Propagation of non-linear circularly polarised Alfven waves in a homogeneous medium

Abstract

We study the evolution of non-linear circularly polarised Alfven waves by solving numerically the time-dependent equations of magnetohydrodynamics (MHD) in one dimension. We examine the behaviour of the waves and find that different physical mechanisms are relevant in different ranges of beta. In a low beta plasma the wave may undergo a parametric decay. This is because the wave excites a density enhancement that travels slower than the wave itself and thus interacts with the wave. When beta is greater or equal to one the density enhancement does not interact with the wave and no decay takes place, instead the Alfven wave is reflected against the density enhancement. The reflection zone propagates with the speed 1/n of the Alfven speed. Because of that the magnetic flux is conserved which results in an amplification of the oscillating magnetic field by a factor 1/n. We find that n depends on beta, and that in particular it is less or equal to one for values of beta ~ 1 and is greater or equal to one for beta >> 1. We discuss the relevance of these mechanisms to the acceleration of the solar wind, and the triggering of MHD turbulence in the polar wind region. In particular these simulations can explain the presence of inward propagating Alfven waves in the solar corona.