Kinetic Alfven Waves Research Articles

Turbulent heating and cross‐field transport near the magnetopause from THEMIS

We demonstrate that the low frequency broadband magnetic fluctuations observed during THEMIS spacecraft traversals near the Earth's magnetopause may be described as a turbulent spectrum of Doppler shifted kinetic Alfvén waves (KAWs). These waves are most intense along reconnected flux‐tubes in the magnetosheath just outside the magnetopause. We identify distinct power‐law scalings of wave spectral energy density in wavenumber and show that Landau (LD) and transit time damping (TD) on ions and electrons is largest at the wavenumber where the power‐law index changes. The threshold amplitude for stochastic ion scattering/acceleration is also exceeded by these waves. These acceleration processes are manifest in observations of field‐aligned and transverse heating of electrons and ions respectively. From integration over the range of observed wavenumbers we show that, if the wave‐normal angles are sufficiently large, these waves can provide diffusive transport of magnetosheath plasmas across the magnetopause at up to the Bohm rate.

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.

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.

Intermittency of electron density in interstellar kinetic Alfvén wave turbulence

The statistics of electron density fluctuations in kinetic Alfvén wave (KAW) turbulence is investigated in connection with the inferred Lévy statistics of pulsar signal broadening. Using analytic theory and computation, decaying KAW turbulence is shown to form coherent, intermittent current filaments in regions where local current intensity exceeds the rms value by a critical factor of a few. Nonlinear mixing is suppressed because the filament magnetic field has sufficient shear to refract away turbulent waves. While the magnetic field and density associated with the filament are as coherent as the current, they are not localized and isolated. Ampere’s law dictates that the magnetic field decays as r−1 outside the current, and KAW equipartition dictates that density has the same envelope. This structure gives the density gradient a Lévy distribution, consistent with pulsar scintillation.

Shear-driven kinetic Alfven wave in the plasma sheet boundary layer

Abstract Shear-driven kinetic Alfven waves (KAWs) at the plasma sheet boundary layer (PSBL) were investigated for substorm events in the presence of a parallel electric field using the general loss-cone distribution function. Using a kinetic approach, we derived the expressions for dispersion relation and growth length of the KAW in the presence of the parallel electric field using the general loss-cone distribution function for both, weak and strong shear regimes. The frequency of the KAW obtained is in agreement with observed values of 0.1–4 Hz in the PSBL. The results explain the generation of the energetic KAWs at the PSBL by the shear at substorm onset. The parallel electric field associated with the energetic KAWs at substorm onset may heat the field-aligned electrons, leading to parallel electron energisation that ultimately causes an intense aurora. The electric field along magnetic field lines enhances the frequency of KAW but decreases the growth length in the case of weak shear. We also found that the parallel electric field can reflect KAW towards the PSBL. The loss-cone distribution index changes the profiles of frequency and growth length plots of the shear-driven KAW. Hence, the loss-cone distribution function is an important factor in the excitation of KAW in the active region of the magnetosphere, such as the PSBL and the auroral acceleration region.

Ion and electron beam effects on kinetic Alfven wave with general loss-cone distribution function—kinetic approach

This work studies the effect of ion and electron beam on kinetic Alfven wave (KAW) with general loss-cone distribution function. The kinetic theory has been adopted to evaluate the dispersion relation and damping rate of the wave in the presence of loss-cone distribution indices J. The variations in wave frequency ω and damping rate with perpendicular wave number k⊥ρi, (k⊥ is perpendicular wave number and ρi is ion gyroradius) and parallel wave number k|| are studied. It is found that the distribution index J and ion beam velocity enhance the wave frequency at lower k⊥ρi, whereas the electron beam velocity enhances the wave frequency at higher k⊥ρi. The calculated values of frequency correspond to the observed values in the range 0.1–4 Hz. Increase in damping rate due to higher distribution indices J and ion beam velocity is observed. The effect of electron beam is to reduce the damping rate at higher k⊥ρi. The plasma parameters appropriate to plasma sheet boundary layer are used. The results may explain the transfer of Poynting flux from the magnetosphere to the ionosphere. It is also found that in the presence of the loss-cone distribution function the ion beam becomes a sensitive parameter to reduce the Poynting flux of KAW propagating towards the ionosphere.

