Non-stationary resonant Alfven surface waves in one^dimensional magnetic, plasmas

摘要

This paper uses incompressible yisco-resistive MHD to study the propagation of linear resonant wayes in an inhoinogeneous 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 andperpendicular 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 .thecoefficients of viscosity and resistivity are sufficiently small that.dissipatipn. of energy is confined to a narrow dissipative la/yer. The solutions to this equationare obtained in the form of decaying normal; surface modes with wavelengths much larger than the characteristic scale of the inhomogeneity. The effect of -stationarity inside the dissipa.tive layer is taken into account, and validhi -lutions are found even when the ratio.of the thickness of the dissipative layer tn the inhomogeneity length scale is of the order of or smaller than the ratio of Mid inhomogeneity length scale, to the wavelength. These,solutions are the fl'iieralization. oLthe solutions obtained by Mok and Ein.au dl, wEich are only jlid when the first ratio is much larger than the .second. The rate of wave clamping is shown to be independent of the values of the viscosity and the listivity. However, the behaviour of the solutions in the dissipative, layer depends strongly on the. viscosity and the resistivity. In the case that the effect ul dissipation c ominates 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 non-hlji.tionarity, the solutions become more and more oscillatory, and their amplitudes grow very rapidly in the dissipative layer. Eventually, when non- stationarity, dominates dissipation, the amplitudes of the solutions become so laige in the diasipative layer in comparison with those outside the dissipative layer that practically all the energy of the perturbations is concentrated in the dihsipative layer.