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.     

Origin of Jovian decameter wave emissions— Conversion from the electron cylotron plasma wave to the ordinary mode electromagnetic wave

Energy conversion rates from the extraordinary mode to the ordinary mode ofthe electromagnetic waves in the Jovian plasmasphere has been calculated for a model of the sharp boundary that is given in the vicinity of the position where ω = ω_p, for an angular frequency ω and the angular plasma frequency ω_p. The extraordinary mode electromagnetic wave that is obtained as a result of the transformation of a longitudinal propa- gating through an inhomogenous plasma is here considered. The results give conversion rates of 1–50 per cent, at the most, when a wave normal direction of an is nearly parallel to the boundary normal direction and when the Jovian magnetic field vector is close to the boundary normal direction within an angle range from 10° to 15°. The electric field intensity, in range from 7 to 70 mV/m, of the original electrostatic electron cyclotron plasma waves can give the power flux in a range from 10^-22 to 10^-20W/m² Hz for the Jovian decameter waves observed at the Earth's surface. Efficient energy conversion is possible only when the ray direction of the emitted wave is in nearly perpendicular direction with respect to the magnetic field; this is the origin of the sharp beam emission of the Jovian decameter wave burst.     

Jovian magnetospheric ion cyclotron instability in the presence of parallel electric field

A dispersion relation for left hand circularly polarized electromagnetic wave propagation in an anisotropic magnetoplasma in the presence of a very weak parallel electrostatic field has been derived with the help of linearized Vlasov and Maxwell equations. An expression of the growth rate has been derived in presence of parallel electric field for ion-cyclotron electromagnetic wave in an anisotropic media. The modification made in the growth rate by introducing parallel electric field and temperature anisotropy has been studied for fully ionized hydrogen plasma with the help of observations made on Jovian ionosphere and magnetosphere atL = 5.6 R_j. It is concluded that the growth (damping) of ion-cyclotron electromagnetic wave is possible when the wave vector is parallel (antiparallel) to the static electric field and effect is more pronounced at higher wave number.     

Effect of parallel electric field on charged particle precipitation

Considering the presence of electric field parallel to geomagnetic field in the magnetosphere, the problem of wave-particle interaction has been considered. Dispersion equation of whistler mode wave in presence of parallel electric field has been derived. Using the effective dispersion equation, the wave-particle interaction has been reformulated to account for the effect of parallel electric field. Using charged particle energy spectrum and magnetospheric field and plasma models, the flux of electron precipitation has been computed. It is shown that the parallel electric field plays an important role and may work in simultaneity with other processes known for enhancement of electron precipitation.     

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.     

Whistler Mode Instability in a Lorentzian (κ) Magnetoplasma in the Presence of Perpendicular A.C. Electric Field and Cold Plasma Injection

The dielectric tensor, modified plasma dispersion function and dispersion relation for Whistler mode instability in an infinite magnetoplasma are obtained in the case of cold plasma injection to background hot anisotropic generalized bi-Lorentzian (κ) plasma in the presence of external perpendicular a.c. electric field. The method of characteristics solutions using perturbed and unperturbed particle trajectories have been used to determine the perturbed distribution function. Integrals and modified plasma dispersion function Z_κ ^*(ξ ) are reduced in power series expansion form. Numerical methods using computer technique have been used to obtained temporal growth rate for magnetospheric plasma at geostationary height. The bi-Lorentzian (κ) plasma is reducible to various forms of distribution function by changing the spectral index κ. The results of bi-Lorentzian (κ) plasma are compared with those of bi-Maxwellian plasma. It has been found that the addition of cold plasma injection gives different frequency spectra. The a.c. frequency of moderate amplitude increases the growth rate and instability in K space to lower range. Growth rate maximum is not affected by a.c. frequencies. However, it shifts the maximum to lower K space in both cases, rather than on the variation of the magnitude. Thus a physical situation like this may explain emission of various high frequency whistler emissions by cold plasma injection. The potential application of controlled plasma experiments in the laboratory and for planetary atmosphere are indicated. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Specific features of VLF wave propagation in the earth’s inner magnetosphere

The ray trajectories of waves in the very low frequency (VLF) range in the case of nonducted propagation in the earth’s inner magnetosphere are studied as functions of location of their source region, frequency, and initial angle between the vector of wave normal and intensity vector of external magnetic field. Simulation is performed on the basis of geometric ray tracing approach in multicomponent plasma. The parameters of the magnetospheric medium were calculated using a diffusion model of the concentration distribution of plasma components and the International Geomagnetic Reference Field (IGRF) model. It is shown that the magnetospheric wave reflection can occur if the lower hybrid resonance frequency is greater than its own wave frequency (ω _LHF > ω), i.e., at the latitudes λ ≈ 50°. The simulation results confirm that the quasi-longitudinal approximation cannot be used to describe the magnetospheric whistler propagation. We present simulations of propagation of chorus-type wave magnetospheric emissions that were performed using realistic wave distributions over initial parameters. In particular, we present distributions of chorus waves over directions of wave vector as functions of geomagnetic latitude; these distributions are required to study the particle scattering and acceleration processes in the radiation belts. Our results well agree with CLUSTER satellite measurements.     