Excitation of ion-acoustic perturbations by incoherent kinetic Alfvén waves in plasmas

The dispersion relation for ion-acoustic perturbations (IAPs) in the presence of incoherent kinetic Alfvén waves (KAWs) in plasmas is derived. The wave-kinetic-approach is used to study the nonlinear interactions between an ensemble of random phase KAWs and IAPs. It is found that incoherent KAW spectrum is unstable against IAPs. The instability growth rates for particular cases are obtained. The present instability offers the possibility of heating ions in a turbulent magnetoplasma composed of incoherent KAWs.

Transient Evolution of Nonlinear Localized Coherent Structures of Kinetic Alfvén Waves

We present numerical simulations of kinetic Alfven waves (KAWs) and inertial Alfven waves (IAWs) applicable to the solar wind, the solar corona, and the auroral regions, respectively, leading to the formation of coherent magnetic structures when the nonlinearity arises from ponderomotive effects and Joule heating. The nonlinear dynamical equation satisfies the modified nonlinear Schrodinger equation. The effect of nonlinear coupling between the main KAW/IAW and the perturbation, producing filamentary structures of the magnetic field, has been studied. Scalings in the spectral index of the power spectrum at different times have been calculated. These filamentary structures can act as a source for particle acceleration by wave – particle interaction because the KAWs/IAWs are mixed modes and Landau damping is possible.

Transport in two-fluid magnetohydrodynamic turbulence

We present a theory of transport of magnetic flux and momentum in two fluid three-dimensional reduced magnetohydrodynamic (MHD) turbulence. By including the effects of shear flows and magnetic fields consistently, we show that kinetic Alfven waves can help weaken the quenching in turbulent transport of a strong magnetic field B0 found in single fluid MHD turbulence, leading to turbulent magnetic diffusivity eta(T) proportional (eta/Omega)(1/3)B(0)(-2). Here, eta and Omega are the Ohmic diffusivity and the shearing rate of the shear flow. Momentum transport is diffusive, with the value of eddy viscosity larger than that in single fluid MHD turbulence. The effects of drift waves are found to be weaker. Implications for the instability of shear flows are discussed.

Coherence and Intermittency of Electron Density in Small‐Scale Interstellar Turbulence

Spatial intermittency in decaying kinetic Alfven wave turbulence is investigated to determine if it produces non Gaussian density fluctuations in the interstellar medium. Non Gaussian density fluctuations have been inferred from pulsar scintillation scaling. Kinetic Alfven wave turbulence characterizes density evolution in magnetic turbulence at scales near the ion gyroradius. It is shown that intense localized current filaments in the tail of an initial Gaussian probability distribution function possess a sheared magnetic field that strongly refracts the random kinetic Alfven waves responsible for turbulent decorrelation. The refraction localizes turbulence to the filament periphery, hence it avoids mixing by the turbulence. As the turbulence decays these long-lived filaments create a non Gaussian tail. A condition related to the shear of the filament field determines which fluctuations become coherent and which decay as random fluctuations. The refraction also creates coherent structures in electron density. These structures are not localized. Their spatial envelope maps into a probability distribution that decays as density to the power -3. The spatial envelope of density yields a Levy distribution in the density gradient.

Solar Microwave Drifting Spikes and Solitary Kinetic Alfvén Waves

Mechanisms driving eruptive phenomena and elementary processes occurring at the smallest coherent scales have been outstanding problems in physics. In this Letter, a novel kind of fine structures of radio bursts, solar microwave drifting spikes (SMDSs), is reported. Our analysis shows that the SMDSs can be produced by a group of solitary kinetic Alfven waves (SKAWs) with small cross-field scales, in which the electrons in the SKAWs are accelerated self-consistently by the SKAW electric fields to tens of keV and trapped within the SKAW potential wells. It is these trapped electrons that trigger the SMDSs. And the frequency drifts of the SMDSs are attributed to the SKAW propagation along the magnetic field. The SKAWs are exact solutions of two-fluid equations for a low-beta plasma and have been experimentally verified in the magnetosphere, where they accelerate auroral electrons to several keV. We believe the SMDSs represent a new observational signature of SKAWs in the atmosphere.

