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.     

Temporal Evolution of Whistler Instability Due to Cold Plasma Injection in the Presence of Perpendicular AC Electric Field in the Magnetosphere of Uranus

Temporal evolution of whistler instability has been studied due to cold plasma injectionin the presence of a perpendicular AC electric field in the magnetosphere of Uranus. Ageneralized distribution function with index j, which is a reducible to a bi-Maxwellianfor j = 0 and to a loss-cone for j = 1, for a plasma in the presence of a perpendicularAC electric field, has been derived from a hot/warm background plasma and atime-dependent plasma described by a simple Maxwellian distribution has been considered to represent the injected cold plasma. An expression for the growth rate of a system with added time-dependent cold plasma injection has been calculated using the method of characteristics and kinetic approach The results obtained for representative value of the parameters suited to the Uranian magnetosphere in both cases have been compared and discussed. It is inferred that the temperature anisotropy remains the major source of free energy whereas a loss-cone background acts as an additional source of free energy for the instability. It is not the magnitude but the frequency of the AC field which Influences the growth rate. In comparison to the Uranian magnetosphere this effect is more significant in Earth's magnetosphere. As the ionisation time of the time-dependent injected cold plasma increases, the growth rate goes on increasing, this effect being much greater in a loss-cone background in comparison to a bi-Maxwellian background plasma time-dependence of thecold plasma has been considered since it represents a more realistic situation in injection experiments.     

Effect of Cold Plasma Injection on Whistler Mode Instability Triggered by Perpendicular Ac Electric Field at Uranus

The effect of cold plasma injection on whistler mode instability has been studied separately for a bi-Maxwellian and a loss-cone hackground plasma with perpendicular AC electric field. The cold plasma is described by a simple Maxwellian distribution, whereas a generalized distribution function with index j that reduces to a bi-Maxwellian for j = 0 and to a loss-cone for j = 1 has been derived for a plasma in the presence of a perpendicular AC electric field, to form a hot/warm background. The dispersion relation is obtained using the method of characteristic solutions and kinetic approach. An expression for the growth rate of a system with added cold plasma injection has been calculated. Results of sample theoretical calculations for representative values of parameters suited to the magnetosphere of Uranus has been obtained. The salient features of the analysis and the results obtained in both cases have been compared and discussed. It is inferred that it is not the magnitude but the frequency of the AC field which influences the growth rate and a loss-cone background plasma has a triggering effect on the growth rate, increasing the value of the real frequency and maximum growth rate by an order of magnitude. These results may go a long way to enable one to get a better understanding of whistlers and diagnostics of plasma parameters in the Uranian magnetosphere.     

Loss-Cone Instability and Formation of Zebra Patterns in Type IV Solar Radio Bursts

The loss-cone instability of energetic electrons at double plasma resonance is considered. Conditions required for the formation of a zebra pattern in type IV solar radio bursts are determined. It is shown that electrons with a power-law energetic spectrum can effectively excite upper-hybrid waves at double plasma resonance. Stripes of a zebra pattern become more pronounced with an increase of the loss-cone opening angle and the power-law spectral index. The growth rate at the resonance frequencies decreases with an increase of the cyclotron harmonic number. Interpretation of observations and diagnostics of plasma for the April 21, 2002, event are performed. Conclusions about the impulsive mode of injection of energetic electrons into a coronal arc are made.     

Shear Driven Kinetic Alfven Wave with General Loss-Cone Distribution Function in the Plasma Sheet Boundary Layer

