Damping of Alfvén waves in solar partially ionized plasmas: effect of neutral helium in multi-fluid approach (original) (raw)
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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.
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.
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.
Collisional and viscous damping of MHD waves in partially ionized plasmas of the solar atmosphere
Astronomy and Astrophysics, 2004
Magnetohydrodynamic (MHD) waves are widely considered as a possible source of heating for various parts of the outer solar atmosphere. Among the main energy dissipation mechanisms which convert the energy of damped MHD waves into thermal energy are collisional dissipation (resistivity) and viscosity. The presence of neutral atoms in the partially ionized plasmas of the solar photosphere, chromosphere and prominences enhances the efficiency of both these energy dissipation mechanisms. A comparative study of the efficiency of MHD wave damping in solar plasmas due to collisional and viscous energy dissipation mechanisms is presented here. The damping rates are taken from Braginskii 1965 and applied to the VAL C model of the quiet Sun (Vernazza et al. 1981). These estimations show which of the mechanisms are dominant in which regions. In general the correct description of MHD wave damping requires the consideration of all energy dissipation mechanisms via the inclusion of the appropriate terms in the generalized Ohm's law, the momentum, energy and induction equations. Specific forms of the generalized Ohm's Law and induction equation are presented that are suitable for regions of the solar atmosphere which are partially ionised.
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.
A comparative study of the e-ciency of MHD wave damping in solar plasmas due to collisional and viscous energy dissipation mechanisms is presented here. The damping rates are taken from Braginskii (1965) and applied to the VAL C model of the quiet Sun (Vernazza et al., 1981). Performed estimations allow to conclude which damping mechanism is dominant in which regions. In general the correct description of MHD wave damping requires the consideration of all energy dissipation mechanisms via the inclusion of the appropriate terms in the generalized Ohm's law, the momentum, energy and induction equations. Speciflc forms of the generalized Ohm's Law and induction equation are presented that are suitable for partially ionized regions of the solar atmosphere. Magnetohydrodynamic (MHD) waves are widely considered as a possible source of heating for various parts of the outer solar atmosphere. The heating efiect of MHD waves is connected with a certain dissipation mechanism which c...
On the mechanisms of MHD wave damping in the partially ionized solar plasmas
Advances in Space Research, 2006
In order to conclude about the role of collisional friction, viscous and thermal conductivity mechanisms of MHD wave damping in the solar partially ionized plasmas, a quantitative comparative study of efficiency of all these mechanisms in different parts of the solar atmosphere is performed. All the important solar MHD modes are considered: Alfvén wave, fast magnetoacoustic wave and slow magnetoacoustic/acoustic wave. In general, the correct description of MHD wave damping requires the consideration of all energy dissipation mechanisms via the inclusion of the appropriate terms in the generalized OhmÕs law, the momentum, energy and induction equations. Specific forms of the generalized OhmÕs law and induction equation, suitable for partially ionized regions of the solar atmosphere, are presented and discussed.
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.
Damping of oscillations by ion-neutral collisions in a prominence plasma
Astronomy and Astrophysics, 2007
Aims. The role of collisions between ions, electrons and neutrals in a partially ionised plasma is assessed as a possible wave damping mechanism. The relevance of this mechanism in the damping of small amplitude prominence oscillations is evaluated. Methods. A one-fluid MHD set of equations taking into account various effects in a partially ionised solar plasma (collisions between different species and Joule dissipation) is derived. Assuming small perturbations, these equations are next linearised about a uniform equilibrium configuration and the dispersion relation of magnetoacoustic waves in an unbounded medium is obtained. Results. The presence of neutrals in the plasma only affects the fast wave in a relevant way. An approximate expression for the damping rate is obtained which shows that the strongest damping takes place in a medium with strong magnetic field, low density and low ionisation fraction. Wave attenuation arises mostly from collisions between ions and neutrals. Conclusions. Given the poor knowledge about the values of the density and ionisation fraction in prominences, it is hard to judge the importance of the physics of partial ionisation in the damping of fast waves in solar prominences. Nevertheless, note that a very idealised case, with no stratification and no equilibrium currents, is considered here, so the addition of these features to the model may change the results of this work.
Collisional dissipation of Alfvén waves in a partially ionised solar chromosphere
Astronomy and Astrophysics, 2005
Certain regions of the solar atmosphere are at sufficiently low temperatures to be only partially ionised. The lower chromosphere contains neutral atoms, the existence of which greatly increases the efficiency of the damping of waves due to collisional friction momentum transfer. More specifically the Cowling conductivity can be up to 12 orders of magnitude smaller than the Spitzer value, so that the main damping mechanism in this region is due to the collisions between neutrals and positive ions (Khodachenko et al. 2004, A&A, 422, 1073). Using values for the gas density and temperature as functions of height taken from the VAL C model of the quiet Sun (Vernazza et al. 1981, ApJS, 45, 635), an estimate is made for the dependance of the Cowling conductivity on height and strength of magnetic field. Using both analytic and numerical approaches the passage of Alfvén waves over a wide spectrum through this partially ionised region is investigated. Estimates of the efficiency of this region in the damping of Alfvén waves are made and compared for both approaches. We find that Alfvén waves with frequencies above 0.6 Hz are completely damped and frequencies below 0.01 Hz unaffected.