Two-wave interaction in ideal magnetohydrodynamics

¹ Georgian National Astrophysical Observatory (Abastumani Astrophysical Observatory), Kazbegi Ave. 2a, Tbilisi 0160, Georgia e-mail: temury@genao.org
² School of Mathematics and Statistics, University of St. Andrews, St. Andrews, Fife, KY16 9SS, Scotland, UK e-mail: bernie@mcs.st-and.ac.uk

Received: 3 June 2005
Accepted: 22 February 2006

Abstract

The weakly nonlinear interaction of sound and linearly polarised Alfvén waves propagating in the same direction along an applied magnetic field is studied. It is found that a sound wave is coupled to the Alfvén wave with double period and wavelength when the sound and Alfvén speeds are equal. The Alfvén wave drives the sound wave through the ponderomotive force, while the sound wave returns energy back to the Alfvén wave through the parametric (swing) influence. As a result, the two waves alternately exchange their energy during propagation. The process of energy exchange is faster for waves with stronger amplitudes. The phenomenon can be of importance in astrophysical plasmas, including the solar atmosphere and solar wind.