Effects of density, temperature and velocity gradients on inertial Alfven wave in cusp region

The kinetic approach is used to evaluate the dispersion relation and growth/damping rate of inertial Alfven wave (IAW) with density, temperature and velocity gradients in an inhomogeneous plasma. The effects of gradient terms are studied for both the regions k_⊥ρ_i<1 and k_⊥ρ_i>1, where k_⊥ is the perpendicular wave number and ρ_i is the ion gyroradius. The relevance of theoretical results so obtained is predicted in accordance to the FAST observations in the cusp region. The results are interpreted for the space plasma parameters appropriate to the cusp region. This study elucidates a possible scenario to account for the particle acceleration and the wave dissipation in inhomogeneous plasmas. This model is also able to explain many features observed in plasma sheet boundary layer as well as to evaluate the dispersion relation, growth/damping rate and growth/damping length of inertial Alfven wave. It is found that density, temperature and velocity gradients control the wave frequency and effectively enhance the growth rate of inertial Alfven wave.     

Study of inertial kinetic Alfven waves around cusp region

The effect of electron inertia on kinetic Alfven wave has been studied. The expressions for the dispersion relation, growth/damping rate and growth/damping length of the inertial kinetic Alfven wave (IKAW) are derived using the kinetic approach in cusp region. The Vlasov-kinetic theory has been adopted to evaluate the dispersion relation, growth/damping rate and growth/damping length with respect to the perpendicular wave number k_⊥ρ_i (ρ_i is the ion gyroradius) at different plasma densities. The growth/damping rate and growth/damping length are evaluated for different m_e/βm_i, where β is the ratio of electron pressure to the magnetic field pressure, m_{i, e} are the mass of ion and electron, respectively, as I=m_e/βm_i represent boundary between the kinetic and inertial regimes. It is observed that frequency of inertial kinetic Alfven wave (IKAW) ω is decreasing with k_⊥ρ_i and plasma density. The polar cusp is an ideal laboratory for studies of nonlinear plasma processes important for understanding the basic plasma physics, as well as the magnetospheric and astrophysical applications of these processes.     

Study of gradient effects on inertial Alfvén waves in plasma sheet boundary layer region—kinetic approach

Inertial Alfvén waves are investigated using Maxwell-Boltzmann-Vlasov equation to evaluate the dispersion relation and growth/damping rate in inhomogeneous plasma. Expressions for the dispersion relation and growth/damping rate are evaluated in inhomogeneous plasma. The effects of density, temperature and velocity gradient are included in the analysis. The results are interpreted for the space plasma parameters appropriate to the plasma sheet boundary layer. It is found that the inhomogeneities of plasma contribute significantly to enhance the growth rate of inertial Alfvén wave. The applicability of this model is assumed for auroral acceleration region and plasma sheet boundary layer.     

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.     

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.     

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.     

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.     

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.     

The role of protons of the radiation belts in the generation of Pc 3–5

A new theory of the Alfvén wave generation in inhomogeneous finite β two component plasma is developed ($\text{β =}\text{8πρ}\text{β}{}_0{}^2$, ρ and B₀ are plasma pressure and unperturbed magnetic field, respectively). The analysis was carried out for these waves both for long wave approximation kρ_i ? 1 as well as for $\text{kρ}{}_{\mathrm{i}}\text{? 1}$ (k and ρ_i are wave vector and larmor radius of protons). The influence of the loss-cone on the development of the instability is considered. The theory is applied to explain the generation mechanism of Pc 3–5.     

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.     

Study of nonlinear interaction of waves through plasma-maser in magnetosphere plasma

A theoretical study is made on the generation mechanism of electrostatic Bernstein mode wave in the presence of electromagnetic Kinetic Alfven wave turbulence in magnetized inhomogeneous plasma on the basis of plasma-maser interaction. It is shown that a test high-frequency electrostatic Bernstein mode wave is unstable in the presence of low-frequency Kinetic Alfven wave turbulence. Because of the universal existence of the Kinetic Alfven waves in large-scale plasmas, the result has potential importance in space and astrophysical radiation process. The growth rate of the test high-frequency Bernstein mode wave is obtained with the involvement of spatial density gradient parameter. A comparative study on the role of density gradient in the generation of Bernstein mode on the basis of plasma-maser effect is presented.     

