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.     

The electron-ion streaming instabilities driven by drift velocities of the order of electron thermal velocity in a nonmagnetized plasma

The kinetic Alfven waves are investigated using Maxwell-Boltzmann-Vlasov equation to evaluate the kinetic dispersion relation and growth/damping rate with magnetic field gradient, density gradient, temperature gradient and velocity gradient with inhomogeneous plasma. The effect of gradient terms is included in the analysis 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. This study elucidates a possible scenario to account for the particle acceleration and the wave dissipation in inhomogeneous plasmas. This model is able to explain many features observed in plasma sheet boundary layer as well as to evaluate the dispersion relation, growth rate, growth length and damping rate of kinetic Alfven wave. The applicability of this model is assumed for auroral acceleration region, plasma sheet boundary layer and cusp region.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Stability of an inhomogeneous two-component plasma with magnetic viscosity

The stability of a semi-infinite quasi-neutral inhomogeneous plasma with magnetic viscosity has been discussed by using JWKB approximation in which the parameters are regarded slowing varying. Dispersion relation is obtained and discussed. It is found that the inhomogeneous system is unstable for all perturbations withk _y= 0. A dispersion relation for homogeneous plasma is also obtained and discussed. It is shown that fast and slow-MHD waves propagate in the homogeneous plasma in the limit of almost perpendicular propagation under certain conditions.     

Ion acoustic instability in the presence of plasma turbulence in the solar wind

The adiabatic theory of interaction between high and low frequency waves has been studied for the case of electron plasma oscillations and ion acoustic waves and the results are applied to the solar wind. The modified dispersion relation for ion acoustic waves has been derived, taking a Gaussian distribution for plasmons. Two limiting cases of the spectrum are studied. For a broad spectrum, the plasma turbulence has a destabilising effect by introducing a growth rate denoted by turbulence, which is positive for k ₀ > (m _e/ m _i )^1/2 _De ^–1 , k ₀ being the central wave numger of the spectrum, _De the electron Debye length. Also, even for v _d(drift velocity between electrons and ions) < c _s, we arrive at unstable ion acoustic modes. For narrow spectrum, the plasma turbulence has a stabilising effect.     

Density variation effect on multi-ions with kinetic Alfven wave around cusp region—a kinetic approach

The kinetic Alfven waves in the presence of homogeneous magnetic field plasma with multi-ions effect are investigated. The dispersion relation and normalised damping rate are derived for low-\(\beta\) plasma using kinetic theory. The effect of density variation of \(\text{H}^{+}\), \(\text{He}^{+}\) and \(\text{O}^{+}\) ions is observed on frequency and damping rate of the wave. The variation of frequency (\(\omega\)) and normalised damping rate (\(\gamma / \varOmega_{H^{ +}} \)) of the wave are studied with respect to \(k_{ \bot} \rho_{j}\), where \(k_{ \bot} \) is the perpendicular wave number, \(\rho_{j}\) is the ion gyroradius and \(j \) denotes \(\text{H}^{+}\), \(\text{He}^{+}\) and \(\text{O}^{+}\) ions. The variation with \(k_{ \bot} \rho_{j}\) is considered over wide range. The parameters appropriate to cusp region are used for the explanation of results. It is found that with hydrogen and helium ions gyration, the frequency of wave is influenced by the density variation of \(\text{H}^{+}\) and \(\text{He}^{+}\) ions but remains insensitive to the change in density of \(\text{O}^{+}\) ions. For oxygen ion gyration, the frequency of wave varies over a short range only for \(\text{O}^{+}\) ion density variation. The wave shows damping at lower altitude due to variation in density of lighter \(\text{H}^{+}\) and \(\text{He}^{+}\) ions whereas at higher altitude only heavy \(\text{O}^{+}\) ions contribute in wave damping. The damping of wave may be due to landau damping or energy transfer from wave to particles. The present study signifies that the both lighter and heavier ions dominate differently to change the characteristics of kinetic Alfven wave and density variation is also an important parameter to understand wave phenomena in cusp region.     

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.     

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.     

Strong and Weak Damping of Slow MHD Standing Waves in Hot Coronal Loops

Slow magnetohydrodynamic (MHD) standing wave oscillations in hot coronal loops for both strong (i.e. τ_d/P∼ 1) and weak (i.e. τ_d/P≥ 2) damping are investigated taking account of viscosity, thermal conductivity and optically thin radiation. The individual effect of the dissipative terms is not sufficient to explain the observed damping. However, the combined effect of these dissipative terms is sufficient to explain the observed strong damping, as well as weak damping seen by SUMER. We find that, the ratio of decay time (τ_d) and period (P) of wave, i.e., τ_d/P (which defines the modes of damping, whether it is strong or weak) is density dependent. By varying density from 10⁸ to 10¹⁰ cm⁻³ at a fixed temperature in the temperature range 6 – 10 MK, observed by SUMER, we get two sets of damping: one for which τ _d/P∼ 1 corresponds to strong damping that occurs at lower density and another that occurs at higher density for which τ_d/P ≥ 2 corresponds to weak damping. Contrary to strong-damped oscillations, the effect of optically thin radiation provides some additional dissipation apart from thermal conductivity and viscosity in weak-damped oscillations. We have, therefore, derived a resultant dispersion relation including the effect of optically thin radiation. Solutions of this dispersion relation illustrate how damping time varies with physical parameters of loops in both strong and weak damping cases.     

