are comparable, the amplitude growth is strongly in hibited but intense gradients are still formed, associated with the creatio n of pancake-like magnetic structures. The transverse focusing of weakly no nlinear dispersive waves still takes place when the spectrum of the initial conditions is broadened, in spite of the fragmentation of the magnetic fil aments into chains of magnetic bubbles and ultimately into randomly distrib uted three-dimensional structures. (C) 2001 Elsevier Science B.V. All right s reserved.