Electrostatic Waves in Inhomogeneous and Magnetized Plasmas

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Abstract
A formalism is presented for the study of electrostatic waves in inhomogeneous plasmas immersed in a finite magnetic field perpendicular to the direction of inhomogeneity. Based on the quasistatic approximation, the dispersion relation is found to depend on the geometrical factors through four quantities which possess certain general properties. The dispersion relation is solved explicitly for the case of cold plasma. It is found that, in stationary plasmas, the density inhomogeneity not only affects the frequencies of oscillation but also alters the propagation and evanescent bands of the two branches of electron plasma waves. For streaming plasmas, the inhomogeneity, the transverse boundary, and the finite magnetic field all contribute to the stabilization of the instability. It is shown that the concept of effective density, developed previously for the infinite magnetic field case, can be extended to the case of finite magnetic field. Various special cases studied previously are recovered by putting appropriate parameters to zero in this general formalism.

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