Dispersion relation and the dieletric tensor for magnetized plasmas with inhomogeneous magnetic field (original) (raw)
The magnetized plasma permittivity tensor
Physics of Plasmas, 2000
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...
Asymptotic approximation for the dispersion relation of a hot magnetized plasma
Journal of Plasma Physics, 1987
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.
Dispersion function for plasmas with loss-cone distributions in an inhomogeneous magnetic field
Physical Review E, 1997
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.
Physics of Plasmas, 2017
In this procedure, the fundamental electromagnetic equations and fluid equations in a cylindrical coordinate system for a new drift plasma configuration have been analyzed. The system is a long nonhomogeneous drift plasma column, which is imbedded in a uniform transverse magnetic field rotating about the symmetric axis of the system. The elements of the dielectric permittivity tensor are obtained for a pattern propagating in an arbitrary direction, and coupling equations of fields will be derived. It will be observed that the time variable dielectric tensor can be written as nonoperational Hermitian and pure spatial operational parts which satisfy the limiting special cases.
Journal of Non-Equilibrium Thermodynamics, 1999
Within the framework of Extended Irreversible Thermodynamics (EIT) a phenomenological theory is proposed for a polarizable and magnetizable plasma in an electromagnetic ®eld. In particular, for the polarization a transport equation is proposed generalizing the well-established Debye's law for dielectric relaxation. For the magnetization a transport equation is proposed generalizing the well-established Langevin's law for magnetic relaxation. The present equations correspond to those obtained by Dixon involving also coupling terms with the heat¯ux. Finally, in the special case in which cross-effects are not taken into account, the dispersion relation for plane weak electromagnetic disturbances is derived.
Polarization transfer in relativistic magnetized plasmas
Monthly Notices of the Royal Astronomical Society, 2013
The polarization transfer coefficients of a relativistic magnetized plasma are derived. These results apply to any momentum distribution function of the particles, isotropic or anisotropic. Particles interact with the radiation either in a non-resonant mode when the frequency of the radiation exceeds their characteristic synchrotron emission frequency, or quasi-resonantly otherwise. These two classes of particles contribute differently to the polarization transfer coefficients. For a given frequency, this dichotomy corresponds to a regime change in the dependence of the transfer coefficients on the parameters of the particle's population, since these parameters control the relative weight of the contribution of each class of particles. Our results apply to either regimes as well as the intermediate one. The derivation of the transfer coefficients involves an exact expression of the conductivity tensor of the relativistic magnetized plasma that has not been used hitherto in this context. Suitable expansions valid at frequencies much larger than the cyclotron frequency allow us to analytically perform the summation over all resonances at high harmonics of the relativistic gyrofrequency. The transfer coefficients are represented in the form of two-variable integrals that can be conveniently computed for any set of parameters by using Olver's expansion of high-order Bessel functions. We particularize our results to a number of distribution functions, isotropic, thermal or power-law, with different multipolar anisotropies of low order, or strongly beamed. Specifically, earlier exact results for thermal distributions are recovered. For isotropic distributions, the Faraday coefficients are expressed in the form of a one-variable quadrature over energy, for which we provide the kernels in the high-frequency limit and in the asymptotic low-frequency limit. An interpolation formula extending over the full energy range is proposed for these kernels. A similar reduction to a one-variable quadrature over energy is derived at high frequency for a large class of anisotropic distribution functions that may form a basis on which any smoothly anisotropic distribution could be expanded.
ESAIM: Mathematical Modelling and Numerical Analysis, 2015
We consider a model for the propagation and absorption of electromagnetic waves (in the time-harmonic regime) in a magnetised plasma. We present a rigorous derivation of the model and several boundary conditions modelling wave injection into the plasma. Then we propose several variational formulations, mixed and non-mixed, and prove their well-posedness thanks to a theorem by Sébelin et al. Finally, we propose a non-overlapping domain decomposition framework, show its well-posedness and equivalence with the one-domain formulation. These results appear strongly linked to the spectral properties of the plasma dielectric tensor. Résumé. Nous considérons un modèle de propagation et d'absorption d'ondesélectromagnétiques (en régime harmonique) dans un plasma magnétique. Nous présentons une justification rigoureuse du modèle et diverses conditions aux limites modélisant l'injection de l'onde dans le plasma. Puis nous proposons plusieurs formulations variationnelles, mixtes ou non, et montrons qu'elles sont bien posées grâceà un théorème de Sébelin et al. Enfin, nous décrivons le principe d'une décomposition de domaine sans recouvrement, etétablissons le caractère bien posé de la formulation décomposée et l'équivalence avec la formulationà un seul domaine. Ces résultats paraissent intimement liés aux propriétés spectrales du tenseur diélectrique du plasma.