Abstract
The wave equation for a spatially dispersive inhomogeneous magnetized plasma is given by an integro-differential equation. The effects caused by spatial dispersion in the directions perpendicular and parallel to the magnetic field are quite different. In this study, we show how to solve the wave equation using a newly developed iterative wavelet spectral method for two cases. In the first case, the method is applied to a propagating kinetic Alfven wave in the perpendicular direction and solved to all orders in FLR. To conserve the kinetic energy flux, first order corrections in equilibrium gradients are used in the dielectric response tensor. In the second case, we verify the method for a fast wave minority heating scenario and study the up- and downshift in the parallel wave number.
Highlights
Magnetized plasma exhibit spatial dispersive effects both in the perpendicular and parallel directions
By expansion of the finite Larmor radius (FLR) effects with respect to the inhomogeneity the integro-differential equation can be approximated with a higher order differential equation that can be solved with finite element method (FEM)
In this study we have shown that this new iterative scheme is capable of solving spatially dispersive wave equation for inhomogeneous media
Summary
Magnetized plasma exhibit spatial dispersive effects both in the perpendicular and parallel directions. Perpendicular spatial dispersion arises due to finite Larmor radius (FLR) effects and becomes important when the perpendicular wavelength is comparable to the Larmor radius of a plasma species. By expansion of the FLR effects with respect to the inhomogeneity the integro-differential equation can be approximated with a higher order differential equation that can be solved with FEM. Methods based on FEM typically neglect the up- and downshift in the parallel wave vector [7,8]. Fourier spectral methods can be used for solving problems with spatial dispersion. These methods tend to produce dense and large matrices which are time consuming to solve
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