Dispersion relation and the dieletric tensor for magnetized plasmas with inhomogeneous magnetic field (original) (raw)
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An alternative form of the nonrelativistic permittivity tensor for a homogeneous magnetized plasma in thermal equilibrium is derived in the linear approximation. The derivation follows the lines of Trubnikov’s derivation of the relativistic permittivity tensor and is restricted to a collisionless electron plasma. In the case of a Maxwellian equilibrium distribution, the final form is equivalent to Gordeev’s integral form of the permittivity tensor. The analysis is, with minor modification, applicable to plasma comprised of multiple particle species. Unlike the standard formulas, the alternative formula presented in this article yields the components of the permittivity tensor by means of partial derivatives of a scalar kernel integral. Besides the cyclotron harmonic resonance frequencies, where the permittivities in the nonrelativistic approximation become singular, the alternative formula is manifestly valid for all wave frequencies without any restrictions on the wave vector and t...
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An asymptotic expression for the dielectric tensor e of a hot magnetized plasma is obtained employing the steepest descents method, via the transformation of the components of e into their integral representation. The electrostatic Bernstein dispersion relation for oblique and perpendicular propagation is discussed under this treatment. It is shown that with this procedure the computation of the dispersion relation is up to 20 times faster when it is compared with the original expression, and the relative accuracy is usually as good as 0-1 % for a typical case.
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The dispersion relation for electromagnetic waves in a magnetized plasma with weakly inhomogeneous magnetic field is investigated within the framework of a WKB approximation. A dispersion function useful for the case of plasma particles described by a generalized loss-cone distribution is introduced, valid for waves propagating in weakly relativistic plasmas, for any direction relative to the ambient magnetic field and to the inhomogeneity. This dispersion function is in some particular cases related to other plasma dispersion functions well known from the study of homogeneous plasmas. An application is made for the case of ordinary mode waves propagating perpendicularly to the magnetic field in inhomogeneous loss-cone plasmas. ͓S1063-651X͑97͒07104-3͔
Brazilian Journal of Physics, 2008
A kinetic approach to the problem of wave propagation in dusty plasmas, which takes into account the variation of the charge of the dust particles due to inelastic collisions with electrons and ions, is utilized as a starting point for the development of a new formulation, which writes the components of the dielectric tensor in terms of a finite and an infinite series, containing all effects of harmonics and Larmor radius. The formulation is quite general and valid for the whole range of frequencies above the plasma frequency of the dust particles, which were assumed motionless. The formulation is employed to the study of electrostatic waves propagating along the direction of the ambient magnetic field, in the case for which ions and electrons are described by Maxwellian distributions. The results obtained in a numerical analysis corroborate previous analysis, about the important role played by the inelastic collisions between electrons and ions and the dust particles, particularly on the imaginary part of the dispersion relation. The numerical analysis also show that additional terms in the components of the dielectric tensor, which are entirely due these inelastic collisions, play a very minor role in the case of electrostatic waves, under the conditions considered in the present analysis.