Linear and nonlinear cyclotron instability and VLF emissions in the magnetosphere

A theoretical study is made of the whistler mode cyclotron instability both in linear and nonlinear regimes in conjunction with the generation of VLF emissions in the magnetosphere. For the nonlinear treatment, a well-established quasilinear method is used and some physical processes of the cyclotron instability viz. energy conservation, mechanism of instability and frequency change of the excited emissions are clarified. The results are applied to some types of the triggered VLF emissions; whistler triggered emissions and artificially stimulated emissions (ASE). It is found that whistler triggered emissions excited around the upper cutoff frequencies of whistlers may be explained by the whistler mode cyclotron instability by a model distribution function inferred from satellite data. In order to see a nonlinear evolution of the whistler mode cyclotron instability, computer simulations were carried out and it is shown that the change of frequency with time of whistler triggered emissions as well as characteristics of ASE are well explained by resonant nonlinear behaviour of whistler mode cyclotron instability considered in the present paper.     

VLF waves in the magnetosphere

The study of VLF waves at ground based stations is an important source of information on particles trapped in the magnetosphere. By various techniques it is also possible to measure plasma densities, electric fields and monitor energetic particle injection. By studying the propagation of waves beneath the ionosphere it is possible to study particle precipitation from the magnetosphere. In this paper we summarise some of the techniques and results obtained from the study of VLF waves at the South African research station in Antarctica.     

VLF two-wave-electron interactions in the magnetosphere

The mutual influence between two whistler mode waves, through cyclotron resonant interaction of each wave with the same set of energetic electrons, is analysed both theoretically and by computer simulations ; this two-wave interaction mechanism seems to be an important process in understanding recently observed phenomena in Siple Station VLF multi-wave injection experiments. A criterion is established to estimate the threshold for the critical frequency spacing (for given wave amplitudes) for a significant mutual interaction between two monochromatic waves to occur. This criterion is based on the overlap of coherence bandwidths associated with the trapping domains of each wave and it takes into account the geomagnetospheric medium inhomogeneity. The effects of a perturbing second wave on electrons trapped by a first wave is discussed, considering the general situation of varying-frequency waves, and a simulation model is used to track the motion of test-electrons in the two-waves field. Conditions leading to detrapping and subsequent trapping by the second wave of previously first-wave trapped electrons are analysed and suggest the possibility of this phenomenon to play an important role in frequency entrainment and energy exchange between two waves.     

Excitation of ULF and VLF waves in the ionosphere

It is shown that a two-dimensional lower-hybrid wave structure can parametrically trigger the growth of VLF and ULF noises in a plasma. Analytical expressions for the increment and threshold of the instability are obtained. Application of our work to the auroral zones of the topside ionosphere is discussed.     

ULF pulsation mode coupling in the ionosphere and magnetosphere

The effect of realistic ionospheric Hall conductances on axisymmetric toroidal mode hydromagnetic wave resonances is investigated. The toroidal modes couple to evanescent poloidal modes near the ionospheres such that the composite modes resonate at the constant frequencies of the corresponding single-field-shell resonances for zero Hall conductance. A model for these composite modes is developed which has narrow but finite latitudinal resonance widths such as to make the modes valid solutions of the hydromagnetic equations. The modes also suggest that “shell” solutions can realistically describe such properties of real pulsations as frequency, damping, phase variation along the field-line and node-antinode behaviour at the ionospheres. Estimates of ionospheric coupling strength are obtained and compared with magnetospheric coupling strength. It is found that magnetospheric coupling dominates ionospheric coupling for any single non-axisymmetric mode. However, ionospherically coupled axisymmetric modes should be necessary components of the Fourier sum of modes required to model any real pulsation of low to moderate apparent azimuthal wave number.Estimates of the range of magnetospheric coupling strength are obtained for pulsations under a variety of conditions.     

