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.     

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.     

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.     

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.     

Electromagnetic Ion Cyclotron Waves in Multi-Ions Hot Anisotropic Plasma in Auroral Acceleration Region-Particle Aspect Approach

Using particle aspect approach, the effect of multi-ions densities on the dispersion relation, growth rate, perpendicular resonant energy and growth length of electromagnetic ion cyclotron wave with general loss-cone distribution function in hot anisotropic multi-ion plasma is presented for auroral acceleration region. It is observed that higher He⁺ and O⁺ ions densities enhance the wave frequency closer to the H⁺ ion cyclotron frequency and growth rate of the wave. The differential heating of He⁺ ions perpendicular to the magnetic field is enhanced at higher densities of He⁺ ions. The waves require longer distances to achieve observable amplitude by wave-particle interactions mechanism as predicted by growth length. It is also found that electron thermal anisotropy of the background plasma enhances the growth rate and reduces the growth length of multi-ions plasma. These results are determined for auroral acceleration region.     

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].     

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.     

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.     

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 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.     

Ion cyclotron instability triggered by drifting minor ion species: Cascade effect and exact results

On the basis of bi-Maxwellian velocity distribution functions it has been recently shown that the combined effect of heavy ion thermal anisotropy and drift velocity can trigger ion-cyclotron instabilities beyond the corresponding heavy ion-cyclotron frequency. (Proton-cyclotron instability induced by the thermal anisotrophy of minor ions. J. Geophys. Res. 107 (2002) 1494; Ion-cyclotron instability due to the thermal anisotrophy of drifting ion species. J. Geophys. Res. 108 (2003) 1050.) Here we show that the cascade-type mechanism proposed by Gomberoff and Valdivia (2002, 2003) can take place in the region where main heating of the fast solar wind seems to occur (i.e. within 10 solar radii). We also compare some of the results obtained by using the semi-cold approximation with the exact kinetic dispersion relation.     

Dust ion acoustic instability with q-distribution in nonextensive statistics

The instability of dust ion acoustic waves (DIAWs) driven by ions and electrons with different drift velocities in an unmagnetized, collisionless, isotropic dusty plasma was investigated. The electrons, ions and dust particles are assumed to be the generalized q-nonextensive distributions. The spectral indices of the q-distributions for the three plasma components are different from each other. Based on kinetic theory, the dispersion relation and the instability growth rate of DIAWs are obtained. It is found that the presence of the nonextensive distribution electrons and ions significantly modify the domain of the instability growth rate, as well as the ion-electron density ratio (ρ) and drifting-thermal velocity ratio (u _i0/v _Te ). In reverse, the index of dust grains has nearly no any effect on the instability growth rate. Furthermore, the effects of these parameters on the growth rate have also been discussed in detail.     

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 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.     

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.     

Fundamental wave of type III solar radio bursts and whistler waves

It is demonstrated by a numerical simulation that both the whistler waves and plasma waves are excited by a common solar electron beam. The excitation of the whistler waves is ascribed to the loss-cone distribution which arises at a later phase of the passage of the beam at a given height due to a velocity dispersion in the electron beam with a finite length. It is highly probable that the fundamental of type III bursts are caused by the coalescence of the whistler waves and the plasma waves excited by a common electron beam, although the plasma waves must suffer induce scatterings by thermal ions to have small wave numbers before the coalescence to occur.     

Proton cyclotron instability in the drifting magnetoplasma

A general expression for the tensor of the dielectrical susceptibility in an anisotropic plasma with particle drifts is derived, and the dispersion equation is found for waves propagating in arbitrary direction with respect to the mean magnetic field. The dispersion equation is solved for the case of electromagnetic ion‐cyclotron waves. It is found that in the plasma of the auroral magnetosphere strong plasma instability may occur so that the value of the growth rate of the waves is of the order of the wave frequency. Besides, the plasma instability is excited at less values of the wave number if the magnetospheric altitude becomes larger.     

Temperature anisotropy instabilities in a plasma containing cold and hot species in the magnetosphere

The nature of convective instability has been investigated for an electromagnetic wave, either right circularly polarised or left circularly polarised, propagating along a magnetic line of force in a plasma whose distribution function exhibits a temperature anisotropy in the hot species, a loss cone structure and a beam of cold electrons or ions travelling along the line of force with velocity V₁. Detailed numerical calculations have been made using a computer for the growth and decay of the wave for different values of the anisotropy ratio T_⊥/T_∥ = δ of the perpendicular and parallel temperatures, the McIlwain parameter L, the loss cone index j, velocity V₁ of the streaming particle and the particle density ratio ε. The ranges of values of ε and δ for which the wave becomes unstable have been studied in detail. It is found that wave propagation shows no dependence on the loss cone index but shows very strong dependence on the temperature anisotropy δ.     

Low-Frequency Drift Wave Instabilities in a Magnetized Dusty Plasma

An investigation is presented on the very low-frequency electrostatic drift waves due to the motion of the plasma particles in the combined effect of the static magnetic field and the inhomogeneous particle distribution in a dusty plasma using the Vlasov-kinetic model of plasmas. These modes arise and are driven unstable due to the equilibrium diamagnetic currents of heavier species of the dusty plasma. The implications of these modes to the structure formations in astrophysical situations have also been pointed out. [PACS Numbers: 52.25.Vy, 52.35.Fp, 52.35.- g, 52.35.Lv]     

Kinetic Alfven waves in plasma sheet boundary layer—particle aspect analysis

The particle aspect approach is adopted to investigate the trajectories of charged particles in the electromagnetic field of kinetic Alfven wave. Expressions are found for the dispersion relation, damping rate and associated currents in homogenous plasma. Kinetic effects of electrons and ions are included to study kinetic Alfven wave because both are important in the transition region. It is found that the ratio β of electron thermal energy density to magnetic field energy density and the ratio of ion to electron thermal temperature (T_i/T_e) affect the dispersion relation, damping-rate and associated currents in both cases (warm and cold electron limits). The treatment of kinetic Alfven wave instability is based on the assumption that the plasma consists of resonant and non-resonant particles. The resonant particles participate in an energy exchange process, whereas the non-resonant particles support the oscillatory motion of the wave.