Dispersion function for plasmas with loss-cone distributions in an inhomogeneous magnetic field

Abstract

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.

The effective dielectric tensor for electromagnetic waves in inhomogeneous magnetized plasmas and the proper formulation in the electrostatic limit

“…We have early on been atracted by the potential usefulness of the concept of effective dielectric tensor and used it for several applications in magnetized plasmas, considering situations where the magnetic field is homogeneous and other parameters are inhomogeneous [5], situations where the magnetic field is inhomogeneous [8,9], and situations where density and magnetic field inhomogeneities are present simultaneously [10,11]. In all these cases, we have obtained expressions which clearly satisfy Onsager symmetry and used them to obtain the solutions of the dispersion relation.…”

The dispersion relation for electrostatic fluctuations in weakly inhomogeneous plasmas

“…Among these investigations, we have considered cases where the magnetic field is homogeneous and other plasma parameters are inhomogeneous [2,3,4], cases where the magnetic field is inhomogeneous and inhomogeneities in the plasma parameters are neglected [5,6], and cases where inhomogeneities are taken into account both in the plasma parameters and in the magnetic field [7]. For all these cases we case considered arbitrary direction of propagation relative to the ambient magnetic field, and we have taken into account relativistic effects.…”

On the Onsager symmetry of the effective dielectric tensor for plasmas in inhomogeneous magnetic field

“…In previous investigations of the effective dielectric tensor for the case of inhomogeneous magnetic field, we have considered high frequency oscillations propagating in arbitrary directions in a plasma, and we have obtained explicit expressions for the components of the effective dielectric tensor, which satisfy Onsager symmetry [4,10]. We now return to the subject, aiming to improve the accuracy of the calculations, in the sense that the unperturbed orbits will be described more precisely than in previous work.…”

“…Using the proposed geometry we solve the equations of movement and obtain the unperturbed orbits, correct up to order k B . In references [4,10], where a dielectric tensor featuring Onsager symmetry was obtained, we had used the unperturbed orbits, but neglecting some corrections of order k B , while keeping the correction to the cyclotron frequency Ω α0 , which is necessary in order to avoid secular terms, and the term proportional to τ in the y coordinate, which describes the drift of the guiding center due to the inhomogeneity. For the present investigation, we keep all the other terms of order k B in the expressions for the unperturbed orbits, re-derive the dielectric tensor, and discuss the ensuing properties of symmetry.…”

“…They certainly require much heavier load of algebraic manipulations than the homogeneous case. Similar calculations must be now developed for the other components of the effective dielectric tensor, in order to verify if Onsager symmetry is indeed satisfied by the tensor, as demonstrated in the case of simpler expressions for the unperturbed orbits [4,10], as well as in the case of homogeneous field and inhomogeneous plasma parameters [14].…”