Author name code: demoortel ADS astronomy entries on 2022-09-14 author:"De Moortel, Ineke" ------------------------------------------------------------------------ Title: Propagating Alfvén waves in open structures with random structuring Authors: Pascoe, D. J.; De Moortel, I.; Pagano, P.; Howson, T. A. Bibcode: 2022MNRAS.tmp.2248P Altcode: We consider the behaviour of Alfvén waves propagating in a medium with random density perturbations. The imposed density perturbations have a broadband spectrum and their characteristic spatial scale may be defined according to the peak in the spectrum. The interaction of the boundary driven Alfvén waves with the medium generates reflections most efficiently when their wavelength is comparable to the spatial scale of the density perturbations. For our monotonic driver, this leads to the generation of quasi-periodic oscillations. The periods of oscillation of the propagating Alfvén waves is no longer only associated with the driver. Additional periodicities may be associated with one or more characteristic spatial scales in the density profile, or with beating between other spectral components. Multiple wave reflections cause oscillatory power to be retained at low altitudes, increasing opportunities to contribute to heating at those locations. Title: The effects of driving time scales on coronal heating in a stratified atmosphere Authors: Howson, T. A.; De Moortel, I. Bibcode: 2022A&A...661A.144H Altcode: 2022arXiv220412205H
Aims: We investigate the atmospheric response to coronal heating driven by random velocity fields with different characteristic time scales and amplitudes.
Methods: We conducted a series of three-dimensional magnetohydrodynamic simulations of random driving imposed on a gravitationally stratified model of the solar atmosphere. In order to understand differences between alternating current (AC) and direct current (DC) heating, we considered the effects of changing the characteristic time scales of the imposed velocities. We also investigated the effects of the magnitude of the velocity driving.
Results: In all cases, complex foot point motions lead to a proliferation of current sheets and energy dissipation throughout the coronal volume. For a given driving amplitude, DC driving typically leads to a greater rate of energy injection when compared to AC driving. This ultimately leads to the formation of larger currents, increased heating rates, and higher coronal temperatures in DC simulations. There is no difference in the spatial distribution of energy dissipation across simulations; however, energy release events in AC cases tend to be more frequent and last for less time than in DC cases. This results in more asymmetric temperature profiles for field lines heated by AC drivers. Higher velocity driving is associated with larger currents, higher temperatures, and the corona occupying a larger fraction of the simulation volume. In all cases, the majority of heating is associated with small energy release events, which occur much more frequently than larger events.
Conclusions: When combined with observational results that highlight a greater abundance of oscillatory power in lower frequency modes, these findings suggest that energy release in the corona is more likely to be driven by longer time scale motions. In the corona, AC and DC driving occur concurrently and their effects remain difficult to isolate. The distribution of field line temperatures and the asymmetry of temperature profiles may reveal the frequency and longevity of energy release events and therefore the relative importance of AC and DC heating.

Movies are available at https://www.aanda.org Title: Coronal Seismology Using Damping of Propagating Kink Waves Authors: Pascoe, D. J.; Van Doorsselaere, T.; De Moortel, I. Bibcode: 2022ApJ...929..101P Altcode: We consider the use of propagating kink waves, such as those observed by the Coronal Multi-channel Polarimeter, as a diagnostic technique. The transverse structuring of the plasma may be inferred by the frequency-dependent wave damping, which is attributed to resonant absorption. We include the effect of reflection of waves at the loop footpoints, which leads to the asymmetry parameter, describing the ratio of driven wave power at the footpoints becoming weakly constrained. The classical model of resonant absorption based on an exponential damping profile significantly overestimates the damping rate in coronal loops with low density contrast ratios. The use of the exponential profile in an analysis of observations therefore leads to underestimates for the density contrast ratio and associated parameters such as the heating rate following phase mixing. Title: Probing the Physics of the Solar Atmosphere with the Multi-slit Solar Explorer (MUSE). I. Coronal Heating Authors: De Pontieu, Bart; Testa, Paola; Martínez-Sykora, Juan; Antolin, Patrick; Karampelas, Konstantinos; Hansteen, Viggo; Rempel, Matthias; Cheung, Mark C. M.; Reale, Fabio; Danilovic, Sanja; Pagano, Paolo; Polito, Vanessa; De Moortel, Ineke; Nóbrega-Siverio, Daniel; Van Doorsselaere, Tom; Petralia, Antonino; Asgari-Targhi, Mahboubeh; Boerner, Paul; Carlsson, Mats; Chintzoglou, Georgios; Daw, Adrian; DeLuca, Edward; Golub, Leon; Matsumoto, Takuma; Ugarte-Urra, Ignacio; McIntosh, Scott W.; the MUSE Team Bibcode: 2022ApJ...926...52D Altcode: 2021arXiv210615584D The Multi-slit Solar Explorer (MUSE) is a proposed mission composed of a multislit extreme ultraviolet (EUV) spectrograph (in three spectral bands around 171 Å, 284 Å, and 108 Å) and an EUV context imager (in two passbands around 195 Å and 304 Å). MUSE will provide unprecedented spectral and imaging diagnostics of the solar corona at high spatial (≤0.″5) and temporal resolution (down to ~0.5 s for sit-and-stare observations), thanks to its innovative multislit design. By obtaining spectra in four bright EUV lines (Fe IX 171 Å, Fe XV 284 Å, Fe XIX-Fe XXI 108 Å) covering a wide range of transition regions and coronal temperatures along 37 slits simultaneously, MUSE will, for the first time, "freeze" (at a cadence as short as 10 s) with a spectroscopic raster the evolution of the dynamic coronal plasma over a wide range of scales: from the spatial scales on which energy is released (≤0.″5) to the large-scale (~170″ × 170″) atmospheric response. We use numerical modeling to showcase how MUSE will constrain the properties of the solar atmosphere on spatiotemporal scales (≤0.″5, ≤20 s) and the large field of view on which state-of-the-art models of the physical processes that drive coronal heating, flares, and coronal mass ejections (CMEs) make distinguishing and testable predictions. We describe the synergy between MUSE, the single-slit, high-resolution Solar-C EUVST spectrograph, and ground-based observatories (DKIST and others), and the critical role MUSE plays because of the multiscale nature of the physical processes involved. In this first paper, we focus on coronal heating mechanisms. An accompanying paper focuses on flares and CMEs. Title: A Fast and Accurate Method to Capture the Solar Corona/Transition Region Enthalpy Exchange in Multi-dimensional Magnetohydrodynamic Simulations Authors: Johnston, Craig; Hood, Alan; De Moortel, Ineke; Daldorff, Lars Bibcode: 2021AGUFMSH12B..03J Altcode: The brightness of the emission from coronal loops in the solar atmosphere is strongly dependent on the temperature and density of the confined plasma. Following an impulsive release of energy, the coronal plasma undergoes phases of upflow and downflow as it cools, with significant variations in its properties. In particular, the sudden increase in coronal temperature leads to an excess downward heat flux that the transition region (TR) is unable to radiate. This generates an upflow of mass and enthalpy from the TR to the corona, increasing the coronal density. The mass and enthalpy exchange is highly sensitive to the TR resolution in numerical simulations. With a numerically under-resolved TR, major errors occur in simulating the coronal density evolution and, thus, the predicted loop emission. We present a new method that addresses the difficulty of obtaining the correct interaction between the corona and corona/chromosphere interface. In the TR, an Adaptive Conduction method is used that artificially broadens any unresolved parts of the atmosphere, allowing them to be resolved while maintaining the correct physics. I will show that this approach, referred to as TRAC, successfully removes the influence of numerical resolution on the coronal density response to heating while maintaining high levels of agreement with fully resolved models. A detailed analytical assessment of the TRAC method will also be presented to demonstrate why the approach works through all phases of an impulsive heating event. Title: Investigating coronal wave energy estimates using synthetic non-thermal line widths Authors: Fyfe, L. E.; Howson, T. A.; De Moortel, I.; Pant, V.; Van Doorsselaere, T. Bibcode: 2021A&A...656A..56F Altcode: 2021arXiv211000257F
Aims: Estimates of coronal wave energy remain uncertain as a large fraction of the energy is likely hidden in the non-thermal line widths of emission lines. In order to estimate these wave energies, many previous studies have considered the root mean squared wave amplitudes to be a factor of \sqrt{2} greater than the non-thermal line widths. However, other studies have used different factors. To investigate this problem, we consider the relation between wave amplitudes and the non-thermal line widths within a variety of 3D magnetohydrodynamic (MHD) simulations.
Methods: We consider the following 3D numerical models: Alfvén waves in a uniform magnetic field, transverse waves in a complex braided magnetic field, and two simulations of coronal heating in an arcade. We applied the forward modelling code FoMo to generate the synthetic emission data required to analyse the non-thermal line widths.
Results: Determining a single value for the ratio between the non-thermal line widths and the root mean squared wave amplitudes is not possible across multiple simulations. It was found to depend on a variety of factors, including line-of-sight angles, velocity magnitudes, wave interference, and exposure time. Indeed, some of our models achieved the values claimed in recent articles while other more complex models deviated from these ratios.
Conclusions: To estimate wave energies, an appropriate relation between the non-thermal line widths and root mean squared wave amplitudes is required. However, evaluating this ratio to be a singular value, or even providing a lower or upper bound on it, is not realistically possible given its sensitivity to various MHD models and factors. As the ratio between wave amplitudes and non-thermal line widths is not constant across our models, we suggest that this widely used method for estimating wave energy is not robust. Title: Magnetic reconnection and the Kelvin-Helmholtz instability in the solar corona Authors: Howson, T. A.; De Moortel, I.; Pontin, D. I. Bibcode: 2021A&A...656A.112H Altcode: 2021arXiv210915019H Context. The magnetic Kelvin-Helmholtz instability (KHI) has been proposed as a means of generating magnetohydrodynamic turbulence and encouraging wave energy dissipation in the solar corona, particularly within transversely oscillating loops.
Aims: Our goal is to determine whether the KHI encourages magnetic reconnection in oscillating flux tubes in the solar corona. This will establish whether the instability enhances the dissipation rate of energy stored in the magnetic field.
Methods: We conducted a series of three-dimensional magnetohydrodynamic simulations of the KHI excited by an oscillating velocity shear. We investigated the effects of numerical resolution, field line length, and background currents on the growth rate of the KHI and on the subsequent rate of magnetic reconnection.
Results: The KHI is able to trigger magnetic reconnection in all cases, with the highest rates occurring during the initial growth phase. Reconnection is found to occur preferentially along the boundaries of Kelvin-Helmholtz vortices, where the shear in the velocity and magnetic fields is greatest. The estimated rate of reconnection is found to be lowest in simulations where the KHI growth rate is reduced. For example, this is the case for shorter field lines or due to shear in the background field.
Conclusions: In non-ideal regimes, the onset of the instability causes the local reconnection of magnetic field lines and enhances the rate of coronal wave heating. However, we found that if the equilibrium magnetic field is sheared across the Kelvin-Helmholtz mixing layer, the instability does not significantly enhance the rate of reconnection of the background field, despite the free energy associated with the non-potential field. Title: Forward modelling of heating within a coronal arcade Authors: Fyfe, L. E.; Howson, T. A.; De Moortel, I. Bibcode: 2021A&A...656A.120F Altcode: 2021arXiv211014257F
Aims: We investigate the synthetic observational signatures generated from numerical models of coronal heating in an arcade in order to determine what features are associated with such heating and what tools can be used to identify them.
Methods: We consider two simulations of coronal arcades driven by footpoint motions with different characteristic timescales. Forward modelling is then conducted, and the synthetic emission data are analysed (e.g., intensities, Doppler shifts, line widths and estimated kinetic energies).
Results: The total intensity and Doppler shift perturbations clearly show the magnetic structure of the coronal arcade. Contrasts in the local Doppler velocity also highlight the locations of separatrix surfaces. The distinguishing feature of the models with short and long timescale photospheric motions (in comparison to the Alfvén travel time along a loop) is that of the frequencies. Through fast Fourier transform analysis of the Doppler velocities, it is clear that when short timescale footpoint motions are present, higher frequency perturbations are observed. For longer timescale footpoint motions, the dominant signal is that of lower frequencies; however, higher (but less powerful) frequencies were also detected, which matched the natural Alfvén frequency of the background magnetic field. Signatures of Alfvénic waves were identified in both models, with fast wave signatures observable when short timescale driving is present. Finally, we examine the estimates of the kinetic energy using the Doppler velocities and find it to be significantly underestimated within these models.
