Kinetic Alfven wave in the presence of general loss-cone distribution function in inhomogeneous magnetoplasma—particle aspect analysis

Particle aspect analysis is extended for kinetic Alfven waves in an inhomogeneous magnetoplasma in the presence of a general loss-cone distribution function. The effect of finite Larmor radius is incorporated in the finite temperature anisotropic plasma. Expressions for the field-aligned current, perpendicular current (to B), dispersion relation, particle energy and growth rate are derived and effects of steepness of loss-cone distribution and plasma density inhomogeneity are discussed. The treatment of the kinetic Alfven wave instability is based on the assumption that the plasma consists of resonant and non-resonant particles. It is assumed that resonant particles support the oscillatory nature of the wave. The excitation of the wave is treated by the wave particle energy exchange method. The applicability of the investigation is discussed for auroral acceleration phenomena. © 1999 Elsevier Science Ltd. All rights reserved.     

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.     

Effect of general loss-cone distribution function on the shear-driven electrostatic ion-cyclotron instability

The shear-driven electrostatic ion-cyclotron instability (EICI) is studied using the loss-cone distribution function by particle aspect analysis. The effect of the loss-cone distribution on the dispersion relation and growth rate of weak shear-driven EICI is studied. The whole plasma is considered to consist of resonant and non-resonant particles. The wave is assumed to propagate obliquely to the static magnetic field. It is found that the frequency of the EICI is Doppler shifted due to the transverse inhomogeneous flow in the direction of the magnetic field. It is also found that for anisotropic plasma the critical velocity shear needed to excite EICI depends upon the loss-cone distribution index (J). With the increasing values the loss-cone distribution indices (J), the critical value of normalized velocity shear needed to generate EICI in anisotropic plasma, decreases and is of the order of the weak shear. The loss-cone distribution acts as a source of free energy and generates the weak shear-driven EICI at longer perpendicular perturbations. It also lowers the transverse and parallel energy of the resonant ions. The study may explain the frequently observed EICI in the auroral acceleration region.     

Hydromagnetic field line resonances and modulation of particle precipitation

Hydromagnetic wave and modulated particle precipitation data are reported from conjugate areas near the particledrift shell L ～ 4. A modulation of electrons precipitating from the magnetosphere is observed in the conjugate regions when the accompanying hydromagnetic wave period is ~ 90 s and the wave polarization is linear. When the wave period changes abruptly to ~ 30 s and the polarizations at the observing stations are no longer linear, the modulation of the precipitating electrons is no longer observed. The change in hydromagnetic wave characteristics does not appear to be related to interplanetary plasma and magnetic field conditions. Rather, it is proposed to arise from a change in the wave generation mechanism from an internal magnetospheric source near the inner edge of the plasmapause (lower frequency) to an externally driven source outside the magnetosphere (higher frequency). This observation of a change in the wave characteristics (frequency and polarization) associated with modulated electron precipitation appears to be related to two previous examples wherein modulated electron precipitation was reported to be closely associated with the existence of a wave resonance region near the observing site.     

Precipitation of charged particles by a parallel electric field

A time-dependent model of the effect of a parallel electric field on particle precipitation from a closed field-line has been constructed and the results are presented. A pattern of field-aligned pitch-angle distributions and energy peaks develops rapidly and then persists unchanged in shape while the intensity decreases for a time of the order of the bounce period of the energetic particles. It is shown that the structures in velocity space are created by the juxtaposition of particles from different source populations. Four sources are found to be sufficient to reproduce the principal features observed frequently by rockets and satellites. They are, a trapped plasma sheet distribution, a loss-cone partially filled by pitch-angle diffusion at the equator, cold ionospheric plasma which has flowed outward along the field line and particles backscattered from the precipitation into the atmosphere.The model develops density gradients and discontinuities far sharper than any observed, so that any parallel electric field actually occurring in an aurora must be accompanied by strong wave-particle interactions either as part of the accelerating mechanism or as a result of the density gradients produced by it.     

