Numerical simulations of kinetic Alfvén waves to study spectral index in solar wind turbulence and particle heating

We present numerical simulations of the modified nonlinear Schrödinger equation satisfied by kinetic Alfvén waves (KAWs) leading to the formation of magnetic filaments at different times. The relevance of these filamentary structures to solar wind turbulence and particle heating has also been pointed out.     

Modulational instability of finite-amplitude Alfvén waves

It is shown that a recent conclusion of Shivamaggi that the modulational instability of finite amplitude Alfvén waves arises when the density cavity travels at subsonic speeds, is incorrect.     

Alfvén waves in the solar atmosphere

We examine the propagation of Alfvén waves in the solar atmosphere. The principal theoretical virtues of this work are: (i) The full wave equation is solved without recourse to the small-wavelength eikonal approximation (ii) The background solar atmosphere is realistic, consisting of an HSRA/VAL representation of the photosphere and chromosphere, a 200 km thick transition region, a model for the upper transition region below a coronal hole (provided by R. Munro), and the Munro-Jackson model of a polar coronal hole. The principal results are:

1. If the wave source is taken to be near the top of the convection zone, where n _H = 5.2 × 10¹⁶ cm^?3, and if B _⊙ = 10.5 G, then the wave Poynting flux exhibits a series of strong resonant peaks at periods downwards from 1.6 hr. The resonant frequencies are in the ratios of the zeroes of J ₀, but depend on B _⊙, and on the density and scale height at the wave source. The longest period peaks may be the most important, because they are nearest to the supergranular periods and to the observed periods near 1 AU, and because they are the broadest in frequency.
2. The Poynting flux in the resonant peaks can be large enough, i.e. P _⊙ ≈ 10⁴–10⁵ erg cm^?2s^?1, to strongly affect the solar wind.
3. ¦δv¦ and ¦δB¦ also display resonant peaks.
4. In the chromosphere and low corona, ¦δv ≈ 7–25 kms^?1 and ¦δB¦ ≈0.3–1.0 G if P _⊙≈10⁴-10⁵ erg cm^?2s^?1.
5. The dependences of ¦δv¦ and ¦δB¦ on height are reduced by finite wavelength effects, except near the wave source where they are enhanced.
6. Near the base, ¦δB¦ ≈ 350–1200 G if P _⊙ ～- 10⁴–10⁵. This means that nonlinear effects may be important, and that some density and vertical velocity fluctuations may be associated with the Alfvén waves.
7. Below the low corona most wave energy is kinetic, except near the base where it becomes mostly magnetic at the resonances.
8. ?₀ < δv ² > v _A or < δB ² > v _A/4π are not good estimators of the energy flux.
9. The Alfvén wave pressure tensor will be important in the transition region only if the magnetic field diverges rapidly. But the Alfvén wave pressure can be important in the coronal hole.

     

Alfvén waves in the solar atmosphere

The linearized propagation of axisymmetric twists on axisymmetric vertical flux tubes is considered. Models corresponding to both open (coronal hole) and closed (active region loops) flux tubes are examined. Principal conclusions are: Open flux tubes: (1) With some reservations, the model can account for long-period (T 1 hr) energy fluxes which are sufficient to drive solar wind streams. (2) The waves are predicted to exert ponderomotive forces on the chromosphere which are large enough to alter hydrostatic equilibrium or to drive upward flows. Spicules may be a consequence of these forces. (3) Higher frequency waves (10 s T few min) are predicted to carry energy fluxes which are adequate to heat the chromosphere and corona. Nonlinear mechanisms may provide the damping. Closed flux tubes: (1) Long-period (T 1 hr) twists do not appear to be energetically capable of providing the required heating of active regions. (2) Loop resonances are found to occur as a result of waves being stored in the corona via reflections at the transition zones. The loop resonances act much in the manner of antireflectance coatings on camera lenses, and allow large energy fluxes to enter the coronal loops. The resonances may also be able to account for the observed fact that longer coronal loops require smaller energy flux densities entering them from below. (3) The waves exert large upward and downward forces on the chromosphere and corona.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Current-driven Alfvén waves in dusty magnetospheric plasmas

It is shown that the sheared flow of electrons and ions in the presence of heavy stationary dust gives rise to unstable Alfvén waves. The coupling of newly studied low frequency electrostatic current-driven mode with the electromagnetic Alfvén and drift waves is investigated. The instability conditions and the growth rates of both inertial and kinetic Alfvén waves are estimated. The theoretical model is applied to the night side boundary regions of Jupiter’s magnetosphere which contain positive dust. The growth rates increase with increase in sheared flow speed. In the nonlinear regime, both inertial and kinetic Alfvén waves form dipolar vortices whose speed and amplitude depend upon the magnitude of the zero-order current.     