Conclusions: All of the observables within this article behave as one would expect, given the evolution of the plasma parameters. Such features were, for example, Alfvén waves, fast waves, the arcade structure and separatrix surfaces. We were able to differentiate between the two models by examining the frequencies present. The Doppler velocities cannot provide accurate estimates of the total kinetic energy or even the component parallel to the line-of-sight (LOS). This is due to some of the plasma being outside the formation temperature of the ion, the multi-directional driver limiting the proportion of the velocity aligned along the LOS, and cancellation of the velocity along the LOS. The exact impact each factor has on the estimation is dependent on the setup of the model and the emission line under investigation. Title: Magnetohydrodynamic Waves in Open Coronal Structures Authors: Banerjee, D.; Krishna Prasad, S.; Pant, V.; McLaughlin, J. A.; Antolin, P.; Magyar, N.; Ofman, L.; Tian, H.; Van Doorsselaere, T.; De Moortel, I.; Wang, T. J. Bibcode: 2021SSRv..217...76B Altcode: 2020arXiv201208802B Modern observatories have revealed the ubiquitous presence of magnetohydrodynamic waves in the solar corona. The propagating waves (in contrast to the standing waves) are usually originated in the lower solar atmosphere which makes them particularly relevant to coronal heating. Furthermore, open coronal structures are believed to be the source regions of solar wind, therefore, the detection of MHD waves in these structures is also pertinent to the acceleration of solar wind. Besides, the advanced capabilities of the current generation telescopes have allowed us to extract important coronal properties through MHD seismology. The recent progress made in the detection, origin, and damping of both propagating slow magnetoacoustic waves and kink (Alfvénic) waves is presented in this review article especially in the context of open coronal structures. Where appropriate, we give an overview on associated theoretical modelling studies. A few of the important seismological applications of these waves are discussed. The possible role of Alfvénic waves in the acceleration of solar wind is also touched upon. Title: A fast multi-dimensional magnetohydrodynamic formulation of the transition region adaptive conduction (TRAC) method Authors: Johnston, C. D.; Hood, A. W.; De Moortel, I.; Pagano, P.; Howson, T. A. Bibcode: 2021A&A...654A...2J Altcode: 2021arXiv210603989J We have demonstrated that the transition region adaptive conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, successfully removing the influence of numerical resolution on the coronal density response to impulsive heating. This is achieved by adjusting the parallel thermal conductivity, radiative loss, and heating rates to broaden the transition region (TR), below a global cutoff temperature, so that the steep gradients are spatially resolved even when using coarse numerical grids. Implementing the original 1D formulation of TRAC in multi-dimensional magnetohydrodynamic (MHD) models would require tracing a large number of magnetic field lines at every time step in order to prescribe a global cutoff temperature to each field line. In this paper, we present a highly efficient formulation of the TRAC method for use in multi-dimensional MHD simulations, which does not rely on field line tracing. In the TR, adaptive local cutoff temperatures are used instead of global cutoff temperatures to broaden any unresolved parts of the atmosphere. These local cutoff temperatures are calculated using only local grid cell quantities, enabling the MHD extension of TRAC to efficiently account for the magnetic field evolution, without tracing field lines. Consistent with analytical predictions, we show that this approach successfully preserves the properties of the original TRAC method. In particular, the total radiative losses and heating remain conserved under the MHD formulation. Results from 2D MHD simulations of impulsive heating in unsheared and sheared arcades of coronal loops are also presented. These simulations benchmark the MHD TRAC method against a series of 1D models and demonstrate the versatility and robustness of the method in multi-dimensional magnetic fields. We show, for the first time, that pressure differences, generated during the evaporation phase of impulsive heating events, can produce current layers that are significantly narrower than the transverse energy deposition.

Movies associated to Figs. 4 and 8 are available at https://www.aanda.org Title: The Heating of the Solar Corona Authors: Viall, Nicholeen M.; De Moortel, Ineke; Downs, Cooper; Klimchuk, James A.; Parenti, Susanna; Reale, Fabio Bibcode: 2021GMS...258...35V Altcode: No abstract at ADS Title: Coronal Heating by MHD Waves Authors: Van Doorsselaere, Tom; Srivastava, Abhishek K.; Antolin, Patrick; Magyar, Norbert; Vasheghani Farahani, Soheil; Tian, Hui; Kolotkov, Dmitrii; Ofman, Leon; Guo, Mingzhe; Arregui, Iñigo; De Moortel, Ineke; Pascoe, David Bibcode: 2020SSRv..216..140V Altcode: 2020arXiv201201371V The heating of the solar chromosphere and corona to the observed high temperatures, imply the presence of ongoing heating that balances the strong radiative and thermal conduction losses expected in the solar atmosphere. It has been theorized for decades that the required heating mechanisms of the chromospheric and coronal parts of the active regions, quiet-Sun, and coronal holes are associated with the solar magnetic fields. However, the exact physical process that transport and dissipate the magnetic energy which ultimately leads to the solar plasma heating are not yet fully understood. The current understanding of coronal heating relies on two main mechanism: reconnection and MHD waves that may have various degrees of importance in different coronal regions. In this review we focus on recent advances in our understanding of MHD wave heating mechanisms. First, we focus on giving an overview of observational results, where we show that different wave modes have been discovered in the corona in the last decade, many of which are associated with a significant energy flux, either generated in situ or pumped from the lower solar atmosphere. Afterwards, we summarise the recent findings of numerical modelling of waves, motivated by the observational results. Despite the advances, only 3D MHD models with Alfvén wave heating in an unstructured corona can explain the observed coronal temperatures compatible with the quiet Sun, while 3D MHD wave heating models including cross-field density structuring are not yet able to account for the heating of coronal loops in active regions to their observed temperature. Title: Effect of coronal loop structure on wave heating through phase mixing Authors: Pagano, P.; De Moortel, I.; Morton, R. J. Bibcode: 2020A&A...643A..73P Altcode: 2020arXiv200904366P Context. The mechanism(s) behind coronal heating still elude(s) direct observation and modelling of viable theoretical processes and the subsequent effect on coronal structures is one of the key tools available to assess possible heating mechanisms. Wave heating via the phase mixing of magnetohydrodynamic (MHD) transverse waves has been proposed as a possible way to convert magnetic energy into thermal energy, but MHD models increasingly suggest this is not an efficient enough mechanism.
Aims: We modelled heating by phase mixing transverse MHD waves in various configurations in order to investigate whether certain circumstances can enhance the heating sufficiently to sustain the million degree solar corona and to assess the impact of the propagation and phase mixing of transverse MHD waves on the structure of the boundary shell of coronal loops.
Methods: We used 3D MHD simulations of a pre-existing density enhancement in a magnetised medium and a boundary driver to trigger the propagation of transverse waves with the same power spectrum as measured by the Coronal Multi-Channel Polarimeter. We consider different density structures, boundary conditions at the non-drive footpoint, characteristics of the driver, and different forms of magnetic resistivity.
Results: We find that different initial density structures significantly affect the evolution of the boundary shell and that some driver configurations can enhance the heating generated from the dissipation of the MHD waves. In particular, drivers coherent on a larger spatial scale and higher dissipation coefficients can generate significant heating, although it is still insufficient to balance the radiative losses in this setup.
Conclusions: We conclude that while phase mixing of transverse MHD waves is unlikely to sustain the thermal structure of the corona, there are configurations that allow for an enhanced efficiency of this mechanism. We provide possible signatures to identify the presence of such configurations, such as the location of where the heating is deposited along the coronal loop.

Movies associated to Figs. 4 and 8 are available at https://www.aanda.org Title: Forward modelling of MHD waves in braided magnetic fields Authors: Fyfe, L. E.; Howson, T. A.; De Moortel, I. Bibcode: 2020A&A...643A..86F Altcode: 2020arXiv200908301F
Aims: We investigate synthetic observational signatures generated from numerical models of transverse waves propagating in complex (braided) magnetic fields.
Methods: We consider two simulations with different levels of magnetic field braiding and impose periodic, transverse velocity perturbations at the lower boundary. As the waves reflect off the top boundary, a complex pattern of wave interference occurs. We applied the forward modelling code FoMo and analysed the synthetic emission data. We examined the line intensity, Doppler shifts, and kinetic energy along several line-of-sight (LOS) angles.
Results: The Doppler shift perturbations clearly show the presence of the transverse (Alfvénic) waves. However, in the total intensity, and running difference, the waves are less easily observed for more complex magnetic fields and may be indistinguishable from background noise. Depending on the LOS angle, the observable signatures of the waves reflect some of the magnetic field braiding, particularly when multiple emission lines are available, although it is not possible to deduce the actual level of complexity. In the more braided simulation, signatures of phase mixing can be identified. We highlight possible ambiguities in the interpretation of the wave modes based on the synthetic emission signatures.
Conclusions: Most of the observables discussed in this article behave in the manner expected, given knowledge of the evolution of the parameters in the 3D simulations. Nevertheless, some intriguing observational signatures are present. Identifying regions of magnetic field complexity is somewhat possible when waves are present; although, even then, simultaneous spectroscopic imaging from different lines is important in order to identify these locations. Care needs to be taken when interpreting intensity and Doppler velocity signatures as torsional motions, as is done in our setup. These types of signatures are a consequence of the complex nature of the magnetic field, rather than real torsional waves. Finally, we investigate the kinetic energy, which was estimated from the Doppler velocities and is highly dependent on the polarisation of the wave, the complexity of the background field, and the LOS angles. Title: The effects of driving time scales on heating in a coronal arcade Authors: Howson, T. A.; De Moortel, I.; Fyfe, L. E. Bibcode: 2020A&A...643A..85H Altcode: 2020arXiv200907535H Context. The relative importance of alternating current (AC) and direct current (DC) heating mechanisms in maintaining the temperature of the solar corona is not well constrained.
Aims: We aim to investigate the effects of the characteristic time scales of photospheric driving on the injection and dissipation of magnetic and kinetic energy within a coronal arcade.
Methods: We conducted three-dimensional magnetohydrodynamic simulations of complex foot point driving imposed on a potential coronal arcade. We modified the typical time scales associated with the velocity driver to understand the efficiency of heating obtained using AC and DC drivers. We considered the implications for the injected Poynting flux and the spatial and temporal nature of the energy release in dissipative regimes.
Results: For the same driver amplitude and complexity, long time scale velocity motions are able to inject a much greater Poynting flux of energy into the corona. Consequently, in non-ideal regimes, slow stressing motions result in a greater increase in plasma temperature than for wave-like driving. In dissipative simulations, Ohmic heating is found to be much more significant than viscous heating. For all drivers in our parameter space, energy dissipation is greatest close to the base of the arcade, where the magnetic field strength is strongest, and at separatrix surfaces, where the field connectivity changes. Across all simulations, the background field is stressed with random foot point motions (in a manner more typical of DC heating studies), and, even for short time scale driving, the injected Poynting flux is large given the small amplitude flows considered. For long time scale driving, the rate of energy injection was comparable to the expected requirements in active regions. The heating rates were found to scale with the perturbed magnetic field strength and not the total field strength.
Conclusions: Alongside recent studies that show that power within the corona is dominated by low frequency motions, our results suggest that, in the closed corona, DC heating is more significant than AC heating.

Movies associated to Fig. 3 are available at https://www.aanda.org Title: Alfvén on heating by waves Authors: De Moortel, Ineke; Falconer, Isobel; Stack, Robert Bibcode: 2020A&G....61b2.34D Altcode: Ineke De Moortel, Isobel Falconer and Robert Stack explore the achievements and influence of Hannes Alfvén, in particular his seminal Monthly Notices paper of 1947 on the heating of the solar corona. Title: Phase mixing and wave heating in a complex coronal plasma Authors: Howson, T. A.; De Moortel, I.; Reid, J. Bibcode: 2020A&A...636A..40H Altcode: 2020arXiv200305226H
Aims: We investigate the formation of small scales and the related dissipation of magnetohydronamic (MHD) wave energy through non-linear interactions of counter-propagating, phase-mixed Alfvénic waves in a complex magnetic field.