Jupiter's ionosphere and magnetosphere

The distribution of ionization and the temperature variation in the Jovian ionosphere is determined by simultaneously solving the momentum and chemical equations for electrons, ions and neutrals together with their respective heat transport equation. The boundary conditions at the bottom of the ionosphere are chosen in accordance with recent infra-red and occultation measurements. The ionosphere is hotter than previously thought. The electron temperature may be as high as 1500 K. A considerable flux of particles can escape from the ionosphere. These particles are trapped in the Jovian magnetosphere by a two-stream instability. A Gledhill disk will form. The variation of plasma density along Io's orbit is calculated.     

VLF emissions and substorm activity

The resonant interaction between the whistler mode waves and the energetic electrons near the plasmapause boundary has been studied in the presence of field aligned currents which seem to exist during substorm activity. It is shown that the electrons which carry the current along the direction of the magnetic field enhance the whistler mode growth considerably if the streaming velocity is small compared to the phase velocity of the wave. It is likely that this is one of the mechanisms explaining the intense VLF emissions observed near the plasmapause during substorm activity.     

Dynamical behavior of thermal protons in the mid-latitude ionosphere and magnetosphere

Satellite and other observations have shown that H⁺ densities in the mid-latitude topside ionosphere are greatly reduced during magnetic storms when the plasmapause and magnetic field convection move to relatively low L-values. In the recovery phase of the magnetic storm the convection region moves to higher L-values and replenishment of H⁺ in the empty magnetospheric field tubes begins. The upwards flow of H⁺, which arises from O⁺—H charge exchange, is initially supersonic. However, as the field tubes fill with plasma, a shock front moves downwards towards the ionosphere, eventually converting the upwards flow to subsonic speeds. The duration of this supersonic recovery depends strongly on the volume of the field tube; for example calculations indicate that for L = 5 the time is approximately 22 hours. The subsonic flow continues until diffusive equilibrium is reached or a new magnetic storm begins. Calculations of the density and flux profiles expected during the subsonic phase of the recovery show that diffusive equilibrium is still not reached after an elapsed time of 10 days and correspondingly there is still a net loss of plasma from the ionosphere to the magnetosphere at that time. This slow recovery of the H⁺ density and flux patterns, following magnetic storms, indicates that the mid-latitude topside ionosphere may be in a continual dynamic state if the storms occur sufficiently often.     

Properties of adiabatic potential transitions in the polar ionosphere and magnetosphere

The properties of adiabatic potential transitions in a current carrying plasma are investigated and classified. It is shown that it is important to include pressure effects since the character of the transition (e.g. whether or not it behaves as a particle accelerator) is determined by whether the speed of a streaming species on entering the transition is less or greater than the “sound speed” of that species. If electrons are the main current carriers in the field aligned current systems associated with the polar ionosphere and magnetosphere we find that, under typical conditions, their drift speed is less than their thermal speed with the implication that if they enter a potential transition their pressure gradient will overcome the electrostatic field so that they are decelerated and heated by the transition. Under disturbed conditions when the field aligned current densities are exceptionally high, potential transitions act as particle accelerators.     

VLF input impedance of a loop antenna embedded in the magnetosphere

An analysis is made to calculate input impedance of a loop antenna for radiation of the VLF whistler mode in the magnetosphere. The magnetosphere is assumed to be represented by a cold, uniform and collisionless magnetoplasma medium. Assuming a uniform current distribution of a circular loop, oriented at an arbitrary angle with respect to the Earth's magnetic field line, several closed-form expressions for the loop impedance have been derived. It is found that the loop input reactance is in substantial agreement with the self-inductance of a loop in free space and that the radiation resistance for a small loop can be as large as ～10 ² Ω. It is also found that a second order quasi-static theory is quite valid for determining the input impedance for small loops radiating VLF whistlers in the magnetosphere.     

A theory of VLF emissions

The work attempts to give a theoretical explanation of the triggering of VLF emissions by magnetospheric whistler morse pulses. First studied is the behaviour of resonant particles in a whistler wave train in an inhomogeneous medium. It is found that second order resonant particles become stably trapped in the wave. After 1–2 trapping periods such particles dominate the resonant particle distribution function, and produce large currents that are readily estimated.     

