Propagating Whistler Mode Waves Research Articles

Excitation of whistler mode instability by high energy electrons in the magnetosphere

Propagation of whistler mode waves through magnetospheric plasma characterised by a double Maxwellian velocity distribution function has been considered. The presence of a high energy electron tail in the composite velocity distribution function provides the needed free energy which excites instability mechanism for propagating whistler mode waves. The presence of the parallel or the antiparallel electric field governs the growth/decay rate variation with normalised parameter k ̃ = kV e ω H . These results are found to be different from those reported, which have used other forms of electron velocity distribution functions. The dependence of growth/decay rate on magnetospheric parameters plays an important role in the interpretation of wave features recorded by in-situ measurements. The presence of a fraction of high energy tail electrons penetrating through magnetospheric plasma exhibits significant change in the growth/decay rate of whistler mode waves.

The effect of multi-duct structure on whistler-mode wave propagation

Ducting of whistler-mode waves is investigated by ray-tracing in a magnetospheric model in which multiple and complex duct structures are superimposed on a smooth magnetospheric plasma distribution. When two or more ducts are present, propagation through a duct in which the ray does not become trapped is found to result in little deviation of the ray path, showing that upgoing waves can traverse several ducts before becoming trapped in one that is suitably positioned. The presence of two ducts situated in the same meridian plane and close together in L-value ( ΔL ~ 0.07) is found to enable a double-duct trapping mode. This has the special property of guiding waves with frequency above half the local electron gyrofrequency across the equatorial plane in such a way that they become retrapped in the duct from which they had previously escaped at its local detrapping frequency. This may explain the observation of whistlers with a particularly high ratio of cut-off frequency to nose frequency ( Bernhardt, 1979). Ducting is also investigated for a more complex duct structure in which fine structure is superimposed on a broader larger enhancement main duct. Here, it is found that rays which are first trapped to propagate in the main duct at low altitude can be further trapped to be ducted inside fine structure enhancements at higher altitude. This can result in certain components of multipath whistlers always being excited together and also having a common exit-point in the lower ionosphere. This is shown to be consistent with experimental observations.

Whistler mode wave propagation in the solar wind near the bow shock

The presence of whistler mode waves in, and upstream from, the bow shock has been well established by observation. Theoretical descriptions of the mode under solar wind conditions have been relatively meagre, however, and it may not be generally appreciated how readily whistler waves generated in the shock could occupy most of the region ahead of the shock most of the time. Graphic descriptions of phase and group velocities and group velocity directions for typical solar wind parameters are presented by using the cold plasma approximation over all appropriate frequencies and directions with respect to the IMF. The relations of whistler phase and group velocities to observations of a quasi‐perpendicular shock crossing by ISEE are illustrated.

Computer simulation of a Cerenkov interaction between obliquely propagating whistler mode waves and an electron beam

A Cerenkov type wave-particle interaction between an obliquely propagating whistler mode wave and an electron beam has been investigated by a computer simulation experiment. A one-dimensional electromagnetic simulation code which is especially designed to deal with the obliquely propagating wave is used. Two cases of such a wave-particle interaction have been investigated. In the first case no initial wave is assumed to exist in the simulation model space. In the second case, an obliquely propagating whistler mode wave with a finite amplitude is initially assumed to exist. In both cases after linear wave growth, nonlinear saturation and amplitude oscillation are observed. This nonlinear behavior of the interaction can be interpreted by particle trapping in the wave potential well just as in the case of longitudinal electrostatic waves. Waves excited by Cerenkov radiation from the beam electrons develop as a coherent wave due to the instability and propagate in the magnetized plasma. By the oblique beam-plasma interaction, electromagnetic waves can be amplified. Amplification of the waves observed by this computer simulation may be closely related to VLF hiss noise occurring in the earth’s magnetosphere.

Effect of a parallel electric field on the whistler mode instability in the magnetosphere

A dispersion relation for the whistler mode wave propagation in an anisotropic warm magnetoplasma in the presence of a weak parallel electrostatic field has been derived from linearized coupled Boltzmann‐Maxwell equations with collision frequency independent of particle velocity. An expression for the growth rate has been derived in the presence of an electric field and for small temperature anisotropy (A<1) for the whistler mode wave. Under suitable approximation we recover the earlier known results. The modifications introduced in the growth rate by the electric field and temperature anisotropy have been discussed using observed plasma parameters at 6.6 RE. It is observed that growth (damping) of whistler mode waves is possible when the wave vector is parallel (antiparallel) to the static electric field. The effect of the electric field is more pronounced at low frequency (higher wave number) wave spectrum.