EMIC waves around the plasma-pause region

Electromagnetic ion-cyclotron (EMIC) instability has been studied using the general loss-cone distribution function by investigating the trajectories of charged particles and using the method of particle aspect analysis. A low β (ratio of plasma pressure to magnetic pressure) plasma consisting of resonant and non-resonant particles has been considered. It is assumed that the resonant particles participate in energy exchange with the wave, whereas non-resonant particles support the oscillatory motion of the wave. The wave is assumed to propagate parallel to the static magnetic field. The effects of steepness of loss-cone distribution with thermal anisotropy are discussed. The growth rate, perpendicular and parallel resonant energies of the particles and marginal instability condition are derived. The effect of general loss-cone distribution function is to enhance the growth rate of EMIC waves. The results are interpreted for the space plasma parameters appropriate to the plasma-pause region of the earth's magnetoplasma. The results of the work is consistent for EMIC emissions observation by SAMPEX and CRRES satellite around the plasma-pause region as reported by Bortnik et al. [Bortnik, J., Thorne, R.M., O’Brien, T.P., Green, J.C., Strongeway, R.J., Shprits, Y.Y., Baker, D.N., 2006. Observation of two distinct, rapid loss mechanisms during the 20 November 2003 radiation belt dropout event. J. Geophys. Res. 111, A12216, doi:10.1029/2006JA011802] and Xinlin et al. [Xinlin, Li., Baker, D.N., O’Brien, T.P., Xie, L., Zong, Q.G., 2006. Correlation between the inner edge of outer radiation belt electrons and the innermost plasmapause location. Geophys. Res. Lett. 33, L14107, doi:10.1029/2006GL026294].     

Effect of parallel electric field on electrostatic ion-cyclotron instability in anisotropic plasma in the presence of ion beam and general distribution function—Particle aspect analysis

Dispersion relation, resonant energy transferred, growth rate and marginal instability criteria for the electrostatic ion-cyclotron wave with general loss-cone distribution in low-β anisotropic, homogeneous plasma in the auroral acceleration region are discussed by investigating the trajectories of the charged particles. Effects of the parallel electric field, ion beam velocity, steepness of the loss-cone distribution and temperature anisotropy on resonant energy transferred and growth rate of the instability are discussed. It is found that the effect of the parallel electric field is to stabilize the wave and enhance the transverse acceleration of ions whereas the effect of steepness of loss-cone, ion beam velocity and the temperature anisotropy is to enhance the growth rate and decrease the transverse acceleration of ions. The steepness of the loss-cone also introduces a peak in the growth rate which shifts towards the lower side of the perpendicular wave number with the increasing steepness of the loss-cone.     

Relativistic effects on parallel whistler-mode propagation and instability

Relativistic effects on parallel whistler-mode propagation and instability are considered analytically in some limiting cases relevant to magnetospheric and/or astrophysical conditions. The corresponding wave dispersion equation for a weakly relativistic anisotropic plasma is expressed in terms of generalized Shkarofsky functions. Asymptotic presentation of these functions is found in the limit of large wave refractive indices. Based on this presentation, a new analytical expression for whistler-mode refractive index is obtained and analysed. It is pointed out that relativistic effects increase the value of anisotropy above which the waves are unstable, in agreement with the results of the earlier numerical analysis. This increase is particularly important for whistler-mode propagation in a rarefied, hot plasma but could be potentially observed in the magnetosphere of the Earth in the region outside the plasmasphere.     

Phase-bunching and other non-linear processes occurring in gyroresonant wave-particle interactions

We consider the movement of individual electrons in a magnetized plasma in which a monochromatic wave is propagating in the whistler mode. We derive simple expressions which give the displacement of the electrons as a function of time, the phase angle that their velocity vector makes with the magnetic component of the wave, their pitch angle and energy changes. A useful formula is obtained which gives the velocity range over which particles remain trapped inside the wave, as a function of the wave intensity and of the initial phase angle of the particle. It is shown that even strictly resonant particles can escape from the wave when their initial phase angle is very small. From the derived expressions, it is possible to compute the phase-bunching effect which occurs approximately at one trapping wavelength behind the leading edge of the interaction region. We deduce also the total amount of energy which is taken from (or given to) the wave by magnetospheric electrons in both cases of naturally existing or artificially injected particles. It is shown that these non-linear amplification processes can lead to very large VLF amplitude in the magnetosphere.     

Quasielectrostatic whistler-mode propagation

An approximate formula is derived for the refractive index of a whistler-mode wave propagating in a hot anisotropic plasma with wave normal angle close to the resonance cone angle (θ_R). Approximations used during the derivation are generally satisfied for magnetospheric conditions. It is pointed out that the derived formula can be considered to be complementary to the corresponding formula for quasilongitudinal whistler-mode propagation in a hot anisotropic plasma which was derived by Sazhin and Sazhina (1982). The limits of applicability of a cold plasma model when determining the height of generation of saucer emissions and V-shaped hiss are discussed.     

Evidence of energy dependent mechanisms for the precipitation of auroral electrons

This paper discusses the experimental results on electron precipitation in a diffuse aurora obtained by a sounding rocket launched from ANDENES (L ～ 6·2) on 3 November 1968. A considerable increase in the intensity of low energy electrons, E_e ? 5 keV, followed a large precipitation of more energetic electrons E_e ? 5 keV. From the observation of angular distributions and an estimate of the diffusion coefficient (D_α ? 10^?3 (sec)^?2), it is suggested that this higher energy precipitation is induced by gyroresonant interactions of magnetospheric electrons with radiation in the whistler mode. The lower energy precipitation separated in time and/or space, shows quasi-periodic modulations in the 5–15 sec range with periods close to the bounce period. It is suggested that this precipitation is the result of bounce-resonance interactions with electrostatic waves in the equatorial plane. Finally, from a comparison between the experimental energy spectra and plasma sheet spectra it can be concluded that these electrons are injected from the plasma sheet during a substorm and are then diffused and precipitated by energy dependent mechanisms.     

