By Rudolf A. Treumann
This e-book builds at the fluid and kinetic thought of equilibria and waves offered in a significant other textbook, uncomplicated area Plasma Physics (by an identical authors), yet may also function a stand-alone textual content. It extends the sector coated there into the area of plasma instability and nonlinear concept. The booklet offers a consultant choice of the numerous attainable macro- and microinstabilities in an area plasma, from the Rayleigh-Taylor and Kelvin-Helmholtz to electrostatic and electromagnetic kinetic instabilities. Their quasilinear stabilization and nonlinear evolution and their software to area physics difficulties are handled. The chapters on nonlinear conception comprise nonlinear waves, susceptible turbulence and robust turbulence, all offered from the point of view in their relevance to house plasma physics. distinct issues comprise auroral particle acceleration, soliton formation and caviton cave in, anomalous shipping, and the speculation of collisionless shocks.
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50) is the dispersion relation of the Kelvin-Helmholtz instability. Formally this relation is very similar to the dispersion relations familiar from investigation of streaming instabilities. However, in the present case the role of the plasma modes is taken over by the two Alfv´en waves propagating in regions 1 and 2. Actually, the first term in Eq. 50) is the Alfv´en wave in the non-streaming region, while the second term is the Alfv´en wave in the streaming region as seen from region 2. The role of the interface is merely to couple these two Alfv´en modes together.
Here the incompressible approximation is quite reasonable because of the strong background magnetic field, but the existence of field-aligned currents and the narrowness of the structures suggest that kinetic Alfv´en wave are involved here. In this region the waves propagate in the shear kinetic Alfv´en mode (see Sec. 6 of our companion book). However, let us neglect all these effects, and just assume a negatively charged layer of auroral electrons with a width 2d in the horizontal x direction, but of infinite extent along the horizontal y and the vertical z axis.
1. Rayleigh-Taylor unstable plasma configuration. 1) Let us for the moment neglect any thermal effects and assume that the plasma is collisionless. When the plasma boundary is distorted by a small purely electrostatic perturbation in the (x, y) plane, an instability can develop. Consider a distortion of the boundary so that the plasma density makes a sinusoidal excursion in the z direction. The gravitational field causes an ion drift and current in the negative y direction, viy = −mi g/eB0 . The electrons, because of their negligible mass, do not participate in this motion.