Methods: We conducted fully three-dimensional, non-ideal MHD simulations of transverse waves in complex magnetic field configurations. Continuous wave drivers were imposed on the foot points of magnetic field lines and the system was evolved for several Alfvén travel times. Phase-mixed waves were allowed to reflect off the upper boundary and the interactions between the resultant counter-streaming wave packets were analysed.
Results: The complex nature of the background magnetic field encourages the development of phase mixing throughout the numerical domain, leading to a growth in alternating currents and vorticities. Counter-propagating phase-mixed MHD wave modes induce a cascade of energy to small scales and result in more efficient wave energy dissipation. This effect is enhanced in simulations with more complex background fields. High-frequency drivers excite localised field line resonances and produce efficient wave heating. However, this relies on the formation of large amplitude oscillations on resonant field lines. Drivers with smaller frequencies than the fundamental frequencies of field lines are not able to excite resonances and thus do not inject sufficient Poynting flux to power coronal heating. Even in the case of high-frequency oscillations, the rate of dissipation is likely too slow to balance coronal energy losses, even within the quiet Sun.
Conclusions: For the case of the generalised phase-mixing presented here, complex background field structures enhance the rate of wave energy dissipation. However, it remains difficult for realistic wave drivers to inject sufficient Poynting flux to heat the corona. Indeed, significant heating only occurs in cases which exhibit oscillation amplitudes that are much larger than those currently observed in the solar atmosphere. Title: Chromospheric evaporation and phase mixing of Alfvén waves in coronal loops Authors: Van Damme, H. J.; De Moortel, I.; Pagano, P.; Johnston, C. D. Bibcode: 2020A&A...635A.174V Altcode: 2020arXiv200211695V Context. Phase mixing of Alfvén waves has been studied extensively as a possible coronal heating mechanism but without the full thermodynamic consequences considered self-consistently. It has been argued that in some cases, the thermodynamic feedback of the heating could substantially affect the transverse density gradient and even inhibit the phase mixing process.
Aims: In this paper, for the first time, we use magnetohydrodynamic (MHD) simulations with the appropriate thermodynamical terms included to quantify the evaporation following heating by phase mixing of Alfvén waves in a coronal loop and the effect of this evaporation on the transverse density profile.
Methods: The numerical simulations were performed using the Lagrangian Remap code Lare2D. We set up a 2D loop model consisting of a field-aligned thermodynamic equilibrium and a cross-field (background) heating profile. A continuous, sinusoidal, high-frequency Alfvén wave driver was implemented. As the Alfvén waves propagate along the field, they undergo phase mixing due to the cross-field density gradient in the coronal part of the loop. We investigated the presence of field-aligned flows, heating from the dissipation of the phase-mixed Alfvén waves, and the subsequent evaporation from the lower atmosphere.
Results: We find that phase mixing of Alfvén waves leads to modest heating in the shell regions of the loop and evaporation of chromospheric material into the corona with upflows of the order of only 5-20 m s-1. Although the evaporation leads to a mass increase in the shell regions of the loop, the effect on the density gradient and, hence, on the phase mixing process, is insignificant.
Conclusions: This paper self-consistently investigates the effect of chromospheric evaporation on the cross-field density gradient and the phase mixing process in a coronal loop. We found that the effects in our particular setup (small amplitude, high frequency waves) are too small to significantly change the density gradient. Title: Modelling the solar transition region using an adaptive conduction method Authors: Johnston, C. D.; Cargill, P. J.; Hood, A. W.; De Moortel, I.; Bradshaw, S. J.; Vaseekar, A. C. Bibcode: 2020A&A...635A.168J Altcode: 2020arXiv200201887J Modelling the solar Transition Region with the use of an Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, capturing the enthalpy exchange between the corona and transition region, when the corona undergoes impulsive heating. The TRAC method eliminates the need for highly resolved numerical grids in the transition region and the commensurate very short time steps that are required for numerical stability. When employed with coarse spatial resolutions, typically achieved in multi-dimensional magnetohydrodynamic codes, the errors at peak density are less than 5% and the computation time is three orders of magnitude faster than fully resolved field-aligned models. This paper presents further examples that demonstrate the versatility and robustness of the method over a range of heating events, including impulsive and quasi-steady footpoint heating. A detailed analytical assessment of the TRAC method is also presented, showing that the approach works through all phases of an impulsive heating event because (i) the total radiative losses and (ii) the total heating when integrated over the transition region are both preserved at all temperatures under the broadening modifications of the method. The results from the numerical simulations complement this conclusion. Title: Resonant absorption in expanding coronal magnetic flux tubes with uniform density Authors: Howson, T. A.; De Moortel, I.; Antolin, P.; Van Doorsselaere, T.; Wright, A. N. Bibcode: 2019A&A...631A.105H Altcode: 2019arXiv190910781H
Aims: We investigate the transfer of energy between a fundamental standing kink mode and azimuthal Alfvén waves within an expanding coronal magnetic flux tube. We consider the process of resonant absorption in a loop with a non-uniform Alfvén frequency profile but in the absence of a radial density gradient.
Methods: Using the three dimensional magnetohydrodynamic (MHD) code, Lare3d, we modelled a transversely oscillating magnetic flux tube that expands radially with height. An initially straight loop structure with a magnetic field enhancement was allowed to relax numerically towards a force-free state before a standing kink mode was introduced. The subsequent dynamics, rate of wave damping and formation of small length scales are considered.
Results: We demonstrate that the transverse gradient in Alfvén frequency required for the existence of resonant field lines can be associated with the expansion of a high field-strength flux tube from concentrated flux patches in the lower solar atmosphere. This allows for the conversion of energy between wave modes even in the absence of the transverse density profile typically assumed in wave heating models. As with standing modes in straight flux tubes, small scales are dominated by the vorticity at the loop apex and by currents close to the loop foot points. The azimuthal Alfvén wave exhibits the structure of the expanded flux tube and is therefore associated with smaller length scales close to the foot points of the flux tube than at the loop apex.
Conclusions: Resonant absorption can proceed throughout the coronal volume, even in the absence of visible, dense, loop structures. The flux tube and MHD waves considered are difficult to observe and our model highlights how estimating hidden wave power within the Sun's atmosphere can be problematic. We highlight that, for standing modes, the global properties of field lines are important for resonant absorption and coronal conditions at a single altitude will not fully determine the nature of MHD resonances. In addition, we provide a new model in partial response to the criticism that wave heating models cannot self-consistently generate or sustain the density profile upon which they typically rely. Title: Magnetohydrodynamic waves in braided magnetic fields Authors: Howson, T. A.; De Moortel, I.; Reid, J.; Hood, A. W. Bibcode: 2019A&A...629A..60H Altcode: 2019arXiv190803089H
Aims: We investigate the propagation of transverse magnetohydrodynamic (MHD) wave fronts through a coronal plasma containing a braided magnetic field.
Methods: We performed a series of three dimensional MHD simulations in which a small amplitude, transverse velocity perturbation is introduced into a complex magnetic field. We analysed the deformation of the wave fronts as the perturbation propagates through the braided magnetic structures and explore the nature of Alfvénic wave phase mixing in this regime. We considered the effects of viscous dissipation in a weakly non-ideal plasma and evaluate the effects of field complexity on wave energy dissipation.
Results: Spatial gradients in the local Alfvén speed and variations in the length of magnetic field lines ensure that small scales form throughout the propagating wave front due to phase mixing. Additionally, the presence of complex, intricate current sheets associated with the background field locally modifies the polarisation of the wave front. The combination of these two effects enhances the rate of viscous dissipation, particularly in more complex field configurations. Unlike in classical phase mixing configurations, the greater spatial extent of Alfvén speed gradients ensures that wave energy is deposited over a larger cross-section of the magnetic structure. Further, the complexity of the background magnetic field ensures that small gradients in a wave driver can map to large gradients within the coronal plasma.
Conclusions: The phase mixing of transverse MHD waves in a complex magnetic field will progress throughout the braided volume. As a result, in a non-ideal regime wave energy will be dissipated over a greater cross-section than in classical phase mixing models. The formation rate of small spatial scales in a propagating wave front is a function of the complexity of the background magnetic field. As such, if the coronal field is sufficiently complex it remains plausible that phase mixing induced wave heating can contribute to maintaining the observed temperatures. Furthermore, the weak compressibility of the transverse wave and the observed phase mixing pattern may provide seismological information about the nature of the background plasma. Title: MHD simulations of the in situ generation of kink and sausage waves in the solar corona by collision of dense plasma clumps Authors: Pagano, P.; Van Damme, H. J.; Antolin, P.; De Moortel, I. Bibcode: 2019A&A...626A..53P Altcode: 2019arXiv190503749P Context. Magnetohydrodynamic (MHD) waves are ubiquitous in the solar corona where the highly structured magnetic fields provide efficient wave guides for their propagation. While MHD waves have been observed originating from lower layers of the solar atmosphere, recent studies have shown that some can be generated in situ by the collision of dense counter-propagating flows.
Aims: In this theoretical study, we analyse the mechanism that triggers the propagation of kink and sausage modes in the solar corona following the collision of counter-propagating flows, and how the properties of the flows affect the properties of the generated waves.
Methods: To study in detail this mechanism we ran a series of ideal 2D and 3D MHD simulations where we varied the properties of the counter-propagating flows; by means of a simple technique to estimate the amplitudes of the kink and sausage modes, we investigated their role in the generation and propagation of the MHD waves.
Results: We find that the amplitude of the waves is largely dependent on the kinetic energy of the flows, and that the onset of kink or sausage modes depends on the asymmetries between the colliding blobs. Moreover, the initial wavelength of the MHD waves is associated with the magnetic configuration resulting from the collision of the flows. We also find that genuine 3D systems respond with smaller wave amplitudes.
Conclusions: In this study, we present a parameter space description of the mechanism that leads to the generation of MHD waves from the collision of flows in the corona. Future observations of these waves can be used to understand the properties of the plasma and magnetic field of the solar corona.

The movies associated to Figs. 2 and 21 are available at https://www.aanda.org Title: The effects of numerical resolution, heating timescales and background heating on thermal non-equilibrium in coronal loops Authors: Johnston, C. D.; Cargill, P. J.; Antolin, P.; Hood, A. W.; De Moortel, I.; Bradshaw, S. J. Bibcode: 2019A&A...625A.149J Altcode: 2019arXiv190407287J Thermal non-equilibrium (TNE) is believed to be a potentially important process in understanding some properties of the magnetically closed solar corona. Through one-dimensional hydrodynamic models, this paper addresses the importance of the numerical spatial resolution, footpoint heating timescales and background heating on TNE. Inadequate transition region (TR) resolution can lead to significant discrepancies in TNE cycle behaviour, with TNE being suppressed in under-resolved loops. A convergence on the periodicity and plasma properties associated with TNE required spatial resolutions of less than 2 km for a loop of length 180 Mm. These numerical problems can be resolved using an approximate method that models the TR as a discontinuity using a jump condition, as proposed by Johnston et al. (2017a, A&A, 597, A81; 2017b, A&A, 605, A8). The resolution requirements (and so computational cost) are greatly reduced while retaining good agreement with fully resolved results. Using this approximate method we (i) identify different regimes for the response of coronal loops to time-dependent footpoint heating including one where TNE does not arise and (ii) demonstrate that TNE in a loop with footpoint heating is suppressed unless the background heating is sufficiently small. The implications for the generality of TNE are discussed. Title: Phase mixing of nonlinear Alfvén waves Authors: Prokopyszyn, A. P. K.; Hood, A. W.; De Moortel, I. Bibcode: 2019A&A...624A..90P Altcode: 2019arXiv190308093P
Aims: This paper presents 2.5D numerical experiments of Alfvén wave phase mixing and aims to assess the effects of nonlinearities on wave behaviour and dissipation. In addition, this paper aims to quantify how effective the model presented in this work is at providing energy to the coronal volume.
