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Non-stationary resonant Alfvén surface waves in one-dimensional magnetic plasmas

Published online by Cambridge University Press:  13 March 2009

M. S. Ruderman ,
W. Tirry  and
M. Goossens
M. S. Ruderman
Affiliation:
Centre for Plasma Astrophysics, Katholiek Universiteit Leuven, Celestijnenlaan 200B, B-3001 Heverlee, Belgium
W. Tirry
Affiliation:
Centre for Plasma Astrophysics, Katholiek Universiteit Leuven, Celestijnenlaan 200B, B-3001 Heverlee, Belgium
M. Goossens
Affiliation:
Centre for Plasma Astrophysics, Katholiek Universiteit Leuven, Celestijnenlaan 200B, B-3001 Heverlee, Belgium
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Abstract

This paper uses incompressible visco-resistive MHD to study the propagation of linear resonant waves in an inhomogeneous plasma. The background density and magnetic field are assumed to depend only on one spartial Cartesian coordinate, and the magnetic field is taken to be unidirectional and perpendicular to the direction of inhomogeneity. The equation that governs the component of the velocity normal to the plane formed by the direction of the inhomogeneity and the magnetic field is derived under the assumption that the coefficients of viscosity and resistivity are sufficiently small that dissipation of energy is confined to a narrow dissipative layer. The solutions to this equation are obtained in the form of decaying normal surface modes with wavelengths much larger than the characteristic scale of the inhomogeneity. The effect of non-stationarity inside the dissipative layer is taken into account, and valid solutions are found even when the ratio of the thickness of the dissipative layer to the inhomogeneity length scale is of the order of or smaller than the ratio of the inhoinogeneity length scale to the wavelength. These solutions are the generalization of the solutions obtained by Mok and Einaudi, which are only valid when the first ratio is much larger than the second. The rate of wave damping is shown to be independent of the values of the viscosity and the resistivity. However, the behaviour of the solutions in the dissipative layer depends strongly on the viscosity and the resistivity. In the case that the effect of dissipation dominates the effect of non-stationarity, the solutions behave in the dissipative layer as found by Mok and Einaudi. When the effect of dissipation is steadily decreased in comparison with the effect of nonstationarity, the solutions become more and more oscillatory, and their amplitudes grow very rapidly in the dissipative layer. Eventually, when nonstationarity dominates dissipation, the amplitudes of the solutions become so large in the dissipative layer in comparison with those outside the dissipative layer that practically all the energy of the perturbations is concentrated in the dissipative layer.

Type
Research Article
Information
Journal of Plasma Physics , Volume 54 , Issue 2 , October 1995 , pp. 129 - 148
Copyright
Copyright © Cambridge University Press 1995

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