Effect of parallel electric fields on whistler mode waves in an anisotropic Jovian magnetospheric plasma

The effect of parallel electrostatic field on the amplification of whistler mode waves in an anisotropic bi-Maxwellian weakly ionized plasma for Jovian magnetospheric conditions has been carried out. The growth rate for different Jovian magnetospheric plasma parameters forL = 5.6R _j has been computed with the help of general dispersion relation for the whistler mode electromagnetic wave of a drifted bi-Maxwellian distribution function. It is observed that the growth or damping of whistler mode waves in Jovian magnetosphere is possible when the wave vector is parallel or antiparallel to the static magnetic field and the effect of this field is more pronounced at low frequency wave spectrum.     

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.     

Comments on the proton whistler generation process

The problem of the propagation of an electromagnetic wave originating for instance in a lightning flash through the ionospheric medium is analysed in order to understand the formation at high ionospheric altitudes of the so-called proton whistler. It is shown that the accessibility of the hydrodynamic (or kinetic) proton resonance at the satellite altitude requires that a mode conversion process must take place slightly above the transition region separating the one ion (O⁺) from the two ion (O⁺ + H⁺) component plasmas. Moreover, the transformation conditions in the wave conversion region imply that the magnetic field should be (almost) perpendicular to the density gradient. Otherwise, the incident electromagnetic wave will never reach the satellite altitude in the frequency range of the proton whistler. However, some former proton whistler theories have postulated that the signal is the result of simple ionospheric propagation effects, in contradiction with the above results. These former proton whistler theories are reviewed and it is shown that the basic flaw in these theories lies in that the incident electromagnetic wave has been supposed from the beginning to have reached the high ionospheric altitudes where is located the satellite without being influenced by the lower ionospheric layers. Some various aspects, like the high variability of the wave electric to magnetic field ratio and the harmonics bands as observed by Injun are analysed in the light of the obtained results. Finally, numerical solutions of the wave dispersion relation for both the fast hydrodynamic mode (the extraordinary mode) and the slow ion kinetic mode are presented which shows that a coupling process between the two modes may take place at various frequencies between the O⁺ and the H⁺ gyrofrequencies.     

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.     

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.     

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.     

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.     

Effect of rotation and self-gravity on the propagation of MHD waves

Magnetohydrodynamics waves and instabilities in rotating, self-gravitating, anisotropic and collision-less plasma were investigated. The general dispersion relation was obtained using standard mode analysis by constructing the linearized set of equations. The wave mode solutions and stability properties of the dispersion relations are discussed in the propagations transverse and parallel to the magnetic field. These special cases are discussed considering the axis of rotation to be in transverse and along the magnetic field. In the case of propagation transverse to the magnetic field with axis of rotation parallel to the magnetic field, we derived the dispersion relation modified by rotation and self-gravitation. In the case of propagation parallel to the magnetic field with axis of rotation perpendicular to the magnetic field, we obtained two separate modes affected by rotation and self-gravitation. This indicates that the Slow mode and fire hose instability are not affected by rotation. Numerical analysis was performed for oblique propagation to show the effect of rotation and self-gravitation. It is found that rotation has an effect of reducing the value of the phase speeds on the fast and Alfven wave modes, but self-gravitation affect only on the Slow modes, thereby reducing the phase speed compare to the ideal magneto hydrodynamic (MHD) case.     

Ion and electron beam effects on kinetic Alfvén waves in an inhomogeneous magnetosphere

Kinetic Alfvén waves are examined in the presence of ion and electron beams with bi-Maxwellian distribution functions. The theory of particle aspect analysis is used to evaluate the trajectories of charged particles in the electromagnetic field of a kinetic Alfvén wave. The expressions for the field-aligned currents, perpendicular currents (with respect to B₀), dispersion relation and growth-rate with marginal instability criteria are derived. The significance of the investigation for the earth's magnetoplasma is discussed.     

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.     

Magnetoacoustic-gravity surface waves

The linearized theory for the parallel propagation of magnetoacoustic-gravity surface waves is developed for an interface of a horizontal magnetic field above a field-free medium. The media either side of the interface are taken to be isothermal. The dispersion relation is obtained for the case of a constant Alfvén speed. In the absence of gravity the interface may support one or two surface modes, determined by the relative temperatures and magnetism of the two media. The effect of gravity on the modes is examined and dispersion diagrams and eigenfunctions are given. In the usual - k _x diagnostic diagram, the domain of evanescence is shown to be divided into two distinct regions determining whether a given mode will have a decaying or growing vertical velocity component. In the absence of a magnetic field the transcendental dispersion relation may be rewritten as a polynomial. This polynomial possesses two acceptable solutions only one of which may exist in any given circumstances (depending on the ratio of the densities). If the gas density within the field exceeds that in the field-free medium, then the f-mode may propagate. The f-mode exists in a restricted band of horizontal wavenumber and only when the field-free medium is warmer than the magnetic atmosphere. An analytical form for the wave speed of the f-mode is obtained for small values of the Alfvén speed. It is shown that the f-mode is related to the fast magnetoacoustic surface wave, merging into that mode at short wavelengths.     