Expressions for the dispersion relation and growth rate of the KAW are derived for weak and strong shear regimes using the kinetic approach in view of the simultaneous observations of the large earthward Alfvenic Poynting flux, small-scale kinetic Alfven wave (KAW), earthward flowing electrons and upward flowing ions, at the substorm event in the plasma sheet boundary layer (PSBL). General loss-cone distribution function is adopted to describe the velocity distribution of the plasma particles. The results explain the generation of the observed KAW in the PSBL by the weak shear at the substorm onset. It is found that during the substorm expansion phase the cyclotron damping of KAW may lead to the upward flowing ion. Whereas, it’s Landau damping that may lead to the parallel energisation of the electrons that explains the observed loss of Alfvenic Poynting flux. It is also noted that the loss-cone distribution index changes the profiles of the frequency and growth rate plots of the shear-driven KAW. The loss-cone distribution function is therefore, an important factor for the excitation of KAW in the active region of the magnetosphere at the PSBL. Results are consistent with the finding of Wu and Seyler (J Geophys Res 108A6:1236, 2003) concerning kinetic Alfven wave generation and its stabilization by the sheared flow.     

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.     

Plasma emission and the decimetre portion of type-IV solar bursts

An attempt is made to account for the decimetre portion of the Type-IV solar radio bursts by plasma emission. Non-thermal electrons (E ～ 500 keV) trapped in a magnetic mirror (IV_dm, burst source) having loss-cone gap distribution excite plasma waves which are transformed into transverse waves through non-linear scattering by ions. A good agreement was reached between the calculated spectrum and the observed fluxes for the event of 1972 August 2. A distribution of the number of non-thermal electrons with height, and a total number of 10³², were obtained. Also it was found that the Langmuir waves can accelerate some background thermal electrons to the MeV range.     

A Theoretical Study Of The Whistler Mode Instability At The Uranian Bow Shock

Relativistic whistler wave mode with a perpendicular AC electric field has been studied for generalized distribution function with an index j, which is reducible to bi-Maxwellian for j = 0, loss-cone for j = 1 and delta function for j = ∞. Based on particle trajectories, the dispersionrelation is obtained using the techniques of a kinetic approach anda method of characteristic solutions Calculations are compassed with observations of low frequency waves of Voyager 2 The growth rates for the plasma parameters suited to the magnetosphere of Uranus are obtained. It is inferred that, not the magnitude but the frequency of the AC field, influences the growth rate. In addition to the temperature anisotropy, plasma particles having a loss-cone provide an additional source of energy. The relativistic electrons along with increasing the growth rate, widen the band width so as to cover a wide frequency range thus may explain the entire spectrum of whistler emissions at Uranian bow shock. This revised version was published online in July 2006 with corrections to the Cover Date.     

Near perpendicular propagation of electromagnetic waves in the magnetosphere

The nature of the damping or instability has been investigated for the “ordinary” and “extraordinary” electromagnetic wave, propagating almost perpendicular to a magnetic line of force in the magnetosphere, for a plasma whose particle distribution function exhibits a temperature anisotropy and a loss-cone structure.     

Slow modes in stellar systems with nearly harmonic potentials: II. Gravitational loss-cone instability

Using a consistent perturbation theory for collisionless disk-like and spherical star clusters, we construct a theory of slow modes for systems having an extended central region with a nearly harmonic potential due to the presence of a fairly homogeneous (on the scales of the stellar system) heavy, dynamically passive halo. In such systems, the stellar orbits are slowly precessing, centrally symmetric ellipses (2: 1 orbits). We consider star clusters with monoenergetic distribution functions that monotonically increase with angular momentum in the entire range of angular momenta (from purely radial orbits to circular ones) or have a growing region only at low angular momenta. In these cases, there are orbits with a retrograde precession, i.e., in a direction opposite to the orbital rotation of the star. The presence of a gravitational loss-cone instability, which is also observed in systems of 1: 1 orbits in near-Keplerian potentials, is associated with such orbits. In contrast to 1: 1 systems, the loss-cone instability takes place even for distribution functions monotonically increasing with angular momentum, including those for systems with circular orbits. The regions of phase space with retrograde orbits do not disappear when the distribution function is smeared in energy. We investigate the influence of a weak inhomogeneity of a heavy halo with a density that decreases with distance from the center.     