Linear wave conversion processes in the theory of the proton whistler

The linear coupling between the different kinds of waves propagating in a warm plasma inhomogeneous along thex direction is investigated in order to locate the regions (,k) space where two of the roots of the characteristic equation coalesce. Firstly, using the approximation of geometrical optics the differential equation is derived and wave propagation at fixed wave numberk _z is studied in these special cases for which the characteristic equation reduces to a biquadratic. When the density gradient is parallel to the magnetic field, a detailed analysis of the different properties of the waves shows that the mechanism proposed by Gurnett and others to explain the characteristics of the proton whistler is unlikely to operate, even if a wave coupling occurs at the so called cross over frequency for small incidence angles. The only relevant process occurs when the density gradient is perpendicular to the magnetic field for waves propagating at small incidence angles. It is shown that, close to a coalescence point, but within the limit of the geometrical optics approximation, one of the WKB solutions is a mixed (transverse-longitudinal) mode which becomes purely longitudinal in the limit of large wave numbers. Consequently, as this wave has E almost parallel tok, coalescence implies that the waves are nearly longitudinal at the singular point, in agreement with other results. Next, application of the theory is made to some relevant space observations. It is shown that the proton whistler could be the result of a linear coupling between the extraordinary and the slow ion cyclotron waves close to the Buchsbaum resonance in ionospheric regions above 300 to 400 km where the H⁺ density begins to grow. Transformation conditions are given which favour the coupling mechanism in regions of strong latitudinal gradients. Finally, a comparison is made with experiment which confirms the principal features of the present theory.     

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.     

EFFECT OF PERPENDICULAR A.C. ELECTRIC FIELD ON THE OBLIQUE WHISTLER MODE INSTABILITY IN THE EARTH’S MAGNETOSPHERE

The elements of dielectric tensor and dispersion relation for obliquely propagating whistler waves with finite in an infinite magnetoplasma are obtained for a kappa distribution in the presence of perpendicular a.c. electric field. Integrals and modified plasma dispersion functions are reduced in power series form. Numerical calculations have been performed to obtain temporal growth rate and real frequencies of the plasma waves for magnetospheric plasma, using linear theory of dispersion relation. The effect and modification introduced by the perpendicular a.c. electric field on the temporal growth rates, real frequencies and resonance condition are discussed for kappa and Maxwellian distributions. Our results and their interpretation are compared with known whistler observations obtained by ground-based techniques and satellite observations.     

Nonlinear Coupling of Langmuir Waves with Whistler Waves in the Solar Wind

Close temporal correlation between high-frequency Langmuir waves and low-frequency electromagnetic whistler waves has been observed recently within magnetic holes of the solar wind. In order to account for these observations, a theory is formulated to describe the nonlinear coupling of Langmuir waves and whistler waves. It is shown that a Langmuir wave can interact nonlinearly with a whistler wave to produce either right-hand or left-hand circularly polarized electromagnetic waves. Nonlinear coupling of Langmuir waves and whistler waves may lead to the formation of modulated Langmuir wave packets as well as the generation of circularly polarized radio waves at the plasma frequency in the solar wind. Numerical examples of whistler frequency, nonlinear growth rate and modulation frequency for solar wind parameters are calculated.     

Excitation of whistler waves driven by an electron temperature anisotropy

A 3-D particle simulation of excitation of whistler waves driven by an electron temperature anisotropy (T > T ) is presented. Results show that whistler waves can have appreciable growth driven by the anisotropy. The maximum intensity of the excited whistler waves increases as a quadratic function of the anisotropy. Due to the presence of a threshold, one needs a relatively large electron temperature anisotropy above threshold to generate large-amplitude whistler waves. The average amplitude of turbulence in the context of whistler waves is up to as large as about 1% of the ambient magnetic field when T /T . The total energy density of the whistler turbulence is adequate for production of relativistic electrons in solar flares through stochastic acceleration.     

