On the Alfvén wave cut-off in partly ionized collisional plasmas (original) (raw)
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Cut-off wavenumber of Alfvén waves in partially ionized plasmas of the solar atmosphere
Astronomy & Astrophysics, 2012
Context. Alfvén wave dynamics in partially ionized plasmas of the solar atmosphere shows that there is indeed a cutoff wavenumber, i.e. the Alfvén waves with wavenumbers higher than the cutoff value are evanescent. The cutoff wavenumber appears in single-fluid magnetohydrodynamic (MHD) approximation but it is absent in a multi-fluid approach. Up to now, an explanation for the existence of the cutoff wavenumber is still missing. Aims. The aim of this paper is to point out the reason for the appearance of a cutoff wavenumber in single-fluid MHD. Methods. Beginning with three-fluid equations (with electrons, protons and neutral hydrogen atoms), we performed consecutive approximations until we obtained the usual single-fluid description is obtained. We solved the dispersion relation of linear Alfvén waves at each step and sought the approximation responsible of the cutoff wavenumber appearance. Results. We have found that neglecting inertial terms significantly reduces the real part of the Alfvén frequency although it never becomes zero. Therefore, the cutoff wavenumber does not exist at this stage. However, when the inertial terms together with the Hall term in the induction equation are neglected, the real part of the Alfvén frequency becomes zero. Conclusions. The appearance of a cutoff wavenumber, when Alfvén waves in partially ionized regions of the solar atmosphere are studied, is the result of neglecting inertial and Hall terms, therefore it has no physical origin.
Energy flux of Alfvén waves in weakly ionized plasma
Astronomy and Astrophysics, 2008
The overshooting convective motions in the solar photosphere are frequently proposed as the source for the excitation of Alfvén waves. However, the photosphere is a) very weakly ionized, and, b) the dynamics of the plasma particles in this region is heavily influenced by the plasma-neutral collisions. The purpose of this work is to check the consequences of these two facts on the above scenario and their effects on the electromagnetic waves. It is shown that the ions and electrons in the photosphere are both un-magnetized; their collision frequency with neutrals is much larger than the gyrofrequency. This implies that eventual Alfvén-type electromagnetic perturbations must involve the neutrals as well. This has the following serious consequences: i) in the presence of perturbations, the whole fluid (plasma + neutrals) moves; ii) the Alfvén velocity includes the total (plasma + neutrals) density and is thus considerably smaller compared to the collision-less case; iii) the perturbed velocity of a unit volume, which now includes both plasma and neutrals, becomes much smaller compared to the ideal (collision-less) case; and iv) the corresponding wave energy flux for the given parameters becomes much smaller compared to the ideal case.
Alfvén Waves in a Partially Ionized Two-Fluid Plasma
The Astrophysical Journal, 2013
Alfvén waves are a particular class of magnetohydrodynamic waves relevant in many astrophysical and laboratory plasmas. In partially ionized plasmas the dynamics of Alfvén waves is affected by the interaction between ionized and neutral species. Here we study Alfvén waves in a partially ionized plasma from the theoretical point of view using the two-fluid description. We consider that the plasma is composed of an ion-electron fluid and a neutral fluid, which interact by means of particle collisions. To keep our investigation as general as possible we take the neutral-ion collision frequency and the ionization degree as free parameters. First, we perform a normal mode analysis. We find the modification due to neutral-ion collisions of the wave frequencies and study the temporal and spatial attenuation of the waves. In addition, we discuss the presence of cutoff values of the wavelength that constrain the existence of oscillatory standing waves in weakly ionized plasmas. Later, we go beyond the normal mode approach and solve the initial-value problem in order to study the time-dependent evolution of the wave perturbations in the two fluids. An application to Alfvén waves in the low solar atmospheric plasma is performed and the implication of partial ionization for the energy flux is discussed.
Astronomy & Astrophysics, 2011
Context. Chromospheric and prominence plasmas contain neutral atoms, which may change the plasma dynamics through collision with ions. Most of the atoms are neutral hydrogen, but a significant amount of neutral helium may also be present in the plasma with a particular temperature. Damping of MHD waves due to ion collision with neutral hydrogen is well studied, but the effects of neutral helium are largely unknown. Aims. We aim to study the effect of neutral helium in the damping of Alfvén waves in solar partially ionized plasmas. Methods. We consider three-fluid magnetohydrodynamic (MHD) approximation, where one component is electron-proton-singly ionized helium and other two components are the neutral hydrogen and neutral helium atoms. We derive the dispersion relation of linear Alfvén waves in isothermal and homogeneous plasma. Then we solve the dispersion relation and derive the damping rates of Alfvén waves for different plasma parameters. Results. The presence of neutral helium significantly enhances the damping of Alfvén waves compared to the damping due to neutral hydrogen at certain values of plasma temperature (10000 − 40000 K) and ionization. Damping rates have a peak near the ion-neutral collision frequency, but decrease for the higher part of wave spectrum. Conclusions. Collision of ions with neutral helium atoms can be of importance for the damping of Alfvén waves in chromospheric spicules and in prominence-corona transition regions.
