Quasi-linear interaction of whistler-mode waves and nonthermal electrons

In this investigation, we attempt to analyze the quasi-linear cyclotron instability (under the weak turbulence regime) for whistler-mode waves due to pitch angle anisotropy of nonthermal electrons. The motivation of this study is to explain the triggered discrete VLF emissions occurring in the terrestrial magnetosphere. The time evolution of the growth rate and the induced waves spectrum for a loss cone type of nonthermal electrons is analyzed numerically. The diffusion of particles in pitch angles due to quasilinear cyclotron instability is illustrated. It is shown that several major features of triggered VLF emissions can be explained by the stated instability. Some predictions of the theory is given and suggestions for further research are presented.On special leave during the summer of 1971 from the Physics Department, Faculty of Science, University of Hong Kong.     

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.     

Parallel electric field-induced instability in the magnetospheric ion-electron plasma

A complete dispersion relation for a whistler mode wave propagation in an anisotropic warm ion-electron magnetoplasma in the presence of parallel electric field using the dispersion relation for a circularly polarized wave has been derived. The dispersion relation includes the effect of anisotropy for the ion and electron velocity distribution functions. The growth rate of electron-ion cyclotron waves for different plasma parameters observed atL = 6.6R _E has been computed and the results have been discussed in detail in the light of the observed features of VLF emissions and whistlers. The role of the combination of ion-cyclotron and whistler mode electromagnetic wave propagation along the magnetic field in an anisotropic Maxwellian weakly-ionized magnetoplasma has been studied.     

Hook whistlers observed at low latitude ground station Varanasi

Employing the Haselgrove ray tracing equations and a diffusive equilibrium model of the ionosphere, the propagation characteristics of hook whistlers recorded at low-latitude ground station Varanasi (geomag. lat., 16°6′.N) are discussed. It is shown that the two traces of the hook whistlers are caused by the VLF waves radiated from the return stroke of a lightning discharge which after penetrating the ionosphere at two different entry points, propagated to the opposite hemisphere in the whistler mode and were received at 16 geomagnetic latitude. Further the crossing of ray paths for the same frequency leads to the explanation of the hook whistler. The lower and higher cut-off frequencies are explained in terms of their deviating away from the bunch of the recorded whistler waves and crossing of ray paths for the same frequency.     

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.     

On the influence of a CW whistler on magnetospheric noise

Analysis of the modifications introduced in a turbulent whistler noise spectrum with the injection of a coherent whistler leads to a nonlinear dispersion equation for the stochastic modes. These modes are submitted to real frequency shifts and corrections to their growth rates which are in qualitative agreement with observations made in the Siple Station VLF wave injection experiment showing the creation of noise-free bands when CW whistler modes are transmitted.     

Discrete emissions and whistler precursors recorded at low latitude ground station Gulmarg

Discrete chorus-type emission and whistler precursors recorded in March 1972 during day time hours at our ground based station Gulmarg are presented. It is shown that discrete chorus type emissions are generated in the equatorial region (L 1.2) during cyclotron resonance interaction between the propagating whistler wave and the gyrating electrons. The whistler precursors are explained in terms of the mechanism suggested by Dowden (1972).     

VLF goniometer observations at Halley Bay,Antarctica—I. The equipment and the measurement of signal bearing

A transistorized wide-band (0.5–11 kHz) VLF goniometer has been developed for the study of whistlers and ELF/VLF emissions. It consists of two crossed vertical loops from which a single loop aerial, rotating about a vertical axis at a frequency of 25 sec^?1, is synthesized electronically. During periods of high whistler activity, when the same propagation paths may be identified in successive whistler groups, it is possible to determine the bearing of the exit point of such a magnetospheric path with an error, typically, of ± 10–20°.     