Formation of the localized structures and the generation of turbulence by 3-dimensional kinetic Alfvén waves in solar wind plasmas

In the present paper, we have investigated nonlinear interaction of three dimensional kinetic Alfvén wave with perpendicularly propagating magnetosonic wave for intermediate β-plasma (m _e /m _i ?β?1). We have developed the set of dimensionless equations in the presence of ponderomotive nonlinearity due to three dimensional kinetic Alfvén wave in the dynamics of perpendicularly propagating magnetosonic wave. Numerical simulation has been carried out to study the effect of nonlinear coupling of three dimensional kinetic Alfvén wave with perpendicularly propagating magnetosonic wave on power spectrum for the plasma parameters applicable to solar wind around 1 AU. Relevance of the obtained results is pointed out with observation received by Cluster spacecraft for the solar wind around 1 AU.     

Discrete Alfvén waves in solar loop prominences

It is shown that a discrete Alfvén wave can explain the natural oscillations of solar loop prominences by considering the existence of a current flow. Discrete Alfvén waves are a new class of Alfvén waves which is described by the inclusion of the finite ion cyclotron frequency (/ _cl 0) and/or the equilibrium plasma current. In this paper we consider only the effect of the current since in solar prominences (/ _cl 0). We have modeled the solar prominences as a cylindrical plasma, surrounded by vacuum (corona), with L a where L and a are the plasma column, length, and radius, respectively. We have calculated the spectrum of the discrete Alfvén waves as function of the magnitude and shape of the plasma current.     

Non-linear damping of visco-resistive Alfvén waves in solar spicules

Interaction of Alfvén waves with plasma inhomogeneities generates phase mixing which can lead to dissipate Alfvén waves and to heat the solar plasma. Here we study the dissipation of Alfvén waves by phase mixing due to viscosity and resistivity variations with height. We also consider nonlinear magnetohydrodynamic (MHD) equations in our theoretical model. Non-linear terms of MHD equations include perturbed velocity, magnetic field, and density. To investigate the damping of Alfvén waves in a stratified atmosphere of solar spicules, we solve the non-linear MHD equations in the x–z plane. Our simulations show that the damping is enhanced due to viscosity and resistivity gradients. Moreover, energy variations is influenced due to nonlinear terms in MHD equations.     

Nonlinear dynamics of Landau damped kinetic Alfvén waves

In the present paper we have studied the nonlinear dynamical equation of Landau damped kinetic Alfvén wave (KAW) to investigate the nonlinear evolution of KAW and the resulting turbulent spectra in solar wind plasmas. We have introduced a parameter g which governs the coupling between the amplitude of the pump KAW and the density perturbation. The numerical solution has been carried out to see the dependence on the parameter g in the nonlinear part of our equation. Our results reveal the formation of damped localized structures of KAW as well as steepening of the turbulent spectra by increasing g when damping is taken into account. The power spectra of magnetic field fluctuations indicate the redistribution of energy among the higher wave numbers. Each power spectrum with and without damping splits up into two different scaling ranges, Kolmogorov scaling followed by a steeper scaling. The steepening in the power spectra with Landau damping is more than without Landau damping case (for the same value of g). This type of steeper spectra has also been observed in the solar wind and is attributed to the Landau damping effects.     

Numerical simulations to study kinetic Alfvén wave and whistler wave spectra in solar wind plasma

The numerical simulations of the model equation governing the nonlinear evolution of kinetic Alfvén wave (KAW) in solar wind plasmas are performed. The nonlinear dynamical equation of KAW satisfies the modified nonlinear Schrödinger MNLS equation when the ponderomotive nonlinearity is incorporated in the KAW dynamics. The effect of Landau damping is taken into account in the KAW dynamics. The coherent (in the absence of Landau damping) and damped (with Landau damping) localized structures of pump KAW as a consequence of ponderomotive nonlinearity have been studied in the solar wind at 1 AU. A weak whistler signal propagating in these localized structures is amplified which leads to the development of its own coherent and damped localized structures. Magnetic field (KAW) and electric field (whistler wave) power spectra and their spectral indices are calculated. Our results reveal the change in spectral index because of the damping effect which has good agreement with the observations. These damped structures and steeper spectra may be one of the reasons responsible for the plasma heating and particles acceleration in solar wind.     

On searching for observational manifestations of Alfvén waves in solar faculae

In an effort to detect torsional oscillations, we have studied the periodic half-width variations for several spectral lines in solar faculae. The duration of the series being analyzed was from 40 to 150 min. We have determined the dominant frequencies and amplitudes of the half-width oscillations and considered their phase relations to the intensity and line-of-sight velocity oscillations. Five-minute profile halfwidth oscillations with a peak-to-peak amplitude of ～10 m ?A are recorded with confidence in the upperphotospheric Si I 10 827 ?A line in faculae. The chromospheric He I 10 830 A? and Hα line profiles shows ～40–60 m ?A variations in two frequency bands, 2.5–4 and 1–1.9 mHz. No center-to-limb dependence that, according to the theory, must accompany the torsional oscillations has been revealed in the behavior of the oscillation amplitudes. According to present views, these variations cannot be caused by periodic temperature and magnetic field changes. Our observations do not allow us to explain these variations by the sausage mode action either, which should manifest itself at the double frequency.     

