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Linear properties of kinetic Alfvén waves (KAWs) and kinetic slow waves (KSWs) are studied in the framework of two-fluid magnetohydrodynamics. We obtain the wave dispersion relations that are valid in a wide range of the wave frequency ω and plasma-to-magnetic pressure ratio β. The KAW frequency can reach and exceed the ion cyclotron frequency at ion kinetic scales, whereas the KSW frequency remains sub-cyclotron. At β ∼ 1, the plasma and magnetic pressure perturbations of both modes are in anti-phase, so that there is nearly no total pressure perturbations. However, these modes exhibit also several opposite properties. At high β, the electric polarization ratios of KAWs and KSWs are opposite at the ion gyroradius scale, where KAWs are polarized in sense of electron gyration (right-hand polarized) and KSWs are left-hand polarized. The magnetic helicity σ ∼ 1 for KAWs and σ ∼ −1 for KSWs, and the ion Alfvén ratio R Ai ≪ 1 for KAWs and R Ai ≫ 1 for KSWs. We also found transition wavenumbers where KAWs change their polarization from leftto right-hand. These new properties can be used to discriminate KAWs and KSWs when interpreting kinetic-scale electromagnetic fluctuations observed in various solar-terrestrial plasmas. This concerns, in particular, identification of modes responsible for kinetic-scale pressure-balanced fluctuations and turbulence in the solar wind.

Voitenko and Goossens Reply: Recently [1], we presented a new channel for nonlocal spectral transport of wave energy from large MHD scales to small dissipative scales. The nonlocal transport is initiated by the resonant decay of MHD Alfvén waves into kinetic Alfvén waves (KAWs) and is possible if the plasma (gas/magnetic pressure ratio) is smaller than the electron/ion mass ratio m e =m p . In their Comment [2] (and in their related paper [3]), Shukla and Stenflo aim to point out the deficiencies of our Letter [1] and suggest a similar decay channel but with a circularly polarized Alfvén wave pump.First, Shukla and Stenflo state that the terms due to thermal effects and the terms due to electron inertial effects cannot be kept simultaneously, as we did in our Letter. Instead, they allow only two opposite limits when the phase velocity of Alfvén waves !=kz is either much slower or much faster than the electron thermal velocity V Te . Then the electron inertia can be neglected in the kinetic regime, !=kz V Te (valid for m e =m p 1), and thermal effects can be neglected in the inertial regime, !=kz V Te (valid for m e =m p ). Their reasoning is that the plasma dispersion function, which appears in kinetic theory, cannot be expanded in the Taylor series if its argument !=kzV Te is not much different from 1. We disagree with this approach, which excludes from consideration many situations where m e =m p (e.g., in the auroral zones at heights 3 4 Earth radii, or in solar corona at 3 4 solar radii), and where KAWs do exist and propagate with phase velocity !=kz V A V Te . In two-fluid MHD, when the thermal effects dominate (as in the case of > m e =m p ), it does not mean that the electron inertia must be disregarded. And vice versa, in the case of < m e =m p the electron inertia is more important, but it does not mean that the thermal effects do not play a role. Moreover, since the inertial and thermal effects act in antiphase, the corresponding terms weaken each other when approaches m e =m p , and can completely cancel.This behavior with a smooth transition between inertial and thermal regimes of KAWs has been demonstrated also in kinetic theory by numerical solutions of the kinetic dispersion equation [4]. Therefore, both the inertial and the thermal effects must be taken into account simultaneously, especially when the plasma is not significantly different from m e =m p . In kinetic theory, even if the plasma dispersion function cannot be expanded in the Taylor series in these situations, it can be calculated numerically or approximated. In the framework of two-fluid MHD this can be done by keeping both the electron inertia term (m e @v z =@t) and the electron pressure term (@p e @z) in the parallel momentum equation for electrons, n 0 m e @v z =@t ÿen 0 E z ÿ @p e =@z, which leads to the two-fluid KAW dispersion that we have used in [1]. (EzkB 0 is the parallel electric field, B 0 kz is the background magnetic field.) This two-fluid dispersion is consistent with numerical solutions of the kinetic dispersion equati...