Discrete VLF emissions (7–9 kHz) displaying unusual banded and periodic structure

Rising frequency VLF emissions having unusually high frequency and exhibiting banded structure were recorded between 14.55 and 15.30 U.T. on 28 June 1972 by the VLF goniometer receiver at Halley, Antarctica. The risers were split into two frequency groups, one with frequencies in the range 6.0–7.7 kHz and the other with frequencies between 7.8 and 9.4 kHz, the former being more numerous. The gap between the lower and upper frequency risers is superficially similar to, though at a higher frequency than, the missing bands in emissions observed by satellites. However, it is found to be unlikely that the risers received at Halley can be explained by any of the mechanisms advanced to explain the banded satellite-observed emissions. Several other explanations are considered and it is shown that the most likely is partial suppression by magnetospheric line radiation propagating in the same duct.The risers are interpreted as being generated via cyclotron resonance with counterstreaming electrons. A computer program based on Helliwell's (1967) phenomenological theory is used to determine the generation region and electron energies involved.Both frequency groups of risers display a 4 min periodicity in occurrence. It is shown that this time period is consistent with that required to replenish the flux of resonant electrons, by eastwards drift into the duct, after the emissions have been quenched due to the reduction of the flux by pitch-angle diffusion into the loss cone.     

Stability analysis of magnetosheath lion roars

Whistler mode wave emissions in the magnetosheath, known as lion roars, are thought to be generated by an electron cyclotron instability. Using reported satellite data we model a magnetosheath medium where lion roars emissions occurred and we study the character, absolute or convective, of the associated electron cyclotron instability. We use a linear hot plasma dispersion equation for parallel and oblique propagation to the static magnetic field and apply Derfler's frequency cusp criterion to discriminate between absolute and convective instability. Our results show that an absolute instability is compatible with experimental data. From the linear temporal growth rate we extrapolate the saturated wave magnetic field and find a good agreement with the measurements.     

Propagation Characteristics and Generation Mechanism of ELF/VLF Hiss Observed at Low-latitude Ground Station (L = 1.17)

Extremely low frequency (ELF)/Very low frequency (VLF) hiss is whistler mode wave that interacts with energetic electrons in the magnetosphere. The characteristics features of ELF/VLF hiss observed at low latitude ground station Jammu (Geomag. lat. 22°16′ N, L=1.17) are reported. It is observed that most of hiss events first propagate in ducted mode along higher L-values (L = 4–5), after reaching lower edge of ionosphere excite the Earth-ionosphere waveguide and propagate towards equator to be received at low-latitude station Jammu. To understand the generation mechanism of ELF/VLF hiss, incoherent Cerenkov radiated power from the low-latitude and mid-latitude plasmasphere are evaluated. Considering this estimated power as an input for wave amplification through wave–particle interaction, the growth rate and amplification factor is evaluated which is too small to explain the observed wave intensity. It is suggested that some non-linear mechanism is responsible for the generation of ELF/VLF hiss.     

Properties of storm-time magnetospheric VLF emissions as deduced from the Ariel 3 satellite and ground-based observations

The characteristics of VLF emissions during the two magnetic storms on 5–7 June and 19–21 September, 1967 are investigated based on the Ariel 3 satellite data and ground observation at a low-latitude station in Japan. During the study of the June event, the satellite lay in the dawn-dusk plane. Soon after the onset of the main phase there appeared VLF emissions on the morning side of the magnetosphere on the ground as well as on the satellite, but the emissions were at very low level in the evening. It was not until the recovery phase that we could recognize the stationary occurrence of intense emissions in the evening. Furthermore, it is found that the chorus-type morning emissions are observed outside the plasmapause, while the narrow-banded hiss-type evening emissions lay within the plasmapause. It is shown that the cyclotron instability of ring current electrons can, on the whole, account for the many properties of the storm-like emissions. Similarly, we discuss the characteristics of the September event.     

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.     

Damping of electrostatic noise by warm auroral electrons

Cyclotron damping by warm electrons limits the amplitude of high frequency electrostatic waves propagating in discrete auroral arcs. The effect of this damping on whistler VLF hissupper hybrid noise and Bernstein modes is examined by calculating temporal growth rates and power flux intensities of amplified noise produced by precipitating electrons. The auroral electrons are described by a realistic distribution function. The effect of varying ionospheric conditions is also considered. Whistler mode noise is found to be less sensitive to the warm electron model than the upper hybrid mode. Bernstein modes are rapidly absorbed by the ionospheric and warm electrons. The difference in the peak power flux of the whistler and upper hybrid modes is indicative of the local value of the ratio of electron plasma frequency to electron gyrofrequency. For peak upper hybrid noise to exceed peak whistler noisethis ratio should be greater than 1. Ionospheric electron temperature has little effect on the spectrum, and intense narrow beams in the distribution function should be most effective at producing high noise levels for a given warm electron model.     

