Resonant Alfvén waves in partially ionized plasmas of the solar atmosphere (original) (raw)
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Observational Evidence of Resonantly Damped Propagating Kink Waves in the Solar Corona
The Astrophysical Journal, 2010
In this Letter we establish clear evidence for the resonant absorption damping mechanism by analyzing observational data from the novel Coronal Multi-Channel Polarimeter (CoMP). This instrument has established that in the solar corona there are ubiquitous propagating low amplitude (≈1 km s −1 ) Alfvénic waves with a wide range of frequencies. Realistically interpreting these waves as the kink mode from magnetohydrodynamic (MHD) wave theory, they should exhibit a frequency dependent damping length due to resonant absorption, governed by the TGV relation showing that transversal plasma inhomogeneity in coronal magnetic flux tubes causes them to act as natural low-pass filters. It is found that observed frequency dependence on damping length (up to about 8 mHz) can be explained by the kink wave interpretation and furthermore, the spatially averaged equilibrium parameter describing the length scale of transverse plasma density inhomogeneity over a system of coronal loops is consistent with the range of values estimated from TRACE observations of standing kink modes.
The Transverse and Rotational Motions of Magnetohydrodynamic Kink Waves in the Solar Atmosphere
The Astrophysical Journal, 2014
Magnetohydrodynamic (MHD) kink waves have now been observed to be ubiquitous throughout the solar atmosphere. With modern high spatial/temporal resolution instruments they have now been detected in the chromosphere, interface region and corona. The key purpose of this paper is to show that kink waves do not only involve purely transverse motions of solar magnetic flux tubes, but the velocity field is a spatially and temporally varying sum of both transverse and rotational motion. Taking this fact into account is particularly important for the accurate interpretation of varying Doppler velocity profiles across oscillating structures such as spicules. It has now been shown, that as well as bulk transverse motions, spicules have omnipresent rotational motions. Here we emphasise that caution should be used before interpreting the particular MHD wave mode/s responsible for these rotational motions. The rotational motions are not necessarily signatures of the classic axisymmetric torsional Alfvén wave alone, because kink motion itself can also contribute substantially to varying Doppler velocity profiles observed across these structures. In this paper the displacement field of the kink wave is demonstrated to be a sum of its transverse and rotational components, both for a flux tube with a discontinuous density profile at its boundary and one with a more realistic density continuum between the internal and external plasma. Furthermore the Doppler velocity profile of the kink wave is forward modeled to demonstrate, that depending on the line-of-sight, it can either be quite distinct or very similar to that expected from a torsional Alfvén wave.
Clack Thesis: Nonlinear Resonant MHD Waves in Solar Plasmas
In solar physics many questions remain unanswered, such as the solar coronal heating problem in the solar atmosphere or magnetic field generation in the solar interior. However, there is a growing consensus that many different physical phenomena will combine to give a solution to these problems. From the solar coronal heating point of view, one possible phenomenon to study is resonant absorption, which allows the natural transfer of wave energy to and from the background plasma. If the plasma is dissipative this energy can be converted into heat. One of the stumbling blocks when studying resonant absorption is that linear theory can breakdown around the resonant point. This causes a dilemma: use linear theory as an approximation regardless to try and find sensible solutions or try and solve the difficult, but realistic, nonlinear equations. The present thesis will investigate the nonlinearity associated with resonant absorption. There are two different resonances in solar plasmas, one is the Alfve ́n resonance and the other is the slow resonance. Previous studies, in nonlinear theory, have concentrated mainly on the slow resonances as they are more affected by nonlinearity. We will study both the Alfve ́n and the slow resonances. The present thesis will analytically investigate these resonances in anisotropic, dispersive and dissipative plasmas - typical conditions of the solar upper atmosphere. The second manifestation of nonlinearity is the generation of a mean shear flow outside the layer enclosing the resonant surface. We will derive the governing equations for this gener- ated flow at the Alfve ́n resonance. These flows (like all flows) are completely determined by the boundary conditions and we produce an example flow. The thesis culminates by studying coupled resonances; when the distance between an Alfve ́n and slow resonance is so small (in comparison to the incoming wave) they act as if they interact with an incoming wave simultaneously. We derive the governing equations for the absorption of fast magnetoacoustic waves at the coupled resonance, and then numerically analyse the coeffi- cient of wave energy absorption to compare with the results found for single resonances. We find that the absorption of fast magnetoacoustic waves is far more efficient under coronal conditions compared with chromospheric conditions despite an increase in absorption due to the coupled resonance.