Mapping electrostatic potentials from the ionosphere to the magnetosphere

With the advent of long duration incoherent scatter radar experiments measuring ionospheric plasma convection over a wide range of latitudes and at all local times, the mapping and study of the spatial and temporal distribution of electric fields within the magnetosphere becomes possible. We consider the problems of mapping the ionospheric electrostatic potential distribution into the magnetosphere under the assumption that magnetic field lines are electrostatic equipotentials. We address the practical problem of developing a mapping technique which can adequately project ionospheric observations, acquired at different geographic longitudes, into the magnetosphere. The mapping must include the effects of a magnetotail when considering auroral latitudes and is a function of diurnal and seasonal effects and is ionospheric longitude dependent. Mapping observed ionospheric potential distributions into the magnetosphere yields parameters such as: the distribution of electric fields in the magnetosphere, the cross tail potential, the location of plasmapause, the local time of the ‘stagnation’ bulge region and the gradients of the electric field in the vicinity of the plasmapause.     

DP2 current system in the ionosphere and magnetosphere

Some years ago Nishida (1966) identified an equivalent current system which appeared to reflect a coherent magnetic field fluctuation observed at the equator and at high latitudes. This equivalent current system was subsequently labelled DP2, and since its existence was proposed it has been a topic of some controversy. In this paper we utilize the fact that DP2 intensity is regulated by the B_z component of the interplanetary magnetic field to decouple the DP2 variation from the very similar S_q perturbation pattern. We demonstrate how DP2 can arise as a manifestation of the overall three-dimensional magnetospheric-ionospheric current system which couples the magnetosphere to the high latitude ionosphere, and suggest how ionospheric conductivity is a major factor in regulating the strength of DP2 disturbances.     

Very low frequency (VLF) hiss in Jupiter's magnetosphere

The particle energy required to generate the observed VLF hiss in the Jovian magnetosphere has been computed under longitudinal and transverse resonance condition. It is shown that the minimum energy required by electrons to generate VLF hiss under the longitudinal resonance condition lies in the range of 100eV–1keV for the wave frequencies of 2–10 kHz, while the corresponding energy range for the transverse resonance condition for the same frequency range comes out to be 8 keV–40 keV. Further, the average radiated power by the erenkov process in the Jupiter's magnetosphere atL=5.6 Rj by electrons of energy 10 eV, 100 eV, and 1 keV for the wave frequency of 5 kHz has also been computed.     

Nonlinear hydrodynamic VLF wave scattering in the earth's magnetosphere

The paper deals with a nonlinear instability of quasi-monochromatic VLF signals and whistlers in the Earth's magnetosphere due to induced scattering. The instability growth rates and the threshold values of the signal amplitude at which the instability occurs have been found. The instability is shown to be more effectively excited when the initial transverse VLF wave transforms into plasma oscillations at the lower hybrid resonance (LHR) frequency and may be responsible for the phenomena such as trigger LHR emission, the amplitude and phase modulation of artificial VLF signals and be the origin of some types of discrete VLF signals.     

A model of quasiperiodic VLF emissions

A self-consistent quasilinear model of the interaction between VLF emissions and geomagnetic pulsation is set forth. As a result an explicit expression of a modulation frequency dependence can be obtained.     

Non-linear effects of VLF noise generation by electron beams in the polar magnetosphere

A theory of VLF noise excitation by electron beams in the polar magnetosphere is proposed. Two modes of excited oscillations are considered: waves with frequencies in the vicinity of the lower hybrid resonance (LHR) from about 50 to 1000 kHz and whistler-mode waves in the frequency range of several kHz.The spectral distribution and the level of turbulent noise, having been excited by means of two counterstreaming electron beams, are deduced in magnetized plasma at the LHR frequency. It is also shown that the growth of noise up to the quasistationary level oscillates with time. Energy density of oscillations at the LHR frequency in the region of the dayside polar cusp agrees with the experimental data.The processes of whistler excitation by electron beams are discussed. The growth rate of excitation of whistler-mode by electrostatic oscillations at the LHR frequency is calculated.