Methods: The model is presented and explored through the use of several numerical experiments which were carried out using the Lare2D code. The experiments study footpoint driven Alfvén waves in the neighbourhood of a two-dimensional x-type null point with initially uniform density and plasma pressure. A continuous sinusoidal driver with a constant frequency is used. Each experiment uses different driver amplitudes to compare weakly nonlinear experiments with linear experiments.
Results: We find that the wave trains phase-mix owing to variations in the length of each field line and variations in the field strength. The nonlinearities reduce the amount of energy entering the domain, as they reduce the effectiveness of the driver, but they have relatively little effect on the damping rate (for the range of amplitudes studied). The nonlinearities produce density structures which change the natural frequencies of the field lines and hence cause the resonant locations to move. The shifting of the resonant location causes the Poynting flux associated with the driver to decrease. Reducing the magnetic diffusivity increases the energy build-up on the resonant field lines, however, it has little effect on the total amount of energy entering the system. From an order of magnitude estimate, we show that the Poynting flux in our experiments is comparable to the energy requirements of the quiet Sun corona. However a (possibly unphysically) large amount of magnetic diffusion was used however and it remains unclear if the model is able to provide enough energy under actual coronal conditions. Title: Contribution of observed multi frequency spectrum of Alfvén waves to coronal heating Authors: Pagano, P.; De Moortel, I. Bibcode: 2019A&A...623A..37P Altcode: 2019arXiv190102310P Context. Whilst there are observational indications that transverse magnetohydrodynamic (MHD) waves carry enough energy to maintain the thermal structure of the solar corona, it is not clear whether such energy can be efficiently and effectively converted into heating. Phase-mixing of Alfvén waves is considered a candidate mechanism, as it can develop transverse gradient where magnetic energy can be converted into thermal energy. However, phase-mixing is a process that crucially depends on the amplitude and period of the transverse oscillations, and only recently have we obtained a complete measurement of the power spectrum for transverse oscillations in the corona.
Aims: We aim to investigate the heating generated by phase-mixing of transverse oscillations triggered by buffeting of a coronal loop that follows from the observed coronal power spectrum as well as the impact of these persistent oscillations on the structure of coronal loops.
Methods: We considered a 3D MHD model of an active region coronal loop and we perturbed its footpoints with a 2D horizontal driver that represents a random buffeting motion of the loop footpoints. Our driver was composed of 1000 pulses superimposed to generate the observed power spectrum.
Results: We find that the heating supply from the observed power spectrum in the solar corona through phase-mixing is not sufficient to maintain the million-degree active region solar corona. We also find that the development of Kelvin-Helmholtz instabilities could be a common phenomenon in coronal loops that could affect their apparent life time.
Conclusions: This study concludes that is unlikely that phase-mixing of Alfvén waves resulting from an observed power spectrum of transverse coronal loop oscillations can heat the active region solar corona. However, transverse waves could play an important role in the development of small scale structures.

Movies associated to Figs. 12, 13, 15, 18, and 19 are available at https://www.aanda.org Title: Heating Effects from Driven Transverse and Alfvén Waves in Coronal Loops Authors: Guo, Mingzhe; Van Doorsselaere, Tom; Karampelas, Konstantinos; Li, Bo; Antolin, Patrick; De Moortel, Ineke Bibcode: 2019ApJ...870...55G Altcode: 2018arXiv181107608G Recent numerical studies revealed that transverse motions of coronal loops can induce the Kelvin-Helmholtz instability (KHI). This process could be important in coronal heating because it leads to dissipation of energy at small spatial scale plasma interactions. Meanwhile, small-amplitude decayless oscillations in coronal loops have been discovered recently in observations of SDO/AIA. We model such oscillations in coronal loops and study wave heating effects, considering a kink and Alfvén driver separately and a mixed driver at the bottom of flux tubes. Both the transverse and Alfvén oscillations can lead to the KHI. Meanwhile, the Alfvén oscillations established in loops will experience phase mixing. Both processes will generate small spatial scale structures, which can help the dissipation of wave energy. Indeed, we observe the increase of internal energy and temperature in loop regions. The heating is more pronounced for the simulation containing the mixed kink and Alfvén driver. This means that the mixed wave modes can lead to a more efficient energy dissipation in the turbulent state of the plasma and that the KHI eddies act as an agent to dissipate energy in other wave modes. Furthermore, we also obtained forward-modeling results using the FoMo code. We obtained forward models that are very similar to the observations of decayless oscillations. Due to the limited resolution of instruments, neither Alfvén modes nor the fine structures are observable. Therefore, this numerical study shows that Alfvén modes probably can coexist with kink modes, leading to enhanced heating. Title: Contribution of phase-mixing of Alfvén waves to coronal heating in multi-harmonic loop oscillations Authors: Pagano, P.; Pascoe, D. J.; De Moortel, I. Bibcode: 2018A&A...616A.125P Altcode: 2018arXiv180410562P Context. Kink oscillations of a coronal loop are observed and studied in detail because they provide a unique probe into the structure of coronal loops through magnetohydrodynamics (MHD) seismology and a potential test of coronal heating through the phase mixing of Alfvén waves. In particular, recent observations show that standing oscillations of loops often involve higher harmonics in addition to the fundamental mode. The damping of these kink oscillations is explained by mode coupling with Alfvén waves.
Aims: We investigate the consequences for wave-based coronal heating of higher harmonics and which coronal heating observational signatures we may use to infer the presence of higher harmonic kink oscillations.
Methods: We performed a set of non-ideal MHD simulations in which we modelled the damping of the kink oscillation of a flux tube via mode coupling. We based our MHD simulation parameters on the seismological inversion of an observation for which the first three harmonics are detected. We studied the phase mixing of Alfvén waves, which leads to the deposition of heat in the system, and we applied seismological inversion techniques to the MHD simulation output.
Results: We find that the heating due to phase mixing of Alfvén waves triggered by the damping of kink oscillation is relatively small. We can however illustrate how the heating location drifts from subsequent damping of lower order harmonics. We also address the role of higher order harmonics and the width of the boundary shell in the energy deposition.
Conclusions: We conclude that the coronal heating due to phase mixing does not seem to provide enough energy to maintain the thermal structure of the solar corona even when multi-harmonic oscillations are included; these oscillations play an inhibiting role in the development of smaller scale structures. Title: Reconnection Microjets in the Solar Corona Authors: Antolin, Patrick; Pagano, Paolo; De Moortel, Ineke Bibcode: 2018cosp...42E..96A Altcode: Coronal rain is one of the highest resolution tracers of the coronal magnetic field. In this work the dynamics of a prominence/coronal rain complex are analysed based on spectroscopic and imaging observations with IRIS, Hinode/SOT and SDO/AIA. The loop-like magnetic field arcade hosting the rain is observed to slowly expand in height. Prior and especially during this movement, several ( 100) small ( 1 arcsec) and short (<20 sec) bursts of plasma perpendicular to the loop arcade are captured in the Si IV and Mg II lines. The line profiles are broad and asymmetric with long tails above 100 km/s. These microjets are accompanied with strong intensity enhancements co-spatially and along the loop in most of the AIA channels, indicating significant energy release increasing the temperature to several MK. Some events generate transverse MHD waves and the strongest events are accompanied by ejection of plasmoid-like structures. We interpret these microjets as magnetic reconnection outflows, produced by component reconnection in a strong guide field. The originally cold conditions of the rain allows, in this case, a unique high resolution glance into the reconnection dynamics in low beta plasmas, and marks the X-target in the Sun for next-generation telescopes. Title: In Situ Generation of Transverse Magnetohydrodynamic Waves from Colliding Flows in the Solar Corona Authors: Antolin, Patrick; Pagano, Paolo; De Moortel, Ineke; Nakariakov, Valery M. Bibcode: 2018ApJ...861L..15A Altcode: 2018arXiv180700395A Transverse magnetohydrodynamic (MHD) waves permeate the solar atmosphere and are a candidate for coronal heating. However, the origin of these waves is still unclear. In this Letter, we analyze coordinated observations from Hinode/Solar Optical Telescope (SOT) and Interface Region Imaging Spectrograph ( IRIS) of a prominence/coronal rain loop-like structure at the limb of the Sun. Cool and dense downflows and upflows are observed along the structure. A collision between a downward and an upward flow with an estimated energy flux of 107-108 erg cm-2 s-1 is observed to generate oscillatory transverse perturbations of the strands with an estimated ≈40 km s-1 total amplitude, and a short-lived brightening event with the plasma temperature increasing to at least 105 K. We interpret this response as sausage and kink transverse MHD waves based on 2D MHD simulations of plasma flow collision. The lengths, density, and velocity differences between the colliding clumps and the strength of the magnetic field are major parameters defining the response to the collision. The presence of asymmetry between the clumps (angle of impact surface and/or offset of flowing axis) is crucial for generating a kink mode. Using the observed values, we successfully reproduce the observed transverse perturbations and brightening, and show adiabatic heating to coronal temperatures. The numerical modeling indicates that the plasma β in this loop-like structure is confined between 0.09 and 0.36. These results suggest that such collisions from counter-streaming flows can be a source of in situ transverse MHD waves, and that for cool and dense prominence conditions such waves could have significant amplitudes. Title: Impact of Type II Spicules in the Corona: Simulations and Synthetic Observables Authors: Martínez-Sykora, Juan; De Pontieu, Bart; De Moortel, Ineke; Hansteen, Viggo H.; Carlsson, Mats Bibcode: 2018ApJ...860..116M Altcode: 2018arXiv180506475M The role of type II spicules in the corona has been a much debated topic in recent years. This paper aims to shed light on the impact of type II spicules in the corona using novel 2.5D radiative MHD simulations, including ion-neutral interaction effects with the Bifrost code. We find that the formation of simulated type II spicules, driven by the release of magnetic tension, impacts the corona in various manners. Associated with the formation of spicules, the corona exhibits (1) magneto-acoustic shocks and flows, which supply mass to coronal loops, and (2) transversal magnetic waves and electric currents that propagate at Alfvén speeds. The transversal waves and electric currents, generated by the spicule’s driver and lasting for many minutes, are dissipated and heat the associated loop. These complex interactions in the corona can be connected with blueshifted secondary components in coronal spectral lines (red-blue asymmetries) observed with Hinode/EIS and SOHO/SUMER, as well as the EUV counterpart of type II spicules and propagating coronal disturbances observed with the 171 Å and 193 Å SDO/AIA channels. Title: Transverse Wave Induced Kelvin-Helmholtz Rolls in Spicules Authors: Antolin, P.; Schmit, D.; Pereira, T. M. D.; De Pontieu, B.; De Moortel, I. Bibcode: 2018ApJ...856...44A Altcode: 2018arXiv180300821A In addition to their jet-like dynamic behavior, spicules usually exhibit strong transverse speeds, multi-stranded structure, and heating from chromospheric to transition region temperatures. In this work we first analyze Hinode and IRIS observations of spicules and find different behaviors in terms of their Doppler velocity evolution and collective motion of their sub-structure. Some have a Doppler shift sign change that is rather fixed along the spicule axis, and lack coherence in the oscillatory motion of strand-like structure, matching rotation models, or long-wavelength torsional Alfvén waves. Others exhibit a Doppler shift sign change at maximum displacement and coherent motion of their strands, suggesting a collective magnetohydrodynamic (MHD) wave. By comparing with an idealized 3D MHD simulation combined with radiative transfer modeling, we analyze the role of transverse MHD waves and associated instabilities in spicule-like features. We find that transverse wave induced Kelvin-Helmholtz (TWIKH) rolls lead to coherence of strand-like structure in imaging and spectral maps, as seen in some observations. The rapid transverse dynamics and the density and temperature gradients at the spicule boundary lead to ring-shaped Mg II k and Ca II H source functions in the transverse cross-section, potentially allowing IRIS to capture the Kelvin-Helmholtz instability dynamics. Twists and currents propagate along the spicule at Alfvénic speeds, and the temperature variations within TWIKH rolls, produce the sudden appearance/disappearance of strands seen in Doppler velocity and in Ca II H intensity. However, only a mild intensity increase in higher-temperature lines is obtained, suggesting there is an additional heating mechanism at work in spicules. Title: Observations and Modeling of Transition Region and Coronal Heating Associated with Spicules Authors: De Pontieu, B.; Martinez-Sykora, J.; De Moortel, I.; Chintzoglou, G.; McIntosh, S. W. Bibcode: 2017AGUFMSH43A2793D Altcode: Spicules have been proposed as significant contributorsto the coronal energy and mass balance. While previous observationshave provided a glimpse of short-lived transient brightenings in thecorona that are associated with spicules, these observations have beencontested and are the subject of a vigorous debate both on the modelingand the observational side so that it remains unclear whether plasmais heated to coronal temperatures in association with spicules. We use high-resolution observations of the chromosphere and transition region with the Interface Region Imaging Spectrograph (IRIS) and ofthe corona with the Atmospheric Imaging Assembly (AIA) onboard theSolar Dynamics Observatory (SDO) to show evidence of the formation of coronal structures as a result of spicular mass ejections andheating of plasma to transition region and coronaltemperatures. Our observations suggest that a significant fraction of the highly dynamic loop fan environment associated with plage regions may be the result of the formation of such new coronal strands, a process that previously had been interpreted as the propagation of transient propagating coronal disturbances (PCD)s. Our observationsare supported by 2.5D radiative MHD simulations that show heating tocoronal temperatures in association with spicules. Our results suggest that heating and strong flows play an important role in maintaining the substructure of loop fans, in addition to the waves that permeate this low coronal environment. Our models also matches observations ofTR counterparts of spicules and provides an elegant explanation forthe high apparent speeds of these "network jets". Title: Energetics of the Kelvin-Helmholtz instability induced by transverse waves in twisted coronal loops Authors: Howson, T. A.; De Moortel, I.; Antolin, P. Bibcode: 2017A&A...607A..77H Altcode: 2017arXiv170804124H
Aims: We quantify the effects of twisted magnetic fields on the development of the magnetic Kelvin-Helmholtz instability (KHI) in transversely oscillating coronal loops.