The dynamic equation and coupling coefficient of the three-wave interaction among kinetic Alfvén waves (KAWs) are derived by use of plasma kinetic theory. Linear and nonlinear effects of finite ion Larmor radius are kept for arbitrary value of the ‘kinetic variable’ κ=k⊥ρi. The parametric decay KAW→KAW+KAWis investigated and the threshold amplitude for decay instability in a Maxwellian plasma is calculated. The growth rate of decay instability varies as k2⊥ in both limits κ2[Lt ]1 and κ2[Gt ]1. The main tendency of KAWs is towards nonlinear destabilization at very low wave amplitudes Bk/B0[lsim ]10−3. Two applications concerning KAW dynamics in the magnetosphere and in the solar corona show that three-wave resonant interaction among KAWs may be responsible for the turbulent character of their behaviour, often observed in space plasmas.

The Farley-Buneman instability is studied in the partially ionized plasma of the solar chromosphere taking into account the finite magnetization of the ions and Coulomb collisions. We obtain the threshold value for the relative velocity between ions and electrons necessary for the instability to develop. It is shown that Coulomb collisions play a destabilizing role in the sense that they enable the instability even in the regions where the ion magnetization is greater than unity. By applying these results to chromospheric conditions, we show that the Farley-Buneman instability can not be responsible for the quasi-steady heating of the solar chromosphere. However, in the presence of strong cross-field currents it can produce small-scale, ∼ 0.1−3 m, density irregularities in the solar chromosphere. These irregularities can cause scintillations of radio waves with similar wave lengths and provide a tool for remote chromospheric sensing.

Alfvénic turbulence in space is usually imbalanced: amplitudes of waves propagating parallel and anti-parallel to the mean magnetic field B 0 are unequal. It is commonly accepted that the turbulence is driven by (counter-) collisions between these counter-propagating wave fractions. Contrary to this, we found a new ion-scale dynamical range of the turbulence established by (co-) collisions among waves co-propagating in the same direction along B 0 . Co-collisions become stronger than counter-collisions and produce steep non-universal spectra above certain wavenumber dependent on the imbalance. Spectral indexes of the strong turbulence vary around −3, such that steeper spectra follow larger imbalances. Intermittency steepens the −3 spectra further, up to −3.7. Our theoretical predictions are compatible with steep variable spectra observed in the solar wind at ion kinetic scales, but further verification is needed by correlating observed spectra with measured imbalances.

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We study the nonlocal nonlinear coupling and generation of kinetic Alfvén waves (KAWs) and kinetic slow waves (KSWs) by magnetohydrodynamic Alfvén waves (MHD AWs) in conditions typical for the solar wind in the inner heliosphere. This cross-scale process provides an alternative to the turbulent energy cascade passing through many intermediate scales. The nonlinearities we study are proportional to the scalar products of wave vectors and hence are called "scalar" ones. Despite the strong Landau damping of kinetic waves, we found fast growing KAWs and KSWs at perpendicular wavelengths close to the ion gyroradius. Using the parametric decay formalism, we investigate two independent decay channels for the pump AW: forward decay (involving co-propagating product waves) and backward decay (involving counter-propagating product waves). The growth rate of the forward decay is typically 0.05 but can exceed 0.1 of the pump wave frequency. The resulting spectral transport is nonlocal and anisotropic, sharply increasing perpendicular wavenumbers but not parallel ones. AWs and KAWs propagating against the pump AW grow with about the same rate and contribute to the sunward wave flux in the solar wind. Our results suggest that the nonlocal decay of MHD AWs into KAWs and KSWs is a robust mechanism for the cross-scale spectral transport of the wave energy from MHD to dissipative kinetic scales in the solar wind and similar media.