On the stability of almost perpendicularly propagating ion cyclotron waves

The dispersion relation for the near perpendicular propagation of the electromagnetic ion cyclotron wave, having a wavelength much larger than the ion Larmour radius r_L and a frequency $\text{ω ≈ Ω}{}^{\mathrm{+}}\text{(Ω}{}^{\mathrm{+}}$ is the ion cyclotron frequency), has been derived for a plasma consisting of a hot and a cold ion component. The hot ions and electrons have been described by loss-cone distribution functions; an ordering of the parameters was used to derive the cold ion contributions. Two modes, one with an increasing frequency and another with a constant frequency can propagate in the plasma. The two modes interact resulting in an instability of the former in the wavelength range k_⊥r_⊥ = 0.4?0.6 (for n_C/n_H = 0) and from k_⊥r_L = 0.5?0.8 (for n_C/n_H = 1.0) for a propagation angle of 70°. The instability of the mode is found to decrease with increasing cold ion densities and propagation angles.     

Effect of ion collisions on TM models in cylindrical wave guide filled with hot plasma

The expression for damping coefficients (K _i) is derived and discussed numerically, for a cylindrical wave guide, filled with hot collisional and uniaxially magnetised plasma. It is observed that TM modes suffer a very high damping for high values of plasma frequency (w _pe/w = 10) and low values of ion collision frequency (v _i/v _e = 10^?3), where as for low values of plasma frequency (w _pe/w = 0.1) the damping is low. The damping also increases as the ion temperature increases.     

The effect of pressure anisotropy on the equilibrium structure of magnetic current sheets

The equilibrium structure of two-dimensional magnetic current sheets is investigated for systems in which the plasma pressure dominates the bulk flow energy, as appears appropriate for the quiet time plasmasheet in the geomagnetic tail. A simple model is studied in which the field is contained between plane parallel boundaries and varies exponentially along the system, while the plasma pressure is anisotropic, the anisotropy being arbitrary but constant along the centre plane. When the field is highly inflated by the plasma current it is found that adiabatic solutions exist only when the plasma pressure is close to isotropic. For the case P_∥ > P_⊥ it is argued that a thin, non-adiabatic current layer will in general form at the sheet centre, usually embedded within a much broader adiabatic current distribution. When P_⊥ > P_∥, a broad region of very depressed fields develops about the centre of the current sheet, terminated at its outer boundary by a spike in the current density. This central region becomes unstable to the mirror mode well before the limiting adiabatic solution is reached.     

Nonlinear Evolution of Kinetic Alfvén Waves and Filament Formation

The transfer of wave energy to plasma energy is a very crucial issue in coronal holes and helmet streamer regions. Mixed mode Alfvén waves, also known as kinetic Alfvén wave (KAW) can play an important role in the energization of the plasma particles because of their potential ability to heat and accelerate the plasma particles via Landau damping. This paper presents an investigation of the growth of a Gaussian perturbation on a non-uniform kinetic Alfvén wave having Gaussian wave front. The effect of the nonlinear coupling between the main KAW and the perturbation has been studied. The dynamical equations for the field of the main KAW and the perturbation have been established and their semi-analytical solution has been obtained in the low (β≪ m_e/m_i≪ 1) and the high (β≫ m_e/m_i≪ 1) β cases. The critical field of the main KAW and the perturbation has been evaluated. Nonlinear evolution of the main KAW and the perturbation into the filamentary structures and its dependence on various parameters of the solar wind and the solar corona have been investigated in detail. These filamentary structures can act as a source for the particle acceleration by wave particle interaction because the KAWs are mixed modes and Landau damping is possible. Especially, in the solar corona, the low β and the high β cases could correspond to the coronal holes and the helmet streamer. The presence of the primary and the secondary filaments of the perturbation may change the spectrum of the Alfvénic turbulence in the solar wind.     

Velocity shear effect on the longitudinal wave in a strongly coupled dusty plasma

The characteristics of longitudinal dust acoustic wave (DAW) in presence of velocity shear have been investigated in a strongly coupled dusty plasma using the generalized hydrodynamic (GH) model. In the hydrodynamic regime (ωτ _m ?1), i.e. when characteristic time τ _m is slower than inverse of wave frequency, the viscosity in the GH model plays the usual role of wave damping, whereas in the kinetic regime (ωτ _m ?1), i.e. when characteristic time τ _m is larger than inverse of wave frequency, viscosity shows energy storing property in the wave. In the kinetic regime, we have studied the longitudinal mode $\omega^{2}=k^{2} (c_{d}^{2}+c_{l}^{2})$ (where ω is the frequency, k is the wave number, c _d is the dust acoustic velocity and c _l is the longitudinal velocity that arises due to viscosity) in presence of velocity shear. It is shown that velocity shear can destabilize this mode. Both nonmodal and modal techniques are employed to demonstrate the growth rate of the instability.     