A Study of Alfvén Wave Propagation and Heating the Chromosphere
The Astrophysical Journal, 2013
Alfvén wave propagation, reflection, and heating of the chromosphere are studied for a one-dimensional solar atmosphere by self-consistently solving plasma, neutral fluid, and Maxwell's equations with incorporation of the Hall effect and strong electron-neutral, electron-ion, and ion-neutral collisions. We have developed a numerical model based on an implicit backward difference formula of second-order accuracy both in time and space to solve stiff governing equations resulting from strong inter-species collisions. A non-reflecting boundary condition is applied to the top boundary so that the wave reflection within the simulation domain can be unambiguously determined. It is shown that due to the density gradient the Alfvén waves are partially reflected throughout the chromosphere and more strongly at higher altitudes with the strongest reflection at the transition region. The waves are damped in the lower chromosphere dominantly through Joule dissipation, producing heating strong enough to balance the radiative loss for the quiet chromosphere without invoking anomalous processes or turbulences. The heating rates are larger for weaker background magnetic fields below ∼500 km with higher-frequency waves subject to heavier damping. There is an upper cutoff frequency, depending on the background magnetic field, above which the waves are completely damped. At the frequencies below which the waves are not strongly damped, the interaction of reflected waves with the upward propagating waves produces power at their double frequencies, which leads to more damping. The wave energy flux transmitted to the corona is one order of magnitude smaller than that of the driving source.
Resonant and phase-mixed magnetohydrodynamic waves in the solar atmosphere
Physics of Plasmas, 2001
The magnetic field in the solar atmosphere is not uniformly distributed but organized in typical configurations: e.g., intense flux tubes in the photosphere, magnetic loops in the corona, plumes in the solar wind. Each of these magnetic configurations can support magnetohydrodynamic ͑MHD͒ waves and observations show that this is indeed the case. The intrinsic inhomogeneity of the magnetic configurations enables local ͑slow and͒ Alfvén waves to exist on individual magnetic surfaces. These local Alfvén waves provide a means for dissipating wave energy which is far more efficient in a weakly dissipative plasma than classical resistive or viscous MHD wave damping in a uniform plasma. This property has inspired a lot of work on the dissipation of driven Alfvén waves and wave heating in the solar atmosphere by resonant absorption and phase mixing. This review concentrates on the interaction between fast magnetosonic waves, local Alfvén waves and quasimodes and discusses recent results on the time evolution of phase mixing of resonant waves driven by footpoint motions.
Selective spatial damping of propagating kink waves due to resonant absorption
Astronomy & Astrophysics, 2010
Context. There is observational evidence of propagating kink waves driven by photospheric motions. These disturbances, interpreted as kink magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the solar corona. Aims. To show that resonant absorption provides a simple explanation to the spatial damping of these waves. Methods. Kink MHD waves are studied using a cylindrical model of solar magnetic flux tubes which includes a non-uniform layer at the tube boundary. Assuming that the frequency is real and the longitudinal wavenumber complex, the damping length and damping per wavelength produced by resonant absorption are analytically calculated in the thin tube (TT) approximation, valid for coronal waves. This assumption is relaxed in the case of chromospheric tube waves and filament thread waves. Results. The damping length of propagating kink waves due resonant absorption is a monotonically decreasing function of frequency. For kink waves with low frequencies the damping length is exactly inversely proportional to frequency and we denote this as the TGV relation. When moving to high frequencies the TGV relation continues to be an exceptionally good approximation of the actual dependency of the damping length on frequency. This dependency means that resonant absorption is selective as it favours low frequency waves and can efficiently remove high frequency waves from a broad band spectrum of kink waves. The efficiency of the damping due to resonant absorption depends on the properties of the equilibrium model, in particular on the width of the non-uniform layer and the steepness of the variation of the local Alfvén speed. Conclusions. Resonant absorption is an effective mechanism for the spatial damping of propagating kink waves. It is selective as the damping length is inversely proportional to frequency so that the damping becomes more severe with increasing frequency. This means that radial inhomogeneity can cause solar waveguides to be a natural low-pass filter for broadband disturbances. Hence kink wave trains travelling along, e.g., coronal loops, will have a greater proportion of the high frequency components dissipated lower down in the atmosphere. This could have important consequences with respect to the spatial distribution of wave heating in the solar atmosphere.
