Alfven-wave filamentation

Transverse focusing or filamentation of weakly nonlinear Alfven waves propagating in a dispersive medium is studied using an amplitude-equation formalism. Special attention is devoted to the small-beta regime, where kinetic effects are weak and Alfven-wave trains are unstable to convective filamentation. It is shown that, according to their initial duration, focusing wave packets can collapse in a finite distance or, conversely, the focusing can be arrested by the development of magnetosonic waves, which in both cases may lead to the formation of sharp acoustic fronts. This effect, which dominates the usual longitudinal steepening, provides an efficient mechanism to heat the plasma without requiring large-amplitude waves. It can significant ly contribute to the acceleration of the solar mind.