Kinetic Alfvén wave driven by the density inhomogeneity in the presence of loss-cone distribution function—particle aspect analysis

Kinetic Alfven waves (KAWs) driven by the diamagnetic drift instability that is excited by the density inhomogeneity in low-β plasmas, such as plasmas in the auroral region, are investigated by adopting the particle aspect analysis and loss-cone distribution function. The results obtained in this paper indicate that the propagation and evolution of kinetic Alfven waves decrease and the kinetic Alfven wave excitation becomes not easier with increasing loss-cone index J. But the spatial scales of the perpendicular perturbation driving kinetic Alfven waves have a decreasing tendency with the larger values of J, which perhaps is in relation with the decreasing width of loss-cone. A single hump appears in the plots of the growth rate of the instability when J=2. But the hump cannot emerge when J=0 or J=1. The density inhomogeneity of ions plays an important role in driving KAWs and it cannot be ignored. KAWs can be easier driven and KAWs can propagate and evolve faster with the increasing level of density inhomogeneity. However, the range of the perpendicular wave number of the wave instability decreases, namely, the longer the scale of perpendicular disturbance the easier the excitation of KAW. As the density inhomogeneity increases, the tendency of numerical solutions of the dispersion relation is similar to that obtained by the kinetic theory and Maxwellian distribution function (Duan and Li, 2004). But the profiles of the plots of numerical solutions are different. This means that the velocity distribution function of particles is important for KAW driven in magnetoplasmas, especially in the active regions of the magnetosphere, such as auroral region, and plasma sheet boundary.     

Generation of intermediate drift bursts in solar type IV radio continua through coupling of whistlers and Langmuir waves

The possible generation of intermediate drift bursts in type IV dm continua through coupling between whistler waves, traveling along the magnetic field, and Langmuir waves, excited by a loss-cone instability in the source region, is elaborated. We investigate the generation, propagation and coupling of whistlers. It is shown that the superposition of an isotropic background plasma of 10⁶K and a loss-cone distribution of fast electrons is unstable for whistler waves if the loss-cone aperture 2α is sufficiently large (sec α?4); a typical value of the excited frequencies is 0.1 ω _ce (ω _ce is the angular electron cyclotron frequency). The whistlers can travel upwards through the source region of the continuum along the magnetic field direction with velocities of 21.5–28 v _A (v _A is the Alfvén velocity). Coupling of the whistlers with Langmuir waves into escaping electromagnetic waves can lead to the observed intermediate drift bursts, if the Langmuir waves have phase velocities around the velocity of light. In our model the instantaneous bandwith of the fibers corresponds to a frequency of 0.1–0.5 ω _ce and leads to estimates of the magnetic field strength in the source region. These estimates are in good agreement with those derived from the observed drift rate, corresponding to 21.5–28 v _A, if we use a simple hydrostatic density model.     

Partcle precipitation caused by a single whistler-mode wave injected into the magnetosphere

The resonant interaction of electrons with a coherent whistler-mode wave in the magnetosphere, and corresponding particle precipitation through the loss-cone, are considered. We show that, due to the inhomogeneity of the magnetic field, the phase untrapped resonant electrons play a basic role in the precipitation process. An effective change of their pitch-angles near the loss-cone is calculated and particle fluxes are estimated for quiet magnetospheric conditions (weak diffusion without the wave). It appears that observation of the precipitation caused by a single whistler-mode wave is within the scope of experimental possibilities. The duration of the precipitation process is of the order of the electron bounce period. It is also shown that precipitating current may produce an observable magnetospheric disturbance with a time characteristic of the order of the bounce period.     

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.     

Sodium in the Jovian magnetosphere

Observations of sodium D-line emission from Io and the magnetosphere of Jupiter are reported. A disk-shaped cloud of sodium is found to exist in the Jovian magnetosphere with an inner edge at about 4R and an outer edge at about 10R . The gravitational scale height above the equatorial plane is a few Jovian radii. The data are interpreted in terms of a sputtering model, in which the sodium required to maintain the cloud is sputtered off the surface of Io by trapped energetic radiation-belt protons. Conditions on the atmospheric density are obtained. The Keplerian orbits attainable by such escaping sputtered atoms can provide the observed spatial distribution. The required 500-keV proton flux required to provide the 1–10 keV protons which will sputter the sodium at the surface of Io is consistent with the limiting trapped flux determined by ion-cyclotron turbulence.Publication No. 1410, Institute of Geophysics and Planetary Physics, University of California, Los Angeles 90024, Cal., U.S.A.     

