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.     

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.     

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.     

Nonlinear Alfvén waves in a plasma with a finite conductivity

Nonlinear Alfvén waves, which in the infinitely conducting plasma are noncompressive and have a constant magnetic field strength (B ²=const), propagate in a turbulent plasma. The latter is characterized by a big (but finite) electrical conductivity _eff due to micro-instabilities. The Alfvén wave in such a medium is governed by the diffusion equation. It is shown that an initial periodic perturbation (withB ²=const) while still being incompressive, decays due to dissipation.     

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.     

The effects of Alfvén waves on heating plasma in post-flare loops

In investigating the effects of collision Alfvén waves on the heating of a cool-type solar loop, like the post-flare loop, models are proposed, and the distributions of ion or electron density, temperature, pressure, and wave energy density are simulated. We assumed the magnetic field strength in the loop is about 100 G and found that Alfvén waves can propagate through the whole loop, that is to say, the decay length of collision Alfvén waves which we consider can reach to the height or length of the loop. Thus, the Alfvén wave heating is a considerable heating mechanism in cool loops. And we also found that the variations of density, pressure, and wave energy density are more significant than those of the temperature. In the whole loop, the temperature is of the order of 10⁴ K. In comparison with other parameters, the temperature can be considered as homogeneous; hence, the heat conductive flux in the simulations is omitted.     

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.     

On the dissipation rates for Alfvén waves in the solar transition region

The present paper concerns Alfvén waves, in a resistive and viscous atmosphere, under a steep temperature gradient (Section 1). The dissipative Alfvén wave equation is deduced assuming uniform vertical background magnetic field, and allowing for arbitrary profiles of Alfvén speed, and viscous and resistive diffusivities as functions of altitude (Section 2). A three-parameter family of temperature profiles, allowing for independent choice of initial and asymptotic temperature, and of initial temperature gradient, is used to re-write the wave equation, with the temperature as the independent variable, instead of altitude (Section 3). It is shown that, for the conditions prevailing in the solar transition region between the chromosphere and corona, two approximations of the dissipative wave equations may be considered, the simplest leading to solution in terms of Gaussian hypergeometric functions (Section 4). The exact analytical solution allows calculation of the (i) velocity and (ii) magnetic field perturbations, (iii) kinetic, (iv) magnetic and (v) total energy density, (vi) energy flux, (vii) rate-of-strain and (viii) electric current, and (ix) viscous, (x) resistive and (xi) total rate of dissipation (Section 5). These are plotted versus temperature, across the transition region from the chromosphere to the corona, for the quiet and active Sun (Section 6). The feasibility of heating of the transition region by dissipation of Alfvén waves is discussed (Section 7), by comparing empirical heating rates, with theoretical values for a range of physical conditions, including initial velocity perturbations 5 to 15 km s ^–1, background magnetic field 12 to 120 G, wave periods 60 to 300 s, thickness of the transition region 100 to 300 km, resistive and anomalous diffusivities to 100 and viscous and turbulent diffusivities to 100 . The conclusion is that dissipation of Alfvén waves is not an effective heating mechanism for the transition region and corona, although it may be for the chromosphere (see Campos and Mendes, 1995, and references therein).     

Kinetic Alfvén waves in extended radio sources

We study a model of extended radio sources (ERS), in particular, extragalactic jets and radio lobes, which are inhomogeneous and where noncompressive Alfvén and surface Alfvén waves (and not shocks and magnetosonic waves) are primarily excited. We assume that a negligible thermal population exists (i.e., the ion density at the low-energy cut-off of the power law distribution is greater than the ion density of the thermal population, if present). Due to internal instabilities and/or the interaction of the ERS with the ambient medium, surface Alfvén waves (SAW) are created. We show that even very small amplitude SAW are mode converted to kinetic Alfvén waves (KAW) which produce large moving accelerating potentials , parallel to the magnetic field. Neglecting nonlinear perturbations, and for typical physical parameters of ERS, we obtaine1 MeV. Wesuggest that these potentials are important in acceleration (e.g., injection energy) and reacceleration of electrons in ERS. We show that energy losses by synchrotron radiation can be compensated by reacceleration by KAW. The relation between KAW acceleration, and previously studied cyclotron-resonance acceleration by Alfvén waves, is discussed.     

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.     

Discrete Alfvén waves in planar flux tubes

Properties of discrete Alfvén wave modes are derived, at frequencies up to the ion-cyclotron frequency, for current-carrying plasma slabs with non-uniform densities. It is shown that the essential features of the dispersion relations can be derived by examining the dominant terms in the potential function, when the wave equation is cast in the Schrödinger equation form. Analytical predictions for a class of mass and current density profiles are compared with numerically calculated dispersion relations and wavefields for particular profiles.     

Phase mixing of propagating Alfvén waves in a stratified atmosphere: solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Recent observations by Hinode/SOT showed that the spicules mostly exhibit upward propagating high frequency waves. Here we investigate the dissipation of such waves due to phase mixing in stratified environment of solar spicules. Since they are highly dynamic structures with speeds at about significant fractions of the Alfvén phase speed, we take into account the effects of steady flows. Our numerical simulations show that in the presence of stratification due to gravity, damping takes place in space than in time. The exponential damping low, \operatornameexp(-\operatornameAt³)\operatorname{exp}(-\operatorname{At}^{3}), is valid under spicule conditions, however the calculated damping time is much longer than the reported spicule lifetimes from observations.     

Coronal heating by Alfvén waves

Solar Physics - If Alfvén waves are responsible for the heating of the solar corona, what are the various dissipation processes, under what conditions are they important, and what...     

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 and the sunspot phenomenon

Parker's explanation of the sunspot phenomenon in terms of the enhanced emission of Alfvén waves (solar vulcanology) is shown to be compatible with observation only if 90% of the waves propagate downwards. Further difficulties arise if the region of cooling by Alfvén wave generation is restricted to a depth of 2 Mm. However, it is shown that, if Alfvén wave generation is included in a recent model proposed by Meyer, Schmidt, Weiss and Wilson, these difficulties may be resolved. The problem of the sharp umbra and penumbra boundaries is discussed and it is shown that features of this combined model are relevant to the flare phenomenon.     

Coronal loop heating by Alfvén waves

The excitation and dissipation of global and surface Alfvén waves and their conversion into kinetic Alfvén waves have been analyzed for solar coronal loops using a cylindrical model of a magnetized plasma. Also the optimal conditions for coronal loop heating regimes with density of dissipated power 10³ erg cm^–3 s^–1 by the new scheme named combined Alfvén wave resonance are found. Combined Alfvén wave heating regime appears when the global Alfvén wave is immersed into the Alfvén continuum with the condition of not-so-sharp distribution of axial current.Instituto de Matemática, Universidade Federal Fluminense, Niterói, RJ, Brazil