Magnetohydrodynamic waves in solar partially ionized plasmas: two-fluid approach
Astronomy & Astrophysics, 2011
Context. Partially ionized plasma is usually described by single-fluid approach, where the ion-neutral collision effects are expressed by Cowling conductivity in the induction equation. However, the single-fluid approach is not valid for the timescales less than ionneutral collision time. For these timescales the two-fluid description is better approximation. Aims. To derive the dynamics of magnetohydrodynamic waves in two-fluid partially ionized plasmas and to compare the results with those obtained under single-fluid description. Methods. Two-fluid magnetohydrodynamic equations are used, where ion-electron plasma and neutral particles are considered as separate fluids. Dispersion relations of linear magnetohydrodynamic waves are derived for simplest case of homogeneous medium. Frequencies and damping rates of waves are obtained for different parameters of background plasma. Results. We found that two-and single-fluid descriptions give similar results for low frequency waves. However, the dynamics of MHD waves in two-fluid approach is significantly changed when the wave frequency becomes comparable or higher than ion-neutral collision frequency. Alfvén and fast magneto-acoustic waves attain their maximum damping rate at particular frequencies (for example, the peak frequency equals 2.5 ion-neutral collision frequency for 50 % of neutral Hydrogen) in wave spectrum. The damping rates are reduced for higher frequency waves. The new mode of slow magneto-acoustic wave appears for higher frequency branch, which is connected to neutral hydrogen fluid. Conclusions. The single-fluid approach perfectly deals with slow processes in partially ionized plasmas, but fails for timescales smaller than ion-neutral collision time. Therefore, two-fluid approximation should be used for the description of relatively fast processes. Some results of single-fluid description, for example the damping of high-frequency Alfvén waves in the solar chromosphere due to ion-neutral collisions, should be revised in future.
Heating of ions by low-frequency Alfvén waves in partially ionized plasmas
Physics of Plasmas, 2011
In the solar atmosphere, the chromospheric and coronal plasmas are much hotter than the visible photosphere. The heating of the solar atmosphere, including the partially ionized chromosphere and corona, remains largely unknown. In this letter, we demonstrate that the ions can be substantially heated by Alfvén waves with very low frequencies in partially ionized low-beta plasmas. This differs from other Alfvén wave related heating mechanisms such as ion-neutral collisional damping of Alfvén waves and heating described by previous work on resonant Alfvén wave heating. We find that the nonresonant Alfvén wave heating is less efficient in partially ionized plasmas than when there are no ion-neutral collisions, and the heating efficiency depends on the ratio of the ion-neutral collision frequency to the ion gyrofrequency.
Astronomy & Astrophysics, 2013
Context. Ion-neutral collisions may lead to the damping of Alfvén waves in chromospheric and prominence plasmas. Neutral helium atoms enhance the damping in certain temperature interval, where the ratio of neutral helium and neutral hydrogen atoms is increased. Therefore, the height-dependence of ionization degrees of hydrogen and helium may influence the damping rate of Alfvén waves. Aims. We aim to study the effect of neutral helium in the damping of Alfvén waves in stratified partially ionized plasma of the solar chromosphere. Methods. We consider a magnetic flux tube, which is expanded up to 1000 km height and then becomes vertical due to merging with neighboring tubes, and study the dynamics of linear torsional Alfvén waves in the presence of neutral hydrogen and neutral helium atoms. We start with three-fluid description of plasma and consequently derive single-fluid magnetohydrodynamic (MHD) equations for torsional Alfvén waves. Thin flux tube approximation allows to obtain the dispersion relation of the waves in the lower part of tubes, while the spatial dependence of steady-state Alfvén waves is governed by Bessel type equation in the upper part of tubes. Results. Consecutive derivation of single-fluid MHD equations results in a new Cowling diffusion coefficient in the presence of neutral helium which is different from previously used one. We found that shorter-period (< 5 s) torsional Alfvén waves damp quickly in the chromospheric network due to ion-neutral collision. On the other hand, longer-period (> 5 s) waves do not reach the transition region as they become evanescent at lower heights in the network cores. Conclusions. Propagation of torsional Alfvén waves through the chromosphere into the solar corona should be considered with caution: low-frequency waves are evanescent due to the stratification, while high-frequency waves are damped due to ion neutral collisions.
Flux of Alfven Waves in the Solar Photosphere
2008
Context. The overshooting convective motions in the solar photosphere, resulting in the foot point motion of different magnetic structures in the solar atmosphere, are frequently proposed as the source for the excitation of Alfvén waves, which are assumed to propagate towards the chromosphere and corona resulting finally in the heating of these layers by the dissipation of this wave energy. However, the photosphere is a) very weakly ionized, and, b) the dynamics of the plasma particles in this region is heavily influenced by the plasma-neutral collisions.
Ion acceleration in plasmas with Alfvén waves
Physics of Plasmas, 2005
Effects of elliptically polarized Alfvén waves on thermal ions are investigated. Both regular oscillations and stochastic motion of the particles are observed. It is found that during regular oscillations the energy of the thermal ions can reach magnitudes well exceeding the plasma temperature, the effect being largest in low-β plasmas (β is the ratio of the plasma pressure to the magnetic field pressure). Conditions of a low stochasticity threshold are obtained. It is shown that stochasticity can arise even for waves propagating along the magnetic field provided that the frequency spectrum is non-monochromatic. The analysis carried out is based on equations derived by using a Lagrangian formalism. A code solving these equations is developed. Steady-state perturbations and perturbations with the amplitude slowly varying in time are considered.
Problem of Alfvén waves in solar photosphere
2007
The convective motion in the weakly ionized solar photosphere, where only a tiny fraction of the gas is ionized, covers the complete solar surface. The purpose of this work is to check if this motion can be a source for the excitation of electromagnetic Alfvén-type waves. Using the standard plasma theory, the magnetization and collision frequencies of the plasma components are examined. Based on these results, an analysis of small electromagnetic perturbations in the photospheric plasma is performed. It is shown that the convective neutral motion in the lower photosphere can efficiently carry the plasma species along. However, the ions in this region appear to be completely un-magnetized and thus they can not support Alfvén-type electromagnetic perturbations. The collisions remain so frequent that the Alfvén waves are strongly damped.