Astron. Astrophys. 363, 1186-1194 (2000)

A developed stage of Alfvén wave phase mixing

G.J.J. Botha ¹, T.D. Arber ², V.M. Nakariakov ³ and F.P. Keenan <sup>1

1</sup> Queen's University, Department of Pure and Applied Physics, Belfast BT7 1NN, UK (gert@math.ucl.ac.uk; f.keenan@qub.ac.uk)
² University of St. Andrews, School of Mathematical and Computational Sciences, St. Andrews, Fife KY16 9SS, UK (tda@astro.warwick.ac.uk)
³ University of Warwick, Department of Physics, Coventry CV4 7AL, UK (valery@astro.warwick.ac.uk)

Received 17 August 2000 / Accepted 12 October 2000

Abstract

Alfvén wave phase mixing is an extensively studied mechanism for dissipating wave energy in an inhomogeneous medium. It is common in the vast majority of phase mixing papers to assume that even though short scale lengths and steep gradients develop as a result of phase mixing, nonlinear wave coupling does not occur. However, weakly nonlinear studies have shown that phase mixing generates magnetoacoustic modes. Numerical results are presented which show the nonlinear generation of magnetosonic waves by Alfvén wave phase mixing. The efficiency of the effect is determined by the wave amplitude, the frequency of the Alfvén waves and the gradient in the background Alfvén speed. Weakly nonlinear theory has shown that the amplitude of the fast magnetosonic wave grows linearly in time. The simulations presented in this paper extend this result to later times and show saturation of the fast magnetosonic component at amplitudes much lower than that of the Alfvén wave. For the case where Alfvén waves are driven at the boundary, simulating photospheric footpoint motion, a clear modulation of the saturated amplitude is observed. All the results in this paper are for a low amplitude (), single frequency Alfvén wave and a uniform background magnetic field in a two dimensional domain. For this simplified geometry, and with a monochromatic driver, we concluded that the nonlinear generation of fast modes has little effect on classical phase mixing.

Key words: Magnetohydrodynamics (MHD) plasmas waves Sun: corona

Online publication: December 5, 2000

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