Heating of the Solar Chromosphere and Corona by Alfvén Wave Turbulence
2011
A three-dimensional MHD model for the propagation and dissipation of Alfvén waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100 km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfvén waves using the reduced MHD approximation. The increase of Alfvén speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheric and chromospheric parts of the flux tube. Part of the wave energy is transmitted through the TR and produces turbulence in the corona. We find that the hot coronal loops typically found in active regions can be explained in terms of Alfvén wave turbulence, provided the small-scale footpoint motions have velocities of 1-2 km/s and time scales of 60-200 s. The heating rate per unit volume in the chromosphere is 2 to 3 orders of magnitude larger than that in the corona. We construct a series of models with different values of the model parameters, and find that the coronal heating rate increases with coronal field strength and decreases with loop length. We conclude that coronal loops and the underlying chromosphere may both be heated by Alfvénic turbulence.
Spatial Damping of Propagating Kink Waves Due to Resonant Absorption: Effect of Background Flow
The Astrophysical Journal, 2011
Observations show the ubiquitous presence of propagating magnetohydrodynamic (MHD) kink waves in the solar atmosphere. Waves and flows are often observed simultaneously. Due to plasma inhomogeneity in the perpendicular direction to the magnetic field, kink waves are spatially damped by resonant absorption. The presence of flow may affect the wave spatial damping. Here, we investigate the effect of longitudinal background flow on the propagation and spatial damping of resonant kink waves in transversely nonuniform magnetic flux tubes. We combine approximate analytical theory with numerical investigation. The analytical theory uses the thin tube (TT) and thin boundary (TB) approximations to obtain expressions for the wavelength and the damping length. Numerically, we verify the previously obtained analytical expressions by means of the full solution of the resistive MHD eigenvalue problem beyond the TT and TB approximations. We find that the backward and forward propagating waves have different wavelengths and are damped on length scales that are inversely proportional to the frequency as in the static case. However, the factor of proportionality depends on the characteristics of the flow, so that the damping length differs from its static analogue. For slow, sub-Alfvénic flows the backward propagating wave gets damped on a shorter length scale than in the absence of flow, while for the forward propagating wave the damping length is longer. The different properties of the waves depending on their direction of propagation with respect to the background flow may be detected by the observations and may be relevant for seismological applications.
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.
Propagating Kink Waves in Stratified Magnetic Waveguides of the Solar Corona
It has been shown that resonant absorption is a robust physical mechanism for explaining the observed damping of magnetohydrodynamic kink waves in the solar atmosphere due to naturally occurring plasma inhomogeneity in the direction transverse to the direction of the magnetic field. Theoretical studies of this damping mechanism were greatly inspired by the first observations of post-flare standing kink modes in coronal loops using the Transition Region and Coronal Explorer. More recently, these studies have been extended to explain the attenuation of propagating coronal kink waves observed by the Coronal Multi-Channel Polarimeter. In the present study, for the first time we investigate the properties of propagating kink waves in solar waveguides including the effects of both longitudinal and transverse plasma inhomogeneity. Importantly, it is found that the wavelength is only dependent on the longitudinal stratification and the amplitude is simply a product of the two effects. In light of these results the advancement of solar atmospheric magnetoseismology by exploiting high spatial/temporal resolution observations of propagating kink waves in magnetic waveguides to determine the length scales of the plasma inhomogeneity along and transverse to the direction of the magnetic field is discussed.