Interpretation of solar wind reconnection exhaust in terms of kinetic Alfvén wave group‐velocity cones

Recent multi‐satellite measurements of reconnection exhausts in the solar wind have allowed for the first time to determine the reconnection rate (R) and the exhaust wedge angle 2θw. We compare such observations of R and θw with the theoretical predictions based on the half‐cone angles (θg) of the group velocity vectors (Vg) of the kinetic Alfvén (KA) and slow MHD (SMHD) wave modes. We find that for these recently observed reconnection events in the solar wind the exhaust wedge angle and the reconnection rate are determined by the KA waves and not by the SMHD wave mode. Our study suggests a theoretical basis for determining the reconnection rate based on group‐velocity cone angle of certain wave modes depending on the MHD or kinetic reconnection regimes.

Group velocity cones in diverging magnetic reconnection structures

In a typical geometry of magnetic reconnection, the so‐called exhaust regions diverge out of the localized diffusion region. The diverging reconnection structure is conical in shape with its apex near the x‐line. Such conical regions have been seen in both MHD and kinetic simulations of reconnection as well as in satellite observations. We demonstrate here that depending on the reconnection regime, the cone angle of the exhaust regions found in numerical simulations and as well as in satellite observations compare well with the maximum angles of group‐velocity cones associated with the slow MHD mode, or the whistler mode, or the kinetic Alfvén wave (KAW). For each of these three reconnection regimes, we give a quantitative description of the group velocity cones. In the MHD case the cone angle is small and increases almost linearly with the plasma β < 2. In the whistler regime the cone angle is a constant of 19.5°. In the KAW regime the cone angle depends on plasma β as well as on the timescale associated with the diffusion process in the current sheet. The close agreement between the observed and simulated exhaust cone angles and the group‐velocity cone angles in all the three reconnection regimes is highly suggestive that “at least” the geometrical feature of the exhaust region is determined by the group velocity of the disturbances, which propagate out of the diffusion region.

Behaviour of a low frequency wave in a FRC plasma

A low frequency torsional Alfven wave (angular frequency ω ∼ 0.3ωci0, ωci0; ion gyro frequency in vacuum) is induced in an extremely high beta (beta = plasma pressure/pressure of confining magnetic field) plasma with the field reversed configuration (FRC) by an external antenna. When the wave is introduced from outside towards the magnetic axis of the FRC plasma, not only the Alfven velocity vA but also the local ion gyro frequency ωci decreases as the density increases and the magnetic field decreases. The spatial structure of the wave is examined in the region between the separatrix and the location near the O-point. Near the former location, the plasma is tenuous and the magnetic field has nearly external value so that ω ∼ 0.3ωci0, and near the latter location, the beta value is large and ω > 0.7ωci. The observed amplitude of the toroidal component of the magnetic disturbance has a broad peak around the radial location of the resonance position obtained from the cold plasma theory, although the cold plasma theory yields a sharper spatial structure. The polarization of the magnetic disturbance component perpendicular to the static magnetic field is left-handed outside the theoretical resonance position and right-handed deep in the plasma. The measured perpendicular wave number kr is small except for the region near the resonance position where the kinetic Alfven wave is expected to have a large wave number. This behaviour will be interpreted as, with the help of the warm plasma theory, the torsional Alfven wave evolves into the kinetic Alfven wave and is then converted to the compressional wave with a smaller wave number when the wave propagates inside the plasma.

Decay instability of kinetic Alfvén waves in preflare plasmas of the loops in active solar regions

We examine the physical conditions for the origin of the decay instability of kinetic Alfven waves in loop plasmas at the early flare stages. The synchronism conditions are used to derive a modified expression for the nonlinear growth rate of the process of the decay of the primary kinetic Alfven wave (KAW) into an ion-acoustic wave and a secondary KAW. The threshold amplitude of the primary KAW is calculated in units of the background magnetic field strength in the chromospheric section of loop current circuit.