Obliquely propagating whistler mode waves in cold plasmas permeated by dilute low-β anisotropic plasmas

We analyse the growth rate of obliquely propagating whistler mode waves in a cold plasma that also contains some hot electrons in a bi-Maxwellian distribution. Approximate analytic expressions for the growth rate are derived explicitly. They are represented by elementary functions only, consisting of a Landau damping term and a cyclotron instability term. They are found to be valid for a wide range of wave normal angles. Landau damping in the oblique propagation does not always become larger even if the wave normal angles increase. The necessary conditions for the minimal parallel growth are Ω > 0.5Ωe and T≥> 2T∥ in the bi-Maxwellian hot plasma. This method is applied to calculations of the net growth along the ray paths of obliquely propagating non-ducted whistler mode waves in a model magnetosphere.

Some comments on the whistler mode instability at Jupiter

The paper considers the possibility that electrons with energies exceeding 21 MeV at Jupiter interact resonantly with obliquely propagating whistler mode waves. The equatorial pitch angle distributions are deduced from the Pioneer 10 and 11 data points of Van Allen et al. (1975). For the L shell subgroup 7, there is observed a 'hat-shaped' pitch angle distribution which is similar to that found within the earth plasmasphere.

Effect of parallel electric fields on the whistler mode wave propagation in the magnetosphere

The effect of parallel electric fields on whistler mode wave propagation has been studied. To account for the parallel electric fields, the dispersion equation has been analyzed, and refractive index surfaces for magnetospheric plasma have been constructed. The presence of parallel electric fields deforms the refractive index surfaces which diffuse the energy flow and produce defocusing of the whistler mode waves. The parallel electric field induces an instability in the whistler mode waves propagating through the magnetosphere. The growth or decay of whistler mode instability depends on the direction of parallel electric fields. It is concluded that the analyses of whistler wave records received on the ground should account for the role of parallel electric fields.

Modification of a theory of electron precipitation pulsations

The concern of this work is to suggest some improvements in the Coroniti-Kennel theory of electron precipitation pulsations. Some inconsistencies in this theory are remedied by using the relaxation time of the electron velocity distribution as a classifying parameter. Recalculations reveal precipitation pulsations that still may be exponentially strong in the micropulsation amplitude; however, the condition for validity of this result is more restrictive than given by Coroniti and Kennel. In the transition region between weak and strong diffusion, a periodic variation in the upper cut-off frequency of the VLF spectrum may occur. This variation is in anti-phase with the whistler mode wave intensity and the magnetic perturbation causing it. In the simplified model of only parallel propagating whistler mode waves strong pitch angle diffusion probably cannot be self-excited, it must thus be of a parasitic nature.

Analyses of techniques for measuring DC and AC electric fields in the magnetosphere

Methods for measuring the amplitudes and directions of DC electric fields and the directions, power spectra, and dispersion relations of AC electric fields in the magnetosphere are discussed with emphasis on their applicability in various regimes of the magnetospheric plasma. The two classes of techniques that are discussed are measurement of the bulk flow of the plasma and the potential difference between pairs of separated conductors. The plasma bulk flow discussion includes measurements by ionospheric radar backscatter, whistler mode wave propagation, energetic or thermal particle trajectories, artificial ion cloud motion, probe measurements of bulk flow, vehicle wake analyses, effects of bulk flow on the coupling of antennas, and the bulk flow of an artificial electron beam.

Hot plasma theory of whistler mode wave packet propagation along a non-uniform magnetic field

We discuss the propagation of wave packets of the formin an infinite uniform plasma, where G(z, t) is a slowly varying function of space z and time t. One can very simply derive the equation of change of G(z, t) for the stable or unstable case. The terms in the equation are of physical interest and clearly define the limitations of linear theory. We then investigate the problem of whistler mode wave propagation in a collisionless Vlasov plasma in a given non-uniform magnetic field. We choose the electric field to be of a W.K.B. form and the particle distribution to be isotropic. We can express the perturbation in the particle distribution in terms of an integration along the zero-order par tide orbits (an integration overtime). These orbits can be found correct to a term linear in a smallness parameter ε (when ε equals zero we arrive back at a uniform magnetic field). The charge and current density due to the perturbation are related through Maxwell's equations to the electric and magnetic field of the wave in the usual self consistent Boltzmann—Vlasov description. We show that the contribution to the current arises from recent events in the history of a given particle because of the finite temperature of the plasma. This result leads to an expansion of slowly varying parameters which in turn gives rise to the equation governing the motion of the wave packet.