Effect of general loss-cone distribution function on electrostatic ion-cyclotron instability in an inhomogeneous plasma: particle aspect analysis

The electrostatic ion-cyclotron instability (EICI) in low β (ratio of plasma to magnetic pressure), anisotropic, inhomogeneous plasma is studied by investigating the trajectories of the particles using the general loss-cone distribution function (Dory-Guest-Harris type) for the plasma ions. In particular, the role of the loss-cone feature as determined by the loss-cone indices, in driving the drift-cyclotron loss-cone (DCLC) instability is analysed. It is found that for both long and short wavelength DCLC mode the loss-cone indices and the perpendicular thermal velocity affect the dispersion equation and the growth rate of the wave by virtue of their occurrence in the temperature anisotropy. The dispersion relation for the DCLC mode derived here using the particle aspect analysis approach and the general loss-cone distribution function considers the ion diamagnetic drift and also includes the effects of the parallel propagation and the ion temperature anisotropy. It is also found that the diamagnetic drift velocity due to the density gradient of the plasma ions in the presence of the general loss-cone distribution acts as a source of free energy for the wave and leads to the generation of the DCLC instability with enhanced growth rate. The particle aspect analysis approach used to study the EICI in inhomogeneous plasma gives a fairly good explanation for the particle energisation, wave emission by the wave–particle interaction and the results obtained using this particle aspect analysis approach are in agreement with the previous theoretical findings using the kinetic approach.     

Nonlinear frequency shift and self-modulation of the quasi- monochromatic whistlers in the inhomogeneous plasma (magnetosphere)

The nonlinear frequency shift arising from the interaction of the quasimono- chromatic whistler-mode wave with resonant particles in an inhomogeneous plasma is derived. The modulational instability caused by this shift is investigated. The results are applied to the propagation of long-duration VLF whistler-mode signals along the magnetic field in the magnetosphere. It is shown that the modulational instability of these waves in the equatorial region leads to pulsations very similar to those observed experimentally     

Electromagnetic instabilities in an anisotropic loss-cone plasma

A form of general dispersion relation for electromagnetic waves in a fully ionized anisotropic plasma with loss-cone that explicates the contribution of the loss-cone to the dispersion relation is developed. By initially ignoring effects due to anisotropy, it is shown by means of Nyquist diagram technique that an isotropic loss-cone distribution can be unstable to EM waves corresponding to the whistler mode (0<< _e ). The growth rate is then determined analytically for this distribution, assuming cyclotron resonance between the waves in the whistler mode and particles in the high energy tail of the velocity distribution. By including the effects of anisotropy, a general growth rate is obtained which is found to depend on the anisotropy, the size of the loss-cone, the softness of the energy spectrum, and the fraction of the particles which are resonant with the wave. For particular distributions the relative contributions of the anisotropy and of the loss-cone to the growth rate have been determined. It is seen that loss-cone effects, which depend on the size of the loss-cone as well as the softness of the energy spectrum, can be a significant factor in the determination of the growth rate. For the Lorentzian distribution, the half-width of unstable waves is considerably broadened and the growth rates are somewhat more severe as compared to a two-temperature Maxwellian. The threshold frequency is which confirms the presence of unstable EM waves in the magnetospheric plasma leading to turbulence.     

Modulation of energetic particle fluxes due to long-period geomagnetic oscillations

Mechanism of flux modulations of energetic protons and electrons, associated with the long-period geomagnetic pulsations in the outer magnetosphere, is examined theoretically. In the first part, a linear perturbation theory of the guiding centre distribution function averaged over the bounce phase of an interacting particle is developed for the case of the three-dimensional magnetic oscillations with a sufficiently long period compared with the bounce time of the particle. Secondly we extend the formulation to include some effects of the perturbed drift orbit on the particle distribution such as the particle trapping in the wave field and the phase bunching process. The latter is important for the interaction with the coupling Alfvén mode of magnetic oscillations. Applying these results together with the basic characteristics of the coupling hydromagnetic oscillations in a non-uniform plasma, we discuss the possibilities for the observed particle flux modulations in two different cases, separately, i.e. flux oscillations due to the compressional magnetic perturbation and those from the nearly transverse magnetic variations.     