Methods: We modelled a fundamental standing kink mode in a straight, density-enhanced magnetic flux tube using the magnetohydrodynamics code, Lare3d. In order to evaluate the impact of an azimuthal component of the magnetic field, various degrees of twist were included within the flux tube's magnetic field.
Results: The process of resonant absorption is only weakly affected by the presence of a twisted magnetic field. However, the subsequent evolution of the KHI is sensitive to the strength of the azimuthal component of the field. Increased twist values inhibit the deformation of the loop's density profile, which is associated with the growth of the instability. Despite this, much smaller scales in the magnetic field are generated when there is a non-zero azimuthal component present. Hence, the instability is more energetic in cases with (even weakly) twisted fields. Field aligned flows at the loop apex are established in a twisted regime once the instability has formed. Further, in the straight field case, there is no net vertical component of vorticity when integrated across the loop. However, the inclusion of azimuthal magnetic field generates a preferred direction for the vorticity which oscillates during the kink mode.
Conclusions: The KHI may have implications for wave heating in the solar atmosphere due to the creation of small length scales and the generation of a turbulent regime. Whilst magnetic twist does suppress the development of the vortices associated with the instability, the formation of the KHI in a twisted regime will be accompanied by greater Ohmic dissipation due to the larger currents that are produced, even if only weak twist is present. The presence of magnetic twist will likely make the instability more difficult to detect in the corona, but will enhance its contribution to heating the solar atmosphere. Further, the development of velocities along the loop may have observational applications for inferring the presence of magnetic twist within coronal structures. Title: Above the Noise: The Search for Periodicities in the Inner Heliosphere Authors: Threlfall, James; De Moortel, Ineke; Conlon, Thomas Bibcode: 2017SoPh..292..165T Altcode: Remote sensing of coronal and heliospheric periodicities can provide vital insight into the local conditions and dynamics of the solar atmosphere. We seek to trace long (one hour or longer) periodic oscillatory signatures (previously identified above the limb in the corona by, e.g., Telloni et al. in Astrophys. J.767, 138, 2013) from their origin at the solar surface out into the heliosphere. To do this, we combined on-disk measurements taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and concurrent extreme ultra-violet (EUV) and coronagraph data from one of the Solar Terrestrial Relations Observatory (STEREO) spacecraft to study the evolution of two active regions in the vicinity of an equatorial coronal hole over several days in early 2011. Fourier and wavelet analysis of signals were performed. Applying white-noise-based confidence levels to the power spectra associated with detrended intensity time series yields detections of oscillatory signatures with periods from 6 - 13 hours in both AIA and STEREO data. As was found by Telloni et al. (2013), these signatures are aligned with local magnetic structures. However, typical spectral power densities all vary substantially as a function of period, indicating spectra dominated by red (rather than white) noise. Contrary to the white-noise-based results, applying global confidence levels based on a generic background-noise model (allowing a combination of white noise, red noise, and transients following Auchère et al. in Astrophys. J.825, 110, 2016) without detrending the time series uncovers only sporadic, spatially uncorrelated evidence of periodic signatures in either instrument. Automating this method to individual pixels in the STEREO/COR coronagraph field of view is non-trivial. Efforts to identify and implement a more robust automatic background noise model fitting procedure are needed. Title: Observations and Numerical Models of Solar Coronal Heating Associated with Spicules Authors: De Pontieu, B.; De Moortel, I.; Martinez-Sykora, J.; McIntosh, S. W. Bibcode: 2017ApJ...845L..18D Altcode: 2017arXiv171006790D Spicules have been proposed as significant contributors to the mass and energy balance of the corona. While previous observations have provided a glimpse of short-lived transient brightenings in the corona that are associated with spicules, these observations have been contested and are the subject of a vigorous debate both on the modeling and the observational side. Therefore, it remains unclear whether plasma is heated to coronal temperatures in association with spicules. We use high-resolution observations of the chromosphere and transition region (TR) with the Interface Region Imaging Spectrograph and of the corona with the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to show evidence of the formation of coronal structures associated with spicular mass ejections and heating of plasma to TR and coronal temperatures. Our observations suggest that a significant fraction of the highly dynamic loop fan environment associated with plage regions may be the result of the formation of such new coronal strands, a process that previously had been interpreted as the propagation of transient propagating coronal disturbances. Our observations are supported by 2.5D radiative MHD simulations that show heating to coronal temperatures in association with spicules. Our results suggest that heating and strong flows play an important role in maintaining the substructure of loop fans, in addition to the waves that permeate this low coronal environment. Title: A new approach for modelling chromospheric evaporation in response to enhanced coronal heating. II. Non-uniform heating Authors: Johnston, C. D.; Hood, A. W.; Cargill, P. J.; De Moortel, I. Bibcode: 2017A&A...605A...8J Altcode: 2017arXiv170504054J We proposed that the use of an approximate "jump condition" at the solar transition region permits fast and accurate numerical solutions of the one dimensional hydrodynamic equations when the corona undergoes impulsive heating. In particular, it eliminates the need for the very short timesteps imposed by a highly resolved numerical grid. This paper presents further examples of the applicability of the method for cases of non-uniform heating, in particular, nanoflare trains (uniform in space but non-uniform in time) and spatially localised impulsive heating, including at the loop apex and base of the transition region. In all cases the overall behaviour of the coronal density and temperature shows good agreement with a fully resolved one dimensional model and is significantly better than the equivalent results from a 1D code run without using the jump condition but with the same coarse grid. A detailed assessment of the errors introduced by the jump condition is presented showing that the causes of discrepancy with the fully resolved code are (I) the neglect of the terms corresponding to the rate of change of total energy in the unresolved atmosphere; (II) mass motions at the base of the transition region and (III) for some cases with footpoint heating, an over-estimation of the radiative losses in the transition region. Title: The effects of resistivity and viscosity on the Kelvin- Helmholtz instability in oscillating coronal loops Authors: Howson, T. A.; De Moortel, I.; Antolin, P. Bibcode: 2017A&A...602A..74H Altcode: 2017arXiv170302423H
Aims: We investigate the effects of resistivity and viscosity on the onset and growth of the Kelvin-Helmholtz instability (KHI) in an oscillating coronal loop.
Methods: We modelled a standing kink wave in a density-enhanced loop with the three dimensional (3D), resistive magnetohydrodynamics code, Lare3d. We conducted a parameter study on the viscosity and resistivity coefficients to examine the effects of dissipation on the KHI.
Results: Enhancing the viscosity (ν) and resistivity (η) acts to suppress the KHI. Larger values of η and ν delay the formation of the instability and, in some cases, prevent the onset completely. This leads to the earlier onset of heating for smaller values of the transport coefficients. We note that viscosity has a greater effect on the development of the KHI than resistivity. Furthermore, when using anomalous resistivity, the Ohmic heating rate associated with the KHI may be greater than that associated with the phase mixing that occurs in an instability-suppressed regime (using uniform resistivity).
Conclusions: From our study, it is clear that the heating rate crucially depends on the formation of small length scales (influenced by the numerical resolution) as well as the values of resistivity and viscosity. As larger values of the transport coefficients suppress the KHI, the onset of heating is delayed but the heating rate is larger. As increased numerical resolution allows smaller length scales to develop, the heating rate will be higher even for the same values of η and ν. Title: Contribution of mode-coupling and phase-mixing of Alfvén waves to coronal heating Authors: Pagano, P.; De Moortel, I. Bibcode: 2017A&A...601A.107P Altcode: Context. Phase-mixing of Alfvén waves in the solar corona has been identified as one possible candidate to explain coronal heating. While this scenario is supported by observations of ubiquitous oscillations in the corona carrying sufficient wave energy and by theoretical models that have described the concentration of energy in small-scale structures, it is still unclear whether this wave energy can be converted into thermal energy in order to maintain the million-degree hot solar corona.
Aims: The aim of this work is to assess how much energy can be converted into thermal energy by a phase-mixing process triggered by the propagation of Alfvénic waves in a cylindric coronal structure, such as a coronal loop, and to estimate the impact of this conversion on the coronal heating and thermal structure of the solar corona.
Methods: To this end, we ran 3D MHD simulations of a magnetised cylinder where the Alfvén speed varies through a boundary shell, and a footpoint driver is set to trigger kink modes that mode couple to torsional Alfvén modes in the boundary shell. These Alfvén waves are expected to phase-mix, and the system allows us to study the subsequent thermal energy deposition. We ran a reference simulation to explain the main process and then we varied the simulation parameters, such as the size of the boundary shell, its structure, and the persistence of the driver.
Results: When we take high values of magnetic resistivity and strong footpoint drivers into consideration, we find that I) phase-mixing leads to a temperature increase of the order of 105 K or less, depending on the structure of the boundary shell; II) this energy is able to balance the radiative losses only in the localised region involved in the heating; and III) we can determine the influence of the boundary layer and the persistence of the driver on the thermal structure of the system.