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.     

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.     

The polar substorm and electron ‘islands’ in the Earth's magnetic tail

The behaviour of energetic electrons in the distant magnetosphere near the midnight meridian during polar substorms has been studied for the period March 5th–April 4th, 1965, using data from two end window Geiger counters flown on the IMP 2 satellite (apogee 15.8 Earth radii) and magnetic records from a chain of auroral zone stations around the world at magnetic latitudes equivalent to L = 7.4 ± 2.0.

When the satellite was in the distant radiation zone or in the plasma sheet which extends down the Earth's magnetic tail, sudden decreases in the horizontal magnetic field component at ground stations near the midnight meridian (negative magnetic bays) were followed by sudden increases in 40 keV electron fluxes (electron islands) at the satellite. When the satellite was at high latitudes in the magnetic tail ‘bays’ often were not followed by ‘islands.’ When the satellite was near the centre of the plasma sheet, energetic electron fluxes were observed even during magnetically quiet periods. The time delay between the sharp onset of magnetic bays in the auroral zone and the corresponding rapid increase in energetic electron intensity at the satellite, typically some tens of minutes, was least when the satellite was close to the Earth and increased with its increasing radial distance from the Earth. The delay was also a function of distance of the satellite from the centre of the plasma sheet, and of the magnitude of the intensity increase (smaller delays for larger intensity increases). We deduce that the disturbance producing the magnetic bays and associated particle acceleration originates fairly deep in the magnetosphere and propagates outward to higher L values, and down the plasma sheet in the Earth's magnetic tail on the dark side of the Earth. It is unlikely that the accelerated electrons are themselves drifting away from the Earth, because the apparent velocity with which the islands move away from the Earth decreases with increasing distance from the Earth.

It is suggested that the polar substorm and the associated particle acceleration are part of an impulsive ejection mechanism of magnetospheric energy into the ionosphere, rather than an impulsive injection mechanism of solar wind energy into the magnetosphere.     

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.     

Interaction of energetic particles with HM-waves in the magnetosphere

Energetic particle response in electromagnetic fields of ULF HM-waves in the magnetosphere is reviewed. Pc4–5 geomagnetic pulsations observed at the synchronous altitude are classified into three types, in respect to their major magnetic field polarization in different directions, local time dependence, and different characteristics of accompanied flux modulations of energetic particles, i.e., two nearly transverse waves with the azimuthal and the radial polarization, and the compressional stormtime pulsations. Firstly, we formulate the drift kinetic theory of particle flux modulations under the constraint of the magnetic moment conservation. A generalized energy integral of the particle motion interacting with a ULF-wave with the three-dimensional structure propagating to the azimuthal direction is obtained in the L-shell coordinate of a mirror magnetic field. Its linearized form is reduced to the same form as the previously derived energy change, including the bounce-drift resonant interaction. It is shown that the perturbed guiding center distribution function of energetic particles consists of four contributions, the adiabatic mirror effect corresponding to pitch-angle change, the kinetic effects due to energy change and the accompanying L-shell displacement, and the bounceaveraged drift phase bunching. Secondly, the basic HM-wave modes constitutingcoupling ULF oscillations in non-uniform plasmas are discussed in different models of approach for different plasma states. The diamagnetic drift Alfvén wave and the compressional drift wave with a larger azimuthal mode number in a high-beta plasma are candidates for the stormtimes pulsations. The former is intrinsically a guided localized mode, while the latter is a non-localized mode. By making use of the above preparation, we apply the developed drift kinetic theory to interpret the phase relationships between the ion flux modulation and the geomagnetic pulsation in some selected examples of observations, demonstrating a fair agreement in theoretical results with the observations.