Kinetic Alfvén waves and electron physics. II. Oblique slow shocks

One-dimensional (1D) particle-in-cell (PIC; kinetic ions and electrons) and hybrid (kinetic ions; adiabatic and massless fluid electrons) simulations of highly oblique slow shocks (θBn=84° and β=0.1) [Yin et al., J. Geophys. Res., 110, A09217 (2005)] have shown that the dissipation from the ions is too weak to form a shock and that kinetic electron physics is required. The PIC simulations also showed that the downstream electron temperature becomes anisotropic (Te‖>Te⊥), as observed in slow shocks in space. The electron anisotropy results, in part, from the electron acceleration/heating by parallel electric fields of obliquely propagating kinetic Alfvén waves (KAWs) excited by ion-ion streaming, which cannot be modeled accurately in hybrid simulations. In the shock ramp, spiky structures occur in density and electron parallel temperature, where the ion parallel temperature decreases due to the reduction of the ion backstreaming speed. In this paper, KAW and electron physics in oblique slow shocks are further examined under lower electron beta conditions. It is found that as the electron beta is reduced, the resonant interaction between electrons and the wave parallel electric fields shifts to the tail of the electron velocity distribution, providing more efficient parallel heating. As a consequence, for βe=0.02, the electron physics is shown to influence the formation of a θBn=75° shock. Electron effects are further enhanced at a more oblique shock angle (θBn=84°) when both the growth rate and the range of unstable modes on the KAW branch increase. Small-scale electron and ion phase-space vortices in the shock ramp formed by electron-KAW interactions and the reduction of the ion backstreaming speed, respectively, are observed in the simulations and confirmed in homogeneous geometries in one and two spatial dimensions in the accompanying paper [Yin et al., Phys. Plasmas 14, 062104 (2007)]. Results from this study conclude that the inability of the hybrid method to model the Landau resonance of KAW with electrons and the resulting time-evolving electron parallel heating lead to differences between the PIC and hybrid simulations.

Kinetic Alfvén waves and electron physics. I. Generation from ion-ion streaming

Short-wavelength kinetic Alfvén waves (KAWs) that propagate at large angles with respect to the magnetic field and interact with both electrons and ions have broad application to laboratory and space plasmas. Using linear Vlasov theory and particle-in-cell (PIC) simulations, the generation of KAWs by ion-ion streaming along the magnetic field at relatively low (2.5× the Alfvén speed) and low plasma beta (ratio of plasma thermal pressure to magnetic pressure ⩽0.1) are investigated. The instability has been examined previously using linear theory and a hybrid simulation method in which the ions are treated kinetically and the electrons as an adiabatic fluid. In this work it is found that when the electron Landau resonance factor or equivalently the ratio of the Alfvén speed to the electron thermal speed is large enough, the interaction of KAWs with the electrons produces strong parallel electron heating. The electron parallel heating in turn increases both the wave growth rates and the range of unstable modes of the instability, leading to enhanced saturated wave levels, increased perpendicular ion heating and larger spatial fluctuations in the drift speeds of the ions that appear as greater reductions of relative ion streaming in localized regions, compared to results from hybrid simulations. The interaction of KAWs with the electrons shifts from the bulk to the tail of the parallel velocity distribution at larger values of the resonant factor, corresponding to situations at lower electron beta or more obliquely propagating waves. Ion-to-electron mass ratio effects are considered together with the scaling to electron beta and the resonant factor in order to apply the results to systems of interest. In particular, KAWs and electron kinetics are discussed in the context of oblique slow shock formation and structure [Yin et al., Phys. Plasmas 14, 062105 (2007)].