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.     

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.     

On Ponderomotive Effects Induced by Alfvén Waves in Inhomogeneous 2.5D MHD Plasmas

Where spatial gradients in the amplitude of an Alfvén wave are non-zero, a nonlinear magnetic-pressure gradient acts upon the medium (commonly referred to as the ponderomotive force). We investigate the nature of such a force in inhomogeneous 2.5D MHD plasmas by analysing source terms in the nonlinear wave equations for the general case of inhomogeneous B and ρ, and consider supporting nonlinear numerical simulations. Our equations indicate that there are two distinct classes of ponderomotive effect induced by Alfvén waves in general 2.5D MHD, each with both a longitudinal and transverse manifestation. i) Geometric effects: Gradients in the pulse geometry relative to the background magnetic field cause the wave to sustain cospatial disturbances, the longitudinal and transverse daughter disturbances – where we report on the transverse disturbance for the first time. ii) ?(c _A) effects: Where a pulse propagates through an inhomogeneous region (where the gradients in the Alfvén-speed profile c _A are non-zero), the nonlinear magnetic-pressure gradient acts to accelerate the plasma. Transverse gradients (phase mixing regions) excite independently propagating fast magnetoacoustic waves (generalising the result of Nakariakov, Roberts, and Murawski (Solar Phys. 175, 93, 1997)) and longitudinal gradients (longitudinally dispersive regions) perturb along the field (thus creating static disturbances in β=0, and slow waves in β≠0). We additionally demonstrate that mode conversion due the nonlinear Lorentz force is a one-way process, and does not act as a mechanism to nonlinearly generate Alfvén waves due to propagating magnetoacoustic waves. We conclude that these ponderomotive effects are induced by an Alfvén wave propagating in any MHD medium, and have the potential to have significant consequences on the dynamics of energy transport and aspects of dissipation provided the system is sufficiently nonlinear and inhomogeneous.     

Cavitation by Nonlinear Interaction Between Inertial Alfvén Waves and Magnetosonic Waves in Low Beta Plasmas

This paper presents the model equations governing the nonlinear interaction between dispersive Alfvén wave (DAW) and magnetosonic wave in the low-β plasmas (β≪m _e/m _i; known as inertial Alfvén waves (IAWs); here \upbeta = 8pn₀T /B₀²\upbeta = 8\pi n_{0}T /B_{0}^{2} is thermal to magnetic pressure, n ₀ is unperturbed plasma number density, T(=T _e≈T _i) represents the plasma temperature, and m _e(m _i) is the mass of electron (ion)). This nonlinear dynamical system may be considered as the modified Zakharov system of equations (MZSE). These model equations are solved numerically by using a pseudo-spectral method to study the nonlinear evolution of density cavities driven by IAW. We observed the nonlinear evolution of IAW magnetic field structures having chaotic behavior accompanied by density cavities associated with the magnetosonic wave. The relevance of these investigations to low-β plasmas in solar corona and auroral ionospheric plasmas has been pointed out. For the auroral ionosphere, we observed the density fluctuations of ∼ 0.07n ₀, consistent with the FAST observation reported by Chaston et al. (Phys. Scr. T84, 64, 2000). The heating of the solar corona observed by Yohkoh and SOHO may be produced by the coupling of IAW and magnetosonic wave via filamentation process as discussed here.     

The influence of negatively charged heavy ions on the kinetic Alfven wave in a cometary environment

Kinetic Alfven waves are important in a wide variety of areas like astrophysical, space and laboratory plasmas. In cometary environments, waves in the hydromagnetic range of frequencies are excited predominantly by heavy ions. We, therefore, study the stability of the kinetic Alfven wave in a plasma of hydrogen ions, positively and negatively charged oxygen ions and electrons. Each species was modeled by drifting ring distributions in the direction parallel to the magnetic field; in the perpendicular direction the distribution was simulated with a loss cone type distribution obtained through the subtraction of two Maxwellian distributions with different temperatures. We find that for frequencies w^* < w_{cH ⁺}\omega^{*} < \omega_{c\mathrm{H}^{ +}} (ω ^∗ and w_{cH ⁺}\omega_{c\mathrm{H}^{ +}} being respectively the Doppler shifted and hydrogen ion gyro-frequencies), the growth rate increases with increasing negatively charged oxygen ion densities while decreasing with increasing propagation angles, negative ion temperatures and negative ion mass.