Conclusions: Our conclusion is that as a result of the extreme physical parameters we adopted and the moderate impact on the heating of the system, it is unlikely that phase-mixing can contribute on a global scale to the heating of the solar corona. Title: Contribution of mode coupling and phase-mixing of Alfvén waves to coronal heating Authors: Pagano, Paolo; De Moortel, Ineke Bibcode: 2017EGUGA..19.9255P Altcode: 2017arXiv170305707P The solar corona is a million degree plasma that has been investigated for long time to understand the cause of this high heating rate. In particular, phase-mixing of Alfvén waves in the solar corona has been identified as one possible candidate to explain coronal heating by observations of ubiquitous oscillations in the corona carrying sufficient wave energy and by theoretical models that have described the concentration of energy in small scale structures. The aim of this work is to assess how much energy can be converted into thermal energy by a phase-mixing process triggered by the propagation of Alfvénic waves in a cylindric coronal structure, such as a coronal loop, and to estimate the impact of this conversion on the coronal heating and thermal structure of the solar corona plasma. We run 3D MHD simulations of a magnetised cylinder where the Alfvén speed varies through a boundary shell and a footpoint driver is set to trigger kink modes which mode couple to torsional Alfvén modes in the boundary shell. These Alfvén waves are expected to phase-mix and the system allows us to study the following thermal energy deposition on the plasma. We run a reference simulation to explain the main process and then we vary simulation parameters, such as the size of the boundary shell, its structure and the persistence of the driver. Taking into consideration high values of magnetic resistivity and strong footpoint drivers, we find i) that phase-mixing leads to a temperature increase, ii) that this energy is able to balance the radiative losses only in the localised region involved in the heating. Title: Observational Signatures of Transverse Magnetohydrodynamic Waves and Associated Dynamic Instabilities in Coronal Flux Tubes Authors: Antolin, P.; De Moortel, I.; Van Doorsselaere, T.; Yokoyama, T. Bibcode: 2017ApJ...836..219A Altcode: Magnetohydrodynamic (MHD) waves permeate the solar atmosphere and constitute potential coronal heating agents. Yet, the waves detected so far may be but a small subset of the true existing wave power. Detection is limited by instrumental constraints but also by wave processes that localize the wave power in undetectable spatial scales. In this study, we conduct 3D MHD simulations and forward modeling of standing transverse MHD waves in coronal loops with uniform and non-uniform temperature variation in the perpendicular cross-section. The observed signatures are largely dominated by the combination of the Kelvin-Helmholtz instability (KHI), resonant absorption, and phase mixing. In the presence of a cross-loop temperature gradient, we find that emission lines sensitive to the loop core catch different signatures compared to those that are more sensitive to the loop boundary and the surrounding corona, leading to an out-of-phase intensity and Doppler velocity modulation produced by KHI mixing. In all of the considered models, common signatures include an intensity and loop width modulation at half the kink period, a fine strand-like structure, a characteristic arrow-shaped structure in the Doppler maps, and overall line broadening in time but particularly at the loop edges. For our model, most of these features can be captured with a spatial resolution of 0.″33 and a spectral resolution of 25 km s-1, although we do obtain severe over-estimation of the line width. Resonant absorption leads to a significant decrease of the observed kinetic energy from Doppler motions over time, which is not recovered by a corresponding increase in the line width from phase mixing and KHI motions. We estimate this hidden wave energy to be a factor of 5-10 of the observed value. Title: Observational signatures of transverse MHD waves and associated dynamic instabilities Authors: Antolin, Patrick; De Moortel, Ineke; Van Doorsselaere, Tom; Yokoyama, Takaaki Bibcode: 2017arXiv170200775A Altcode: MHD waves permeate the solar atmosphere and constitute potential coronal heating agents. Yet, the waves detected so far may be but a small subset of the true existing wave power. Detection is limited by instrumental constraints, but also by wave processes that localise the wave power in undetectable spatial scales. In this study we conduct 3D MHD simulations and forward modelling of standing transverse MHD waves in coronal loops with uniform and non-uniform temperature variation in the perpendicular cross-section. The observed signatures are largely dominated by the combination of the Kelvin-Helmholtz instability (KHI), resonant absorption and phase mixing. In the presence of a cross-loop temperature gradient we find that emission lines sensitive to the loop core catch different signatures than those more sensitive to the loop boundary and the surrounding corona, leading to an out-of-phase intensity modulation produced by the KHI mixing. Common signatures to all considered models include an intensity and loop width modulation at half the kink period, fine strand-like structure, a characteristic arrow-shaped structure in the Doppler maps, overall line broadening in time but particularly at the loop edges. For our model, most of these features can be captured with a spatial resolution of $0.33\arcsec$ and spectral resolution of 25~km~s$^{-1}$, although severe over-estimation of the line width is obtained. Resonant absorption leads to a significant decrease of the observed kinetic energy from Doppler motions over time, which is not recovered by a corresponding increase in the line width from phase mixing and the KHI motions. We estimate this hidden wave energy to be a factor of $5-10$ of the observed value. Title: JPEG2000 Image Compression on Solar EUV Images Authors: Fischer, Catherine E.; Müller, Daniel; De Moortel, Ineke Bibcode: 2017SoPh..292...16F Altcode: 2017arXiv170201946F For future solar missions as well as ground-based telescopes, efficient ways to return and process data have become increasingly important. Solar Orbiter, which is the next ESA/NASA mission to explore the Sun and the heliosphere, is a deep-space mission, which implies a limited telemetry rate that makes efficient onboard data compression a necessity to achieve the mission science goals. Missions like the Solar Dynamics Observatory (SDO) and future ground-based telescopes such as the Daniel K. Inouye Solar Telescope, on the other hand, face the challenge of making petabyte-sized solar data archives accessible to the solar community. New image compression standards address these challenges by implementing efficient and flexible compression algorithms that can be tailored to user requirements. We analyse solar images from the Atmospheric Imaging Assembly (AIA) instrument onboard SDO to study the effect of lossy JPEG2000 (from the Joint Photographic Experts Group 2000) image compression at different bitrates. To assess the quality of compressed images, we use the mean structural similarity (MSSIM) index as well as the widely used peak signal-to-noise ratio (PSNR) as metrics and compare the two in the context of solar EUV images. In addition, we perform tests to validate the scientific use of the lossily compressed images by analysing examples of an on-disc and off-limb coronal-loop oscillation time-series observed by AIA/SDO. Title: Sub-photosphere to Solar Atmosphere Connection Authors: Komm, Rudolf; De Moortel, Ineke; Fan, Yuhong; Ilonidis, Stathis; Steiner, Oskar Bibcode: 2017hdsi.book..173K Altcode: No abstract at ADS Title: A new approach for modelling chromospheric evaporation in response to enhanced coronal heating. I. The method Authors: Johnston, C. D.; Hood, A. W.; Cargill, P. J.; De Moortel, I. Bibcode: 2017A&A...597A..81J Altcode: 2016arXiv160905075J We present a new computational approach that addresses the difficulty of obtaining the correct interaction between the solar corona and the transition region, in response to rapid heating events. In the coupled corona, transition region, and chromosphere system, an enhanced downward conductive flux results in an upflow (chromospheric evaporation). However, obtaining the correct upflow generally requires high spatial resolution in order to resolve the transition region. With an unresolved transition region, artificially low coronal densities are obtained because the downward heat flux "jumps" across the unresolved region to the chromosphere, underestimating the upflows. Here, we treat the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. To illustrate and benchmark this approach against a fully resolved one-dimensional model, we present field-aligned simulations of coronal loops in response to a range of impulsive (spatially uniform) heating events. We show that our approach leads to a significant improvement in the coronal density evolution than just when using coarse spatial resolutions insufficient to resolve the lower transition region. Our approach compensates for the jumping of the heat flux by imposing a velocity correction that ensures that the energy from the heat flux goes into driving the transition region dynamics, rather than being lost through radiation. Hence, it is possible to obtain improved coronal densities. The advantages of using this approach in both one-dimensional hydrodynamic and three-dimensional magnetohydrodynamic simulations are discussed. Title: IRIS and SDO observations of coronal heating associated with spicules Authors: De Moortel, Ineke Bibcode: 2017psio.confE..55D Altcode: No abstract at ADS Title: Reconnection Microjets in the Pre-eruption Phase of a Prominence/Coronal Rain Complex Authors: Antolin, P.; Mehta, T.; Conlon, T.; De Moortel, I. Bibcode: 2016AGUFMSH43C2582A Altcode: Coronal rain is known to be one of the highest resolution tracers of the coronal magnetic field. In this work the dynamics of a prominence/coronal rain complex are analysed based on imaging and spectroscopic observations with IRIS. Prior to eruption, the loop-like magnetic field arcade hosting the rain is observed to slowly expand in height. This movement is accompanied by several small ( 1 arsec) and short (<20 sec) bursts of plasma perpendicular to the field, captured in the Si IV and Mg II lines. The line profiles are broad and asymmetric with long tails above 100 km/s. These microjets are accompanied with strong intensity enhancements along the loop in most of the AIA channels, indicating significant energy release. We interpret these microjets as reconnection outflows, produced by component reconnection as the magnetic structure expands transversely. The originally cold conditions of the rain allows in this case a unique high resolution glance at the reconnection dynamics in low beta plasmas. Title: IRIS and SDO/AIA observations of coronal heating associated with spicules Authors: De Pontieu, B.; De Moortel, I.; Mcintosh, S. W. Bibcode: 2016AGUFMSH42B..07D Altcode: Chromospheric spicules have been proposed as significant contributors to the coronal energy and mass balance. While previous observations have provided a glimpse of short-lived transient brightenings in the corona that are associated with spicules, these observations have been contested and the subject of a vigorous debate both on the modeling and the observational side so that it remains unclear whether plasma associated with spicules is heated to coronal temperatures. We use high-resolution observations of the chromosphere and transition region with the Interface Region Imaging Spectrograph (IRIS) and of the corona with the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) to show evidence of the formation of coronal structures as a result of spicular mass ejections and subsequent heating of plasma first to transition region and later to coronal temperatures. Our observations suggest that much of the highly dynamic loop fan environment associated with plage regions may be the result of the formation of such new coronal strands, a process that previously had been interpreted as the propagation of transient propagating coronal disturbances (PCD)s. Our results suggest that heating and strong flows play an important role in maintaining the substructure of loop fans, in addition to the waves that permeate this low coronal environment. Title: Impact of flux distribution on elementary heating events Authors: O'Hara, J. P.; De Moortel, I. Bibcode: 2016A&A...594A..67O Altcode: Context. The complex magnetic field on the solar surface has been shown to contain a range of sizes and distributions of magnetic flux structures. The dynamic evolution of this magnetic carpet by photospheric flows provides a continual source of free magnetic energy into the solar atmosphere, which can subsequently be released by magnetic reconnection.
Aims: We investigate how the distribution and number of magnetic flux sources impact the energy release and locations of heating through magnetic reconnection driven by slow footpoint motions.
Methods: 3D magnetohydrodynamic (MHD) simulations using Lare3D are carried out, where flux tubes are formed between positive and negative sources placed symmetrically on the lower and upper boundaries of the domain, respectively. The flux tubes are subjected to rotational driving velocities on the boundaries and are forced to interact and reconnect.
Results: Initially, simple flux distributions with two and four sources are compared. In both cases, central current concentrations are formed between the flux tubes and Ohmic heating occurs. The reconnection and subsequent energy release is delayed in the four-source case and is shown to produce more locations of heating, but with smaller magnitudes. Increasing the values of the background field between the flux tubes is shown to delay the onset of reconnection and increases the efficiency of heating in both the two- and four-source cases. The cases with two flux tubes are always more energetic than the corresponding four flux tube cases, however the addition of the background field makes this disparity less significant. A final experiment with a larger number of smaller flux sources is considered and the field evolution and energetics are shown to be remarkably similar to the two-source case, indicating the importance of the size and separation of the flux sources relative to the spatial scales of the velocity driver. Title: Modeling Observed Decay-less Oscillations as Resonantly Enhanced Kelvin-Helmholtz Vortices from Transverse MHD Waves and Their Seismological Application Authors: Antolin, P.; De Moortel, I.; Van Doorsselaere, T.; Yokoyama, T. Bibcode: 2016ApJ...830L..22A Altcode: 2016arXiv160909716A In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfvén waves. Due to its localized nature, direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction are recent observations that indicate that in the low-amplitude regime such transverse MHD waves can also appear decay-less, a still unsolved phenomenon. Recent numerical work has shown that Kelvin-Helmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modeling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decay-less oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such an effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfvén waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows us to estimate the density contrast at the boundary. Title: On the Connection between Propagating Solar Coronal Disturbances and Chromospheric Footpoints Authors: Bryans, P.; McIntosh, S. W.; De Moortel, I.; De Pontieu, B. Bibcode: 2016ApJ...829L..18B Altcode: The Interface Region Imaging Spectrograph (IRIS) provides an unparalleled opportunity to explore the (thermal) interface between the chromosphere, transition region, and the coronal plasma observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). The SDO/AIA observations of coronal loop footpoints show strong recurring upward propagating signals—“propagating coronal disturbances” (PCDs) with apparent speeds of the order of 100-120 km s-1. That signal has a clear signature in the slit-jaw images of IRIS in addition to identifiable spectral signatures and diagnostics in the Mg iih (2803 Å) line. In analyzing the Mg iih line, we are able to observe the presence of magnetoacoustic shock waves that are also present in the vicinity of the coronal loop footpoints. We see there is enough of a correspondence between the shock propagation in Mg iih, the evolution of the Si IV line profiles, and the PCD evolution to indicate that these waves are an important ingredient for PCDs. In addition, the strong flows in the jet-like features in the IRIS Si IV slit-jaw images are also associated with PCDs, such that waves and flows both appear to be contributing to the signals observed at the footpoints of PCDs. Title: Coronal Density Structure and its Role in Wave Damping in Loops Authors: Cargill, P. J.; De Moortel, I.; Kiddie, G. Bibcode: 2016ApJ...823...31C Altcode: It has long been established that gradients in the Alfvén speed, and in particular the plasma density, are an essential part of the damping of waves in the magnetically closed solar corona by mechanisms such as resonant absorption and phase mixing. While models of wave damping often assume a fixed density gradient, in this paper the self-consistency of such calculations is assessed by examining the temporal evolution of the coronal density. It is shown conceptually that for some coronal structures, density gradients can evolve in a way that the wave-damping processes are inhibited. For the case of phase mixing we argue that (a) wave heating cannot sustain the assumed density structure and (b) inclusion of feedback of the heating on the density gradient can lead to a highly structured density, although on long timescales. In addition, transport coefficients well in excess of classical are required to maintain the observed coronal density. Hence, the heating of closed coronal structures by global oscillations may face problems arising from the assumption of a fixed density gradient, and the rapid damping of oscillations may have to be accompanied by a separate (non-wave-based) heating mechanism to sustain the required density structuring. Title: Transverse, propagating velocity perturbations in solar coronal loops Authors: De Moortel, I.; Pascoe, D. J.; Wright, A. N.; Hood, A. W. Bibcode: 2016PPCF...58a4001D Altcode: 2015arXiv151000976D As waves and oscillations carry both energy and information, they have enormous potential as a plasma heating mechanism and, through seismology, to provide estimates of local plasma properties which are hard to obtain from direct measurements. Being sufficiently near to allow high-resolution observations, the atmosphere of the Sun forms a natural plasma laboratory. Recent observations have revealed that an abundance of waves and oscillations is present in the solar atmosphere, leading to a renewed interest in wave heating mechanisms.