Role of anisotropy of the initial particle distribution in the acceleration in collapsing solar-flare traps

We consider the behavior of charged particles with an anisotropic initial velocity distribution in a magnetic trap with approaching mirrors in connection with the problem of particle acceleration in solar flares. We show that, irrespective of the charge sign, the efficiency of confinement and acceleration increases with increasing anisotropy factor of the initial distribution α = (T_⊥/T_∥)^1/2. For a positive electric potential of the trap plasma relative to the mirrors, the emerging additional effect of ion expulsion form the trap increases with α_i. The derived estimate of the electric potential suggests an amplification of the initial perturbation and the development of instability.     

Effect of linear waves on kinetic Alfvén wave localization and turbulent spectrum

We have presented the localization of kinetic Alfvén wave (KAW) in intermediate β plasma (m _e /m _i ?β?1) by developing a model based on pump kinetic Alfvén wave and finite amplitude magnetosonic fluctuations. When KAW is perturbed by these background magnetosonic fluctuations, filamentary structures of KAW magnetic field are formed. First, a semi analytical model based on paraxial approximation has been developed to understand this evolution process. Localized structures and magnetic fluctuation spectrum of KAW has also been studied numerically for finite frequency of KAW. The calculated magnetic fluctuation spectrum follows two types of scalings. Above the proton gyroradius scale lengths (in inertial range), spectrum follows Kolmogorovian scaling. Below this scale dispersion starts and the spectrum steepens to about \(k_{x}^{-2.5}\) . The result shows the steepening of power spectra which can be responsible for particle acceleration in solar wind due to the energy transfer from larger to smaller lengthscales. Obtained magnetic turbulent spectra are consistent with observations of Cluster spacecraft in solar wind.     

Nonlinear effects associated with the finite frequency pump kinetic Alfvén wave and turbulent spectrum in solar wind

The paper contains a numerical simulation of the nonlinear coupling between the kinetic Alfvén wave and the ion acoustic wave for an intermediate β-plasma (m _e/m _i?β?1). For this study, we have introduced the nonlinear ponderomotive force (due to the finite frequency (ω ₀<ω _ci) kinetic Alfvén wave) in the derivation of the ion acoustic wave. The main aim of the present paper is to study the nonlinear effects associated with the different driving finite frequencies (ω ₀<ω _ci) of the pump kinetic Alfvén wave on the formation of localized structures and a turbulent spectrum applicable to the solar wind around 1 AU. As a result, we found that the different driving frequencies of the pump kinetic Alfvén wave affect the formation of the localized structures. We have also studied the turbulent scaling which follows (～k ^?3.6) for ω ₀/ω _ci≈0.2, (～k ^?3.4) for ω ₀/ω _ci≈0.3 and (～k ^?3.2) for ω ₀/ω _ci≈0.4, at small scales. Further, we have also found that different finite driving frequencies of the pump kinetic Alfvén wave affect the turbulence scaling at small scales, which may affect the heating of the plasma particles in solar wind. The present study is correlated with the observation made by the Cluster spacecraft for the solar wind around 1 AU.     

Effects of ion collisions on the interaction of transverse waves with half-space plasma

For half-space (Z>0), homogeneous, collisonal and warm plasma, the expressions for fields and penetration depth δ/δ _e (in the unit of ion collisionless cold plasma penetration depth, i.e., when v _i =0, υ_0i =) are derived and discussed numerically. It is concluded that the propagation of transverse waves is only slightly affected by the ion collisions and the applied magnetic field when the plasma frequence is greater than the wave frequency (ω _pe >ω). For the case of ω _pe ≤ω, the damping of the wave is not affected by the changes in the ion collision frequency and the ion temperature. However, in this case, the propagation of the wave is drastically affected by the applied magnetic field and the wave damps quickly as the magnetic field strength or the gyrofrequency (Ω _e ) increases.