Alfvén instabilities in streaming plasmas with anisotropic pressures and their relevance for the solar wind

Low frequency or Alfvén waves in streaming plasmas can become unstable when the square of the Alfvén velocity is smaller than the mean square of the bulk motion in a co-moving reference frame, (u –u )², whereu stands for the bulk velocity of each species and u is the average bulk velocity of the plasma as a whole. For these new Alfvén instabilities the streaming effects can be enhanced by a suitable pressure anisotropy. Perpendicular pressure effects are stabilizing, parallel pressure effects are destabilizing, as in the usual firehose instability. The observed velocity differences between helium and the main (hydrogen) flow in the solar wind plasma are such that the Alfvén waves are getting close to marginal instability. These new Alfvén instabilities limit the velocity differences between helium and hydrogen and thus provide a possible mechanism for accelerating the helium particles up to the order of the main flow velocity.     

Properties of dispersive Alfvén waves: 2. Kinetics (finite and high density plasmas)

The work is devoted to the study of the behavior of dispersive Alfvén waves in astrophysical plasma of finite and high pressure. All the main wave characteristics were obtained, namely, the dispersion, fading, polarization, density perturbations, and charge density perturbations. The effect of the parameters of the space environment on the behavior and properties of dispersive Alfvén waves was analyzed. The wave behavior in finite and high-pressure plasmas is shown to differ appreciably from the behavior in very low, intermediate, and low-pressure plasmas.     

Solar coronal heating by high-frequency dispersive Alfvén waves

It is shown that high-frequency dispersive kinetic Alfvén waves can cause significant electron heating in the solar corona. The heating is produced by collisionless electron Landau dissipation of the parallel electron current associated with high-frequency dispersive kinetic Alfvén waves, which have a parallel electric field.     

Phase mixing of standing Alfvén waves with shear flows in solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of such waves due to phase mixing at the presence of shear flow and field in the stratified atmosphere of solar spicules. The initial flow is assumed to be directed along spicule axis and to vary linearly in the x direction and the equilibrium magnetic field is taken 2-dimensional and divergence-free. It is determined that the shear flow and field can fasten the damping of standing Alfvén waves. In spite of propagating Alfvén waves, standing Alfvén waves in Solar spicules dissipate in a few periods. As height increases, the perturbed velocity amplitude does increase in contrast to the behavior of perturbed magnetic field. Moreover, it should be emphasized that the stratification due to gravity, shear flow and field are the facts that should be considered in MHD models in spicules.     

Alfvén waves in stellar winds

A mathematical model for undamped, toroidal, small-amplitude Alfvén waves in a spherically-symmetric or equatorial stellar wind is developed in this paper. The equations are reduced to a very simple form by using real Fourier amplitudes and the ratio of the inward and outward propagating wave amplitudes, which is interpreted as a measure of the relative influence of wave reflection in the flow, on the solution at a given point. Asymptotic solutions at large distances are found to depend only on one parameter, = / _P - the ratio of wave frequency and critical (or cutoff) frequency which is a flow characteristic; a = 1 divides solutions into two qualitatively different groups. When 1 the asymptotic (r-) ratio of the inward and outward propagating wave amplitudes does not depend on wave frequency and is equal to unity, while the phase shift between them changes; in this case the wave pattern is a standing wave. If > 1 the converse occurs with the ratio of the amplitudes decreasing rapidly as the frequency increases, and the phase shift equals to -1/2, corresponding to a propagating wave pattern. The result is also expressed in terms of velocity and magnetic field perturbations.Existence of a finite incoming wave amplitude solution at the Alfvén critical point indicates that this point is stable with respect to the perturbations which originate at the critical point and spend an infinite time in its vicinity.Special attention is paid to the applicability of the WKB approximation. It is argued that it can be used only in finite intervals which do not contain the Alfvén critical point, with inward propagating waves taken into account through the boundary conditions. It is shown that despite the presence of reflection, the outward propagating wave amplitude can be described reasonably well by the WKB formula, perhaps with different constants in different regions. In this context = 1 divides solutions which cannot be approximated by the WKB estimate at all at large distances (the first group), from those which can with any given accuracy.As an illustration of the analytical behaviour some numerical results are shown using a cool wind model. These are likely to express qualitatively the features of the Alfvén waves in any stellar wind, since the only assumptions about the flow used in the analytical study of the wave equations were that: the flow has small velocity at the base of the corona; it then passes through the critical point, and reaches its finite non-zero limit at infinity.     

Non-inductive current driven by Alfvén waves in solar coronal loops

It has been shown that Alfvén waves can drive non-inductive current in solar coronal loops via collisional or collisionless damping. Assuming that all the coronal-loop density of dissipated wave power (W= 10–3 erg cm^–3 s^–1), which is necessary to keep the plasma hot, is due to Alfvén wave electron heating, we have estimated the axial current density driven by Alfvén waves to be jz 10³–10⁵ statA cm^–2. This current can indeed support the quasi-stationary equilibrium and stability of coronal loops and create the poloidal magnetic field up to B 1–5 G.