Mass-injection rate from Io into the Io plasma torus

Theoretical arguments have been presented to the effect that both plasma and energy are supplied to the Jovian magnetosphere primarily from internal sources. If we assume that Io is the source of plasma for the Jovian magnetosphere and that outward flow of plasma from the torus is the means of drawing from the kinetic energy of rotation of Jupiter to drive magnetospheric phenomena, we can obtain a new, independent estimate of the rate of mass injection from Io into the Io plasma torus. We explicitly assume the solar wind supplies neither plasma nor energy to the Jovian magnetosphere in significant amounts. The power expended by the Jovian magnetosphere is supplied by torus plasma falling outward through the corotational-centrifugal-potential field. A lower limit to the rate of mass injection into the torus, which on the average must equal the rate of mass loss from the torus, is therefore derivable if we adopt a value for the power expended to drive the various magnetospheric phenomena. This method yields an injection rate of at least 10³ kg/sec, a value in agreement with the results obtained by two other independent methods of estimating mass injection rate. If this injection rate from Io and extraction of energy from Jupiter's kinetic energy of rotation has been maintained over geologic time, then approximately 0.1% of Io's mass (principally in the form of sulfur and oxygen) has been lost to the Jovian magnetosphere, and Jupiter's spin rate has been reduced by less than 0.1%.     

The Influence of Guiding Field on Low-frequency Electromagnetic Instabilities in Collisionless Current Sheets

This work investigates the effect of guiding field on low-frequency electromagnetic instabilities in collisionless current sheets using the dispersion relation obtained in the collisionless and compressible magnetohydrodynamic model. The results in the following three cases show that the guiding field can strongly affect the 3-dimensional propagating disturbed waves. (1) On the middle plane of the current sheet (z = 0), if there is no guiding field, then no instability is observed. But if there a guiding field, then instability can take place. (2) Near the middle plane of the current sheet (z = 0.2), the current sheet becomes unstable. With increasing the intensity of the guiding field, the instability grows obviously. The wave mode may be whistler or low-hybrid wave. (3) Near the edge of the current sheet (z = 0.8), the guiding field exhibits no evident effect and the unstable wave mode is a quasi-parallel whistler wave.     

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.     

Two-dimensional Non-linear Alfvén Wings Generated by the Electrodynamic Interaction between Callisto and the Jovian Magnetosphere

When a highly conducting magnetized plasma passes an object with lower conductivity, or a body with inhomogeneous conductivity, 2-D structures are formed, the so-called `Alfvén wings'. These structures may arise, for example, at a Jovian moon without an intrinsic magnetic field (Callisto). In this case, Alfvén wings could be generated in the magnetized Jovian magnetospheric plasma flow owing to the in homogeneity of the moon's ionosphere/atmosphere conductivity. Such Alfvén wings may be considered as a satellite magnetosphere; the satellite magnetospheric magnetic field is a disturbed field of the Jovian magnetospheric plasma flow. An analytical solution is obtained in a simple proposed model. This revised version was published online in July 2006 with corrections to the Cover Date.     

The effects of density gradients on the convective amplification of upper hybrid waves in the magnetosphere

Intense (? 10 mVm^?1) electrostatic plasma waves near the upper hybrid frequency have been observed between ± 50° magnetic latitude during spacecraft plasmapause crossings. We present wave growth rate and three-dimensional convective amplification calculations which suggest how intense upper hybrid (IUH) events can occur over such a wide range of latitudes. The effects of wave refraction are shown to be crucial to the proper calculation of convective amplification.We first calculate upper hybrid wave growth for an IUH event at 10° MLAT during which a complete electron distribution function with a loss cone feature was measured simultaneously with the waves. We show that a parallel density gradient may be necessary to account for the observed amplification. Without such a density gradient, the dipole magnetic field gradient would quickly refract the wave vector component parallel to the local field lines out of the unstable region in wave vector space. Upon mapping the distribution function observed at 10° MLAT to other latitudes by conserving the electrons' magnetic moments, we then find that the mapped distribution could produce large amplification at higher latitudes only if there is an appropriate parallel density gradient. At the equator, the long magnetic field gradient scale length enables large amplitudes to be attained without a density gradient.The results of our UH ray tracing analysis are related to theories and observations of magnetospheric continuum radiation.     

Effect of ion and electron beam on kinetic Alfven wave in an inhomogeneous magnetic field

Kinetic Alfven waves are examined in the presence of electron and ion beam and an inhomogeneous magnetic field with bi-Maxwellian distribution function. The theory of particle aspect analysis is used to evaluate the trajectories of the charged particles. The expressions for the field-aligned currents, perpendicular currents (with respect to B ₀), dispersion relation and growth/damping rate with marginal instability criteria are derived. The effect of electron and ion beam and inhomogeneity of magnetic field are discussed. The results are interpreted for the space plasma parameter appropriate to the auroral acceleration region of the earth’s magnetoplasma.