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.     

Propagation of VLF emissions in the magnetosphere and the ionosphere

Comparison of the low altitude polar orbiting Injun 5 Satellite data with the ground VLF data has revealed that there is a definite scarcity of VLF/ELF emissions at the ground level compared with the extent to which they are present at or above the auroral altitudes. Reasons for this have been investigated by performing ray path computations for whistler mode VLF propagation in an inhomogeneous and anisotropic medium, such as the magnetosphere and the ionosphere. Based on wave normal computations in the lower ionosphere, it has been found that many of the near-auroral zone VLF/ELF events are frequently either reflected from, or heavily attenuated in, the lower ionosphere. Besides collisional loss, severe attenuation of VLF signals in the lower ionosphere is also caused by the divergence of ray paths from the vertical (spatial attenuation). Cone of wave normal angles for the wave, within which VLF/ ELF signals are permitted to reach the ground, has been established. Wave normals lying outside this transmission cone are reflected from the lower ionosphere and do not find exit to the Earth-ionosphere cavity. Computations for VLF signals produced at auroral zone distances in the equatorial plane of the magnetosphere indicates that these signals are more or less trapped in the magnetosphere at altitudes > 1R_E.     

Plasmaspheric hiss observed in the topside ionosphere at mid- and low-latitudes

Latitudinal characteristics of ELF hiss in mid- and low-latitudes have been statistically studied by using ELF/VLF electric field spectra (50 Hz-30 kHz) from ISIS-1 and -2 received at Kashima station, Japan from 1973 to 1977. Most ISIS ELF/VLF data observed in mid- and low-latitude include ELF hiss at frequencies below a few kHz. The ELF hiss has the strongest intensity among VLF phenomena observed by the ISIS electric dipole antenna in mid- and low-latitudes, but the ELF hiss has no rising structure like the chorus in the detailed frequency-time spectrum. The ELF hiss is classified into the steady ELF hiss whose upper frequency limit is approximately constant with latitude and the ELF hiss whose upper frequency limit increases with latitude. These two types of ELF hiss occur often in medium or quiet geomagnetic activities. Sometimes there occurs a partial or complete lack of ELF hiss along an ISIS pass.Spectral shape and bandwidth of ELF hiss in the topside ionosphere are very similar to those of plasmaspheric hiss and of inner zone hiss. The occurrence rate of steady ELF hiss is about 0.3 near the geomagnetic equator and decreases rapidly with latitude around L = 3. Hence it seems likely that ELF hiss is generated by cyclotron resonant instability with electrons of several tens of keV in the equatorial outer plasmasphere beyond L = 3.Thirty-seven per cent of ELF hiss events received at Kashima station occurred during storm times and 63% of them occurred in non-storm or quiet periods. Sixty-seven per cent of 82 ELF hiss events during storm times were observed in the recovery phase of geomagnetic storms. This agrees with the previous satellite observations of ELF hiss by search coil magnetometers. The electric field of ELF hiss becomes very weak every 10 s, which is the satellite spin period, in mid- and low-latitudes, but not near the geomagnetic equator. Ray tracing results suggest that waves of ELF hiss generated in the equatorial outer plasmasphere propagate down in the electrostatic whistler mode towards the equatorial ionosphere, bouncing between the LHR reflection points in both the plasmaspheric hemispheres.     

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.     

Fine structure of the ground-observed VLF chorus as an indicator of the wave-particle interaction processes in the magnetospheric plasma

The results of the investigations of chorus type VLF emissions both in the subauroral conjugate regions and along the meridional profile near the plasmapause projection are summarized in order to connect the peculiarities of ground-observed VLF chorus with the plasma processes in the magnetosphere during substorms development. The method for determination of the location of the instability region in the magnetosphere is suggested which is based on the measurement of the upper boundary frequency of the ground-observed VLF chorus (UBF-method). Dynamics of chorus spectra during the substorm development is investigated. On the basis of the revealed regularities the phenomenological model of the VLF chorus source development is constructed. The calculations of some magnetospheric plasma parameters such as plasma density, large-scale electric field etc. are carried out. The conformity between the calculated and typical measured parameters is shown. The diagnostic possibilities of VLF chorus are discussed.