On the dispersion law of low-frequency electron whistler waves in a multi-ion plasma

B V Lundin,C Krafft

doi:10.5194/angeo-26-1605-2008

Abstract

Abstract. A new and simple dispersion law for extra-low-frequency electron whistler waves in a multi-ion plasma is derived. It is valid in a plasma with finite ratio ωc/ωpe of electron gyro-to-plasma frequency and is suitable for wave frequencies much less than ωpe but well above the gyrofrequencies of most heavy ions. The resultant contribution of the ions to the dispersion law is expressed by means of the lower hybrid resonance frequency, the highest ion cutoff frequency and the relative content of the lightest ion. In a frequency domain well above the ions' gyrofrequencies, this new dispersion law merges with the "modified electron whistler dispersion law" determined in previous works by the authors. It is shown that it fits well to the total cold plasma electron whistler dispersion law, for different orientations of the wave vectors and different ion constituents, including negative ions or negatively charged dust grains.

Highlights

One of the typical problems inherent to the application of the Geometrical Optics (GO) or the ray approximation approach consists in the fact that the expression for the local dispersion equation of plane waves of the magnetoactive plasma modes under consideration should be known; one should provide the data about the plasma constituents contributing to the local dielectric permittivity tensor along the rays’ paths
The GO technique was applied to fit the parameters of space density model distributions using the Direction Finding Data of groundbased transmitter signals registered on board the “Ikebono” satellite (Sawada et al, 1993)
Let us demonstrate by numerical calculations that the biquadratic dispersion equation presented in Eqs. (23–24) is relevant, due to its very good agreement with the electron whistler mode branch dispersion law in a cold plasma, at any angle of propagation

Summary

Introduction

An adjacent problem typical of the ray approximation approach consists of simplifying a general plasma dispersion law in order to reduce, if possible, the amount of the physical parameters governing explicitly the wave propagation of a selected plasma mode. It is well known that the peculiarities of the wave dispersion laws in the low frequency range are essentially different for a single ion plasma or a multi-ion species plasma (Hines, 1957; Buchsbaum, 1960; Yakimenko, 1962; Gintzburg, 1963; Smith and Brice, 1964; Gurnett and Burns, 1968; Das and Uberoi, 1972; Mamun et al, 2004, 2005, and references therein) In the latter case, the main feature for plane waves is the appearance of cutoff frequencies in the domains of the ions’ gyrofrequencies and of resonance frequencies, depending on their polarization sense. The possibility to increase significantly the value of the cutoff frequency above the lightest ion gyrofrequency in the presence of negative ions (or dust grains) is discussed in an application to the problem of electron whistler wave propagation and reflection in the upper ionosphere

Electron whistler dispersion law in the lightest ion’s gyrofrequency domain

Numerical fitting and conclusions