This short review paper gives an overview of recently observed transverse, propagating velocity perturbations in coronal loops. These ubiquitous perturbations are observed to undergo strong damping as they propagate. Using 3D numerical simulations of footpoint-driven transverse waves propagating in a coronal plasma with a cylindrical density structure, in combination with analytical modelling, it is demonstrated that the observed velocity perturbations can be understood in terms of coupling of different wave modes in the inhomogeneous boundaries of the loops. Mode coupling in the inhomogeneous boundary layers of the loops leads to the coupling of the transversal (kink) mode to the azimuthal (Alfvén) mode, observed as the decay of the transverse kink oscillations. Both the numerical and analytical results show the spatial profile of the damped wave has a Gaussian shape to begin with, before switching to exponential decay at large heights. In addition, recent analysis of CoMP (Coronal Multi-channel Polarimeter) Doppler shift observations of large, off-limb, trans-equatorial loops shows that Fourier power at the apex appears to be higher in the high-frequency part of the spectrum than expected from theoretical models. This excess high-frequency FFT power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvénic) turbulence. Title: Sub-photosphere to Solar Atmosphere Connection Authors: Komm, Rudolf; De Moortel, Ineke; Fan, Yuhong; Ilonidis, Stathis; Steiner, Oskar Bibcode: 2015SSRv..196..167K Altcode: 2013SSRv..tmp...93K Magnetic fields extend from the solar interior through the atmosphere. The formation and evolution of active regions can be studied by measuring subsurface flows with local helioseismology. The emergence of magnetic flux from the solar convection zone is associated with acoustic perturbation signatures. In near-surface layers, the average dynamics can be determined for emerging regions. MHD simulations of the emergence of a twisted flux tube show how magnetic twist and free energy are transported from the interior into the corona and the dynamic signatures associated with such transport in the photospheric and sub-photospheric layers. The subsurface twisted flux tube does not emerge into the corona as a whole in emerging active regions. Shear flows at the polarity inversion line and coherent vortical motions in the subsurface flux tubes are the major means by which twist is transported into the corona, leading to the formation of sigmoid-shaped coronal magnetic fields capable of driving solar eruptions. The transport of twist can be followed from the interior by using the kinetic helicity of subsurface flows as a proxy of magnetic helicity; this quantity holds great promise for improving the understanding of eruptive phenomena. Waves are not only vital for studying the link between the solar interior and the surface but for linking the photosphere with the corona as well. Acoustic waves that propagate from the surface into the magnetically structured, dynamic atmosphere undergo mode conversion and refraction. These effects enable atmospheric seismology to determine the topography of magnetic canopies in the solar atmosphere. Inclined magnetic fields lower the cut-off frequency so that low frequency waves can leak into the outer atmosphere. Recent high resolution, high cadence observations of waves and oscillations in the solar atmosphere, have lead to a renewed interest in the potential role of waves as a heating mechanism. In light of their potential contribution to the heating of the solar atmosphere, some of the recent observations of waves and oscillations and ongoing modelling efforts are reviewed. Title: Impact of Flux Distribution on Elementary Heating Events Authors: O'Hara, Jennifer; De Moortel, Ineke Bibcode: 2015IAUGA..2254861O Altcode: We present the results of numerical simulations of reconnection between flux tubes driven by rotational footpoint motions using the 3D MHD code, Lare3d. The basic model consists of two, initially aligned, flux tubes that are forced to interact by rotational driving velocities on the flux concentrations on the boundaries. We extend this model by altering the number, distribution and strength of the sources, while maintaining the same total magnetic flux on the boundaries. In all cases, the magnetic field is stressed by the boundary motions and a current grows within the volume. We examine the dynamical evolution and the resultant magnitude, distribution and timing of the heating events for the different flux distributions. Title: On the Parallel and Perpendicular Propagating Motions Visible inPolar Plumes: An Incubator For (Fast) Solar Wind Acceleration? Authors: Liu, Jiajia; McIntosh, Scott W.; De Moortel, Ineke; Wang, Yuming Bibcode: 2015ApJ...806..273L Altcode: 2015arXiv150700143L We combine observations of the Coronal Multi-channel Polarimeter and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the characteristic properties of (propagating) Alfvénic motions and quasi-periodic intensity disturbances in polar plumes. This unique combination of instruments highlights the physical richness of the processes taking place at the base of the (fast) solar wind. The (parallel) intensity perturbations with intensity enhancements around 1% have an apparent speed of 120 km s-1 (in both the 171 and 193 Å passbands) and a periodicity of 15 minutes, while the (perpendicular) Alfvénic wave motions have a velocity amplitude of 0.5 km s-1, a phase speed of 830 km s-1, and a shorter period of 5 minutes on the same structures. These observations illustrate a scenario where the excited Alfvénic motions are propagating along an inhomogeneously loaded magnetic field structure such that the combination could be a potential progenitor of the magnetohydrodynamic turbulence required to accelerate the fast solar wind. Title: Excitation and damping of broadband kink waves in the solar corona Authors: Pascoe, D. J.; Wright, A. N.; De Moortel, I.; Hood, A. W. Bibcode: 2015A&A...578A..99P Altcode: Context. Observations such as those by the Coronal Multi-Channel Polarimeter (CoMP) have revealed that broadband kink oscillations are ubiquitous in the solar corona.
Aims: We consider footpoint-driven kink waves propagating in a low β coronal plasma with a cylindrical density structure. We investigate the excitation and damping of propagating kink waves by a broadband driver, including the effects of different spatial profiles for the driver.
Methods: We employ a general spatial damping profile in which the initial stage of the damping envelope is approximated by a Gaussian profile and the asymptotic state by an exponential one. We develop a method of accounting for the presence of these different damping regimes and test it using data from numerical simulations.
Results: Strongly damped oscillations in low density coronal loops are more accurately described by a Gaussian spatial damping profile than an exponential profile. The consequences for coronal seismology are investigated and applied to observational data for the ubiquitous broadband waves observed by CoMP. Current data cannot distinguish between the exponential and Gaussian profiles because of the levels of noise. We demonstrate the importance of the spatial profile of the driver on the resulting damping profile. Furthermore, we show that a small-scale turbulent driver is inefficient at exciting propagating kink waves. Title: Recent advances in coronal heating Authors: De Moortel, Ineke; Browning, Philippa Bibcode: 2015RSPTA.37340269D Altcode: 2015arXiv151000977D The solar corona, the tenuous outer atmosphere of the Sun, is orders of magnitude hotter than the solar surface. This 'coronal heating problem' requires the identification of a heat source to balance losses due to thermal conduction, radiation and (in some locations) convection. The review papers in this Theo Murphy meeting issue present an overview of recent observational findings, large- and small-scale numerical modelling of physical processes occurring in the solar atmosphere and other aspects which may affect our understanding of the proposed heating mechanisms. At the same time, they also set out the directions and challenges which must be tackled by future research. In this brief introduction, we summarize some of the issues and themes which reoccur throughout this issue. Title: Observational Signatures of Waves and Flows in the Solar Corona Authors: De Moortel, I.; Antolin, P.; Van Doorsselaere, T. Bibcode: 2015SoPh..290..399D Altcode: 2014SoPh..tmp..133D; 2015arXiv151001030D Propagating perturbations have been observed in extended coronal loop structures for a number of years, but the interpretation in terms of slow (propagating) magneto-acoustic waves and/or as quasi-periodic upflows remains unresolved. We used forward-modelling to construct observational signatures associated with a simple slow magneto-acoustic wave or periodic flow model. Observational signatures were computed for the 171 Å Fe IX and the 193 Å Fe XII spectral lines. Although there are many differences between the flow and wave models, we did not find any clear, robust observational characteristics that can be used in isolation (i.e. that do not rely on a comparison between the models). For the waves model, a relatively rapid change of the average line widths as a function of (shallow) line-of-sight angles was found, whereas the ratio of the line width amplitudes to the Doppler velocity amplitudes is relatively high for the flow model. The most robust observational signature found is that the ratio of the mean to the amplitudes of the Doppler velocity is always higher than one for the flow model. This ratio is substantially higher for flows than for waves, and for the flows model used in the study is exactly the same in the 171 Å Fe IX and the 193 Å Fe XII spectral lines. However, these potential observational signatures need to be treated cautiously because they are likely to be model-dependent. Title: Statistical Evidence for the Existence of Alfvénic Turbulence in Solar Coronal Loops Authors: Liu, Jiajia; McIntosh, Scott W.; De Moortel, Ineke; Threlfall, James; Bethge, Christian Bibcode: 2014ApJ...797....7L Altcode: 2014arXiv1411.5094L Recent observations have demonstrated that waves capable of carrying large amounts of energy are ubiquitous throughout the solar corona. However, the question of how this wave energy is dissipated (on which timescales and length scales) and released into the plasma remains largely unanswered. Both analytic and numerical models have previously shown that Alfvénic turbulence may play a key role not only in the generation of the fast solar wind, but in the heating of coronal loops. In an effort to bridge the gap between theory and observations, we expand on a recent study by analyzing 37 clearly isolated coronal loops using data from the Coronal Multi-channel Polarimeter instrument. We observe Alfvénic perturbations with phase speeds which range from 250 to 750 km s-1 and periods from 140 to 270 s for the chosen loops. While excesses of high-frequency wave power are observed near the apex of some loops (tentatively supporting the onset of Alfvénic turbulence), we show that this excess depends on loop length and the wavelength of the observed oscillations. In deriving a proportional relationship between the loop length/wavelength ratio and the enhanced wave power at the loop apex, and from the analysis of the line widths associated with these loops, our findings are supportive of the existence of Alfvénic turbulence in coronal loops. Title: Standing Kink Modes in Three-dimensional Coronal Loops Authors: Pascoe, D. J.; De Moortel, I. Bibcode: 2014ApJ...784..101P Altcode: So far, the straight flux tube model proposed by Edwin & Roberts is the most commonly used tool in practical coronal seismology, in particular, to infer values of the (coronal) magnetic field from observed, standing kink mode oscillations. In this paper, we compare the period predicted by this basic model with three-dimensional (3D) numerical simulations of standing kink mode oscillations, as the period is a crucial parameter in the seismological inversion to determine the magnetic field. We perform numerical simulations of standing kink modes in both straight and curved 3D coronal loops and consider excitation by internal and external drivers. The period of oscillation for the displacement of dense coronal loops is determined by the loop length and the kink speed, in agreement with the estimate based on analytical theory for straight flux tubes. For curved coronal loops embedded in a magnetic arcade and excited by an external driver, a secondary mode with a period determined by the loop length and external Alfvén speed is also present. When a low number of oscillations is considered, these two periods can result in a single, non-resolved (broad) peak in the power spectrum, particularly for low values of the density contrast for which the two periods will be relatively similar. In that case (and for this particular geometry), the presence of this additional mode would lead to ambiguous seismological estimates of the magnetic field strength. Title: Potential Evidence for the Onset of Alfvénic Turbulence in Trans-equatorial Coronal Loops Authors: De Moortel, I.; McIntosh, S. W.; Threlfall, J.; Bethge, C.; Liu, J. Bibcode: 2014ApJ...782L..34D Altcode: This study investigates Coronal Multi-channel Polarimeter Doppler-shift observations of a large, off-limb, trans-equatorial loop system observed on 2012 April 10-11. Doppler-shift oscillations with a broad range of frequencies are found to propagate along the loop with a speed of about 500 km s-1. The power spectrum of perturbations travelling up from both loop footpoints is remarkably symmetric, probably due to the almost perfect north-south alignment of the loop system. Compared to the power spectrum at the footpoints of the loop, the Fourier power at the apex appears to be higher in the high-frequency part of the spectrum than expected from theoretical models. We suggest this excess high-frequency power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvénic) turbulence. Title: The Evolving Magnetic Scales of the Outer Solar Atmosphere and Their Potential Impact on Heliospheric Turbulence Authors: McIntosh, Scott W.; Bethge, Christian; Threlfall, James; De Moortel, Ineke; Leamon, Robert J.; Tian, Hui Bibcode: 2013arXiv1311.2538M Altcode: The presence of turbulent phenomena in the outer solar atmosphere is a given. However, because we are reduced to remotely sensing the atmosphere of a star with instruments of limited spatial and/or spectral resolution, we can only infer the physical progression from macroscopic to microscopic phenomena. Even so, we know that many, if not all, of the turbulent phenomena that pervade interplanetary space have physical origins at the Sun and so in this brief article we consider some recent measurements which point to sustained potential source(s) of heliospheric turbulence in the magnetic and thermal domains. In particular, we look at the scales of magnetism that are imprinted on the outer solar atmosphere by the relentless magneto-convection of the solar interior and combine state-of-the-art observations from the Solar Dynamics Observatory (SDO) and the Coronal Multi-channel Polarimeter (CoMP) which are beginning to hint at the origins of the wave/plasma interplay prevalent closer to the Earth. While linking these disparate scales of observation and understanding of their connection is near to impossible, it is clear that the constant evolution of subsurface magnetism on a host of scales guides and governs the flow of mass and energy at the smallest scales. In the near future significant progress in this area will be made by linking observations from high resolution platforms like the Interface Region Imaging Spectrograph (IRIS) and Advanced Technology Solar Telescope (ATST) with full-disk synoptic observations such as those presented herein. Title: First comparison of wave observations from CoMP and AIA/SDO Authors: Threlfall, J.; De Moortel, I.; McIntosh, S. W.; Bethge, C. Bibcode: 2013A&A...556A.124T Altcode: 2013arXiv1306.3354T Context. Waves have long been thought to contribute to the heating of the solar corona and the generation of the solar wind. Recent observations have demonstrated evidence of quasi-periodic longitudinal disturbances and ubiquitous transverse wave propagation in many different coronal environments.
