Kelvin-Helmholtz instability of anisotropic plasma in a magnetic field

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Abstract
The Kelvin-Helmholtz problem is analyzed by a set of general hydromagnetic equations, which includes ideal magnetohydrodynamic and Chew-Goldberger-Low models as particular cases. A formalism is given that facilitates comparison between results from different models. A sheared flow is one in which the velocity has no component in the y direction, and such that the x and z components of the velocity depend on the y co-ordinate. A sheared field is defined similarly. The differential equations for linear modes of oscillation of a sheared flow in a sheared magnetic field is obtained; and the energy of these modes is studied. As a particular case of oscillations of a sheared flow, the properties of the modes excited by arbitrary modulation of a tangential discontinuity are studied. The relationship between radiation of waves from such a discontinuity and instability of the system is brought out by considering the system energy. Domains of absolute stability are given; and the different hydromagnetic models are compared by examining the predicted domains. It is found that anisotropy plays an important role in the conditions of stability.