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 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.     

The interaction of an obliquely incidents-polarized plane electromagnetic wave at a warm moving magnetized plasma half-space

The interaction of ans-polarized plane electromagnetic wave incident from a dielectric (or vacuum) region on awarm moving magnetized plasma half-space is considered. The external magnetic field is assumed to be normal to the direction of the wave normal and the velocity of the moving medium. Using the first three moment equations, together with Maxwell's electromagnetic equations, we construct the constitutive relations in the rest frame of the moving medium. The constitutive relations are then transformed to the laboratory frame by invokingMinkowski's equations for the moving plasma medium, and the dispersion relation for the propagating ordinary mode in the moving medium is derived. Expressions are obtained for the phase and group velocities and the index of refraction for the ordinary mode, as also for power reflection and transmission coefficients. It is found that in contrast to the case of a cold magnetized plasma, the ordinary electromagnetic mode excited in the warm magnetoplasma medium getsmodified due to the presence of an external magnetic field. In addition, the various reflection and transmission characteristics for a warm magnetoplasma depend on the velocity of the moving plasma as well as on the strength of the applied magnetic field, as against the case for a cold moving magnetized plasma. Numerical results on the reflection coefficient are presented for several values of the parameters characterizing the electron-plasma temperature, the velocity of the moving medium and the strength of the applied magnetic field.     

A full-wave study of downward propagating ELF waves in the ionosphere: Ion cutoff whistlers and the low frequency cutoff of ELF noise

The downward propagation of ELF waves (100–700 Hz) in the ionosphere is studied by means of a generalised multiple-reflection full-wave method. It is shown that for the production of an ion cutoff whistler the incident wave-normal must point inwards (equatorwards) with respect to the vertical, the ion cutoff whistler conversion coefficient R_RL being a maximum when the reflected wave normal lies close to the geomagnetic field direction at the crossover level.For a low frequency cutoff of ELF noise to exist, the incident wave-normals at the crossover level must lie outside a ‘cone of penetration’ of ~40° semi-vertical angle, whose axis coincides with the geomagnetic field line. For propagation in the magnetic meridian plane, total reflection of downgoing whistlers is obtained either for large outward (poleward) incident angles, with reflection heights generally above the crossover level and possibly even above the gyrofrequency level, or else for inward (equatorward) wave-normal directions, in which case the reflection process usually occurs below the crossover level, and involves an R to L mode conversion on the downgoing path.Analysis of a scatter plot of the lower cutoff frequencies of ELF noise as a function of altitude and latitude shows that widely varying abundances must be postulated at all latitudes in order to explain the observations.     

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.     

Non-radial oscillations and energy transport in rotating solar (stellar) wind

The propagation of non-radial, small amplitude perturbations superposed on a zero-order, stationary, non-magnetic, polytropic, rotating stellar wind is studied in the limit of the local theory, i.e. for k r 1, k being the module of the wave vector and r the characteristic scale of the zero-order flow. The resulting dispersion equation is of the 3rd order in (complex) frequency and the possible modes correspond to two acoustic type waves, and to a gravity-shear wave with strongly anisotropic propagation properties, due to coupling between the internal gravity waves and shear motion. The gravity-shear mode allows velocity differences in the medium to exist with no corresponding density fluctuations and hence with no shock wave formation. It is suggested that this mode corresponds to some of the fast-slow velocity streams observed in the interplanetary medium and may provide means for wave energy being transported outwards with the zero-order flow, with little dissipation in the inner region of the solar wind.     

A dispersion relation for open spiral galaxies

The Lin-Shu dispersion relation is applicable in the (asymptotic) case of tight spirals (large wave numberk _R). Here we reconsider the various steps leading to the Lin-Shu dispersion relation in higher approximation, under the assumption that the wave numberk _R is not large [(k _Rr) =O(1)], and derive a new dispersion relation. This is valid for open spiral waves and bars. We prove that this dispersion relation is the appropriate limit of the nonlinear self-consistency condition in the case where the linear theory is applicable.     

VLF input impedance of a loop antenna embedded in the magnetosphere

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

The five-minute period oscillation in magnetically active regions

The magnetohydrodynamic frequency-wavelength relation, derived by McLellan and Winterberg (1968), has been evaluated for an isothermal atmosphere. In particular, the effect which an inclined magnetic field and a finite horizontal wavelength have on the critical sonic and internal-gravity cut-off frequencies has been examined, in which it has been assumed that the magnetic field vector, wave vector, and gravity vector are coplanar. It is shown that the frequency band in which vertical wave propagation is impossible in the non-magnetic photosphere, becomes smaller when an inclined uniform magnetic field is introduced, and that low frequency magnetically coupled internal-gravity waves do not propagate vertically if the horizontal wavelengths associated with this mode are greater than a critical wavelength which decreases with field strength.It is also demonstrated that an inclined magnetic field will inhibit the resonance that occurs at the critical frequency _g in the non-magnetic atmosphere which is a result consistent with recent observations of the wiggly line structure in active regions.This work is supported by the European Space Research Organization.Presently with the Solar Astronomy Group, California Institute of Technology.