LIGKA: A linear gyrokinetic code for the description of background kinetic and fast particle effects on the MHD stability in tokamaks

In a plasma with a population of super-thermal particles generated by heating or fusion processes, kinetic effects can lead to the additional destabilisation of MHD modes or even to additional energetic particle modes. In order to describe these modes, a new linear gyrokinetic MHD code has been developed and tested, LIGKA (linear gyrokinetic shear Alfvén physics) [Ph. Lauber, Linear gyrokinetic description of fast particle effects on the MHD stability in tokamaks, Ph.D. Thesis, TU München, 2003; Ph. Lauber, S. Günter, S.D. Pinches, Phys. Plasmas 12 (2005) 122501], based on a gyrokinetic model [H. Qin, Gyrokinetic theory and computational methods for electromagnetic perturbations in tokamaks, Ph.D. Thesis, Princeton University, 1998]. A finite Larmor radius expansion together with the construction of some fluid moments and specification to the shear Alfvén regime results in a self-consistent, electromagnetic, non-perturbative model, that allows not only for growing or damped eigenvalues but also for a change in mode-structure of the magnetic perturbation due to the energetic particles and background kinetic effects. Compared to previous implementations [H. Qin, mentioned above], this model is coded in a more general and comprehensive way. LIGKA uses a Fourier decomposition in the poloidal coordinate and a finite element discretisation in the radial direction. Both analytical and numerical equilibria can be treated. Integration over the unperturbed particle orbits is performed with the drift-kinetic HAGIS code [S.D. Pinches, Ph.D. Thesis, The University of Nottingham, 1996; S.D. Pinches et al., CPC 111 (1998) 131] which accurately describes the particles’ trajectories. This allows finite-banana-width effects to be implemented in a rigorous way since the linear formulation of the model allows the exchange of the unperturbed orbit integration and the discretisation of the perturbed potentials in the radial direction. Successful benchmarks for toroidal Alfvén eigenmodes (TAEs) and kinetic Alfvén waves (KAWs) with analytical results, ideal MHD codes, drift-kinetic codes and other codes based on kinetic models are reported.

Nonlinear Interaction of Minor Heavy Ions with Kinetic Alfven Waves and Their Anisotropic Energization in Coronal Holes

Some recent observations of the solar corona suggest that minor heavy ions undergo an anisotropic and mass-charge dependent energization in the extended corona. In this paper we investigate the nonlinear interaction of minor heavy ions with kinetic Alfven waves (KAWs) in the extended corona where plasma is low-β, in particular the ion energization by KAWs. We find that the cross-field ion energization depends on the ion mass and charge in the sense that the velocity is proportional to the ion mass-charge ratio and the field-aligned ion energy is directly proportional to the ion charge. Consequently, the effective ion temperature becomes strongly anisotropic, as well as much higher than that of protons. With an empirical model of plasma parameters in a coronal hole and an assumption of anisotropic spectrum for KAWs, we calculate the variations of the ion temperature anisotropy (δi ≡ T/T) and the ion-proton temperature ratio (γi ≡ T/T) with heliocentric distance. The results show that they both increase rapidly with heliocentric distances of 1.5-3.5 R☉. In the lower corona below 1.3 R☉, one has δi and γi 1, and in the higher corona above 4 R☉, they approach the saturation values δi 0.5A and γi 0.9AZi, where Ai is the ion mass-charge ratio in units of the proton mass-charge ratio mp/e, and Zi is the ion charge in units of the elementary charge e. We suggest that not only can the KAW-based model of the anisotropic and mass-charge dependent energization reasonably explain the recent observations of minor heavy ions in polar coronal holes, but KAWs may also be potentially important for understanding the microphysics of the wave-particle interaction in the extended solar corona, where the coronal plasma is heated and accelerated into the solar wind.

Ion-Acoustic Wave Generation by Two Kinetic Alfvén Waves and Particle Heating

In this paper we have investigated the beat wave excitation of an ion-acoustic wave at the difference frequency of two kinetic (or shear) Alfven waves propagating in a magnetized plasma with β<1 (β=8πne0Te/B02, where ne0 is the unperturbed electron number density, Te is the electron temperature, and B0 is the external magnetic field). On account of the interaction between two kinetic Alfven waves of frequencies ω1 and ω2, the ponderomotive force at the difference frequency ω1−ω2 leads to the generation of an ion-acoustic wave. Also because of the filamentation of the Alfven waves, magnetic-field-aligned density dips are observed. In this paper we propose that the ion-acoustic wave generated by this mechanism may be one of the possible mechanisms for the heating and acceleration of solar wind particles.