Electrostatic electron cyclotron harmonic instability near Ganymede

Jupiter’s moon—Ganymede—is the largest satellite in our solar system. Galileo spacecraft made six close flybys to explore Ganymede. More information was acquired about particle population, magnetic field and plasma waves during these encounters. In this paper, our aim is to study the generation of electrostatic electron cyclotron harmonic (ECH) emissions in the vicinity of Ganymede using the observed particle data. The calculated ECH wave’s growth rates are analyzed in the light of observations of plasma waves along the path of Galileo near Ganymede. Dispersion relation for electrostatic mode is solved to obtain the temporal growth rates. A new electron distribution function, fitted to distribution observed near Ganymede, is used in the calculations. A parametric study is performed to evaluate the effect of loss-cone angle and the ratio of plasma to gyro-frequency on growth rates. It is found that ECH waves growth rates generally decrease as the loss-cone angle is increased. However, the ratio plasma to gyro-frequency has almost no effect on the growth rates. These parameters vary considerably along the Galileo trajectory near Ganymede. This is the first study which relates the occurrence of ECH waves with the particle and magnetic field data in the vicinity of Ganymede. The study of ECH wave growth rate near Ganymede is important for the calculation of pitch angle scattering rates of low-energy electrons and their subsequent precipitation into the thin atmosphere of Ganymede producing ultraviolet emissions. Results of the present study may also be relevant for the upcoming JUNO and JUICE missions to Jupiter.     

Analysis of energetic electron drop-outs in the upper atmosphere of Titan during flybys in the dayside magnetosphere of Saturn

We discuss the high energy electron absorption signatures at Titan during the Cassini dayside magnetospheric encounters. We use the electron measurements of the Low Energy Measurement System of the Magnetospheric Imaging Instrument. We also examine the mass loading boundary based on the ion data of the Ion Mass Spectrometer sensor of the Cassini Plasma Spectrometer. The dynamic motion of the Kronian magnetopause and the periodic charged particle flux and magnetic field variations – associated with the magnetodisk of Saturn – of the subcorotating magnetospheric plasma creates a unique and complex environment at Titan. Most of the analysed flybys (like T25–T33 and T35–T51) cluster at similar Saturn Local Time positions. However the instantaneous direction of the incoming magnetospheric particles may change significantly from flyby to flyby due to the very different magnetospheric field conditions which are found upstream of Titan within the sets of encounters.The energetic magnetospheric electrons gyrate along the magnetic field lines of Saturn, and at the same time bounce between the mirror points of the magnetosphere. This motion is combined with the drift of the magnetic field lines. When these flux tubes interact with the upper atmosphere of Titan, their content is depleted over approximately an electron bounce period. These depletion signatures are observed as sudden drop-outs of the electron fluxes. We examined the altitude distribution of these drop-outs and concluded that these mostly detected in the exo-ionosphere of Titan and sometimes within the ionosphere.However there is a relatively significant scatter in the orbit to orbit data, which can be attributed to the which can be attributed to the variability of the plasma environment and as a consequence, the induced magnetosphere of Titan. A weak trend between the incoming electron fluxes and the measured drop-out altitudes has also been observed.     

Diffuse auroral precipitation in the jovian upper atmosphere and magnetospheric electron flux variability

The deposition of energetic electrons in Jupiter's upper atmosphere provides a means, via auroral observations, of monitoring electron and plasma wave activity within the magnetosphere. Not only does particle precipitation indicate a potential change in atmospheric chemistry, it allows for the study of episodic, pronounced flux enhancements in the energetic electron population. A study has been made of the effects of such electron injections into the jovian magnetosphere and of their ability to provide the source population for variations in diffuse auroral emissions. To identify the source region of precipitating auroral electrons, we have investigated the pitch-angle distributions of high-resolution Galileo Energetic Particle Detector (EPD) data that indicate strong flux levels near the loss cone. The equatorial source region of precipitating electrons has been determined from the locations of Galileo's in situ measurements by tracing magnetic field lines using the KK97 model. The primary source region for Jupiter's diffuse aurora appears to lie in the magnetic equator at 15-40 RJ, with the predominant contribution to precipitation flux (tens of ergs cm⁻² s⁻¹ sr⁻¹) stemming from <30 RJ. Variability of flux for energetic electrons in this region is also important to the irradiation of surfaces and atmospheres for the Galilean moons: Europa, Ganymede, and Callisto. The average diffuse auroral precipitation flux has been shown to vary by as much as a factor of six at a given radial location. This variability appears to be associated with electron injection events that have been identified in high-resolution Galileo EPD data. These electron flux enhancements are also associated with increased whistler-mode wave activity and magnetic field perturbations, as detected by the Galileo Plasma Wave Subsystem (PWS) and Magnetometer (MAG), respectively. Resonant interactions with the whistler-mode waves cause electron pitch-angle scattering and lead to pitch-angle isotropization and precipitation.