Aims: This paper investigates signatures of different types of oscillatory behaviour, both above the solar limb and on-disk, by comparing findings from the Coronal Multi-channel Polarimeter (CoMP) and the Atmospheric Imaging Assembly (AIA) on-board the Solar Dynamics Observatory (SDO) for the same active region.
Methods: We study both transverse and longitudinal motion by comparing and contrasting time-distance images of parallel and perpendicular cuts along/across active region fan loops. Comparisons between parallel space-time diagram features in CoMP Doppler velocity and transverse oscillations in AIA images are made, together with space-time analysis of propagating quasi-periodic intensity features seen near the base of loops in AIA.
Results: Signatures of transverse motions are observed along the same magnetic structure using CoMP Doppler velocity (vphase = 600 → 750 km s-1, P = 3 → 6 min) and in AIA/SDO above the limb (P = 3 → 8 min). Quasi-periodic intensity features (vphase = 100 → 200 km s-1, P = 6 → 11 min) also travel along the base of the same structure. On the disk, signatures of both transverse and longitudinal intensity features were observed by AIA, and both show similar properties to signatures found along structures anchored in the same active region three days earlier above the limb. Correlated features are recovered by space-time analysis of neighbouring tracks over perpendicular distances of ≲2.6 Mm. Title: Damping of kink waves by mode coupling. I. Analytical treatment Authors: Hood, A. W.; Ruderman, M.; Pascoe, D. J.; De Moortel, I.; Terradas, J.; Wright, A. N. Bibcode: 2013A&A...551A..39H Altcode:
Aims: We investigate the spatial damping of propagating kink waves in an inhomogeneous plasma. In the limit of a thin tube surrounded by a thin transition layer, an analytical formulation for kink waves driven in from the bottom boundary of the corona is presented.
Methods: The spatial form for the damping of the kink mode was investigated using various analytical approximations. When the density ratio between the internal density and the external density is not too large, a simple differential-integral equation was used. Approximate analytical solutions to this equation are presented.
Results: For the first time, the form of the spatial damping of the kink mode is shown analytically to be Gaussian in nature near the driven boundary. For several wavelengths, the amplitude of the kink mode is proportional to (1 + exp(-z2/Lg2))/2, where Lg2 = 16/ɛκ2k2. Although the actual value of 16 in Lg depends on the particular form of the driver, this form is very general and its dependence on the other parameters does not change. For large distances, the damping profile appears to be roughly linear exponential decay. This is shown analytically by a series expansion when the inhomogeneous layer width is small enough.

Appendix A is available in electronic form at http://www.aanda.org Title: Damping of kink waves by mode coupling. II. Parametric study and seismology Authors: Pascoe, D. J.; Hood, A. W.; De Moortel, I.; Wright, A. N. Bibcode: 2013A&A...551A..40P Altcode: Context. Recent observations of the corona reveal ubiquitous transverse velocity perturbations that undergo strong damping as they propagate. These can be understood in terms of propagating kink waves that undergo mode coupling in inhomogeneous regions.
Aims: The use of these propagating waves as a seismological tool for the investigation of the solar corona depends upon an accurate understanding of how the mode coupling behaviour is determined by local plasma parameters. Our previous work suggests the exponential spatial damping profile provides a poor description of the behaviour of strongly damped kink waves. We aim to investigate the spatial damping profile in detail and provide a guide to the approximations most suitable for performing seismological inversions.
Methods: We propose a general spatial damping profile based on analytical results that accounts for the initial Gaussian stage of damped kink waves as well as the asymptotic exponential stage considered by previous authors. The applicability of this profile is demonstrated by a full parametric study of the relevant physical parameters. The implication of this profile for seismological inversions is investigated.
Results: The Gaussian damping profile is found to be most suitable for application as a seismological tool for observations of oscillations in loops with a low density contrast. This profile also provides accurate estimates for data in which only a few wavelengths or periods are observed. Title: The Source of 3 Minute Magnetoacoustic Oscillations in Coronal Fans Authors: Jess, D. B.; De Moortel, I.; Mathioudakis, M.; Christian, D. J.; Reardon, K. P.; Keys, P. H.; Keenan, F. P. Bibcode: 2012ApJ...757..160J Altcode: 2012arXiv1208.3194J We use images of high spatial, spectral, and temporal resolution, obtained using both ground- and space-based instrumentation, to investigate the coupling between wave phenomena observed at numerous heights in the solar atmosphere. Analysis of 4170 Å continuum images reveals small-scale umbral intensity enhancements, with diameters ~0farcs6, lasting in excess of 30 minutes. Intensity oscillations of ≈3 minutes are observed to encompass these photospheric structures, with power at least three orders of magnitude higher than the surrounding umbra. Simultaneous chromospheric velocity and intensity time series reveal an 87° ± 8° out-of-phase behavior, implying the presence of standing modes created as a result of partial wave reflection at the transition region boundary. We find a maximum waveguide inclination angle of ≈40° between photospheric and chromospheric heights, combined with a radial expansion factor of <76%. An average blueshifted Doppler velocity of ≈1.5 km s-1, in addition to a time lag between photospheric and chromospheric oscillatory phenomena, confirms the presence of upwardly propagating slow-mode waves in the lower solar atmosphere. Propagating oscillations in EUV intensity are detected in simultaneous coronal fan structures, with a periodicity of 172 ± 17 s and a propagation velocity of 45 ± 7 km s-1. Numerical simulations reveal that the damping of the magnetoacoustic wave trains is dominated by thermal conduction. The coronal fans are seen to anchor into the photosphere in locations where large-amplitude umbral dot (UD) oscillations manifest. Derived kinetic temperature and emission measure time series display prominent out-of-phase characteristics, and when combined with the previously established sub-sonic wave speeds, we conclude that the observed EUV waves are the coronal counterparts of the upwardly propagating magnetoacoustic slow modes detected in the lower solar atmosphere. Thus, for the first time, we reveal how the propagation of 3 minute magnetoacoustic waves in solar coronal structures is a direct result of amplitude enhancements occurring in photospheric UDs. Title: Propagating Disturbances in Coronal Loops: A Detailed Analysis of Propagation Speeds Authors: Kiddie, G.; De Moortel, I.; Del Zanna, G.; McIntosh, S. W.; Whittaker, I. Bibcode: 2012SoPh..279..427K Altcode: 2012arXiv1205.0891K Quasi-periodic disturbances have been observed in the outer solar atmosphere for many years. Although first interpreted as upflows (Schrijver et al., Solar Phys.187, 261, 1999), they have been widely regarded as slow magneto-acoustic waves, due to their observed velocities and periods. However, recent observations have questioned this interpretation, as periodic disturbances in Doppler velocity, line width, and profile asymmetry were found to be in phase with the intensity oscillations (De Pontieu and McIntosh, Astrophys. J.722, 1013, 2010; Tian, McIntosh, and De Pontieu, Astrophys. J. Lett.727, L37, 2011), suggesting that the disturbances could be quasi-periodic upflows. Here we conduct a detailed analysis of the velocities of these disturbances across several wavelengths using the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We analysed 41 examples, including both sunspot and non-sunspot regions of the Sun. We found that the velocities of propagating disturbances (PDs) located at sunspots are more likely to be temperature dependent, whereas the velocities of PDs at non-sunspot locations do not show a clear temperature dependence. This suggests an interpretation in terms of slow magneto-acoustic waves in sunspots but the nature of PDs in non-sunspot (plage) regions remains unclear. We also considered on what scale the underlying driver is affecting the properties of the PDs. Finally, we found that removing the contribution due to the cooler ions in the 193 Å wavelength suggests that a substantial part of the 193 Å emission of sunspot PDs can be attributed to the cool component of 193 Å. Title: Nonlinear wave propagation and reconnection at magnetic X-points in the Hall MHD regime Authors: Threlfall, J.; Parnell, C. E.; De Moortel, I.; McClements, K. G.; Arber, T. D. Bibcode: 2012A&A...544A..24T Altcode: 2012arXiv1202.3648T Context. The highly dynamical, complex nature of the solar atmosphere naturally implies the presence of waves in a topologically varied magnetic environment. Here, the interaction of waves with topological features such as null points is inevitable and potentially important for energetics. The low resistivity of the solar coronal plasma implies that non-magnetohydrodynamic (MHD) effects should be considered in studies of magnetic energy release in this environment.
Aims: This paper investigates the role of the Hall term in the propagation and dissipation of waves, their interaction with 2D magnetic X-points and the nature of the resulting reconnection.
Methods: A Lagrangian remap shock-capturing code (Lare2d) was used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth (δi) in resistive Hall MHD. A magnetic null-point finding algorithm was also used to locate and track the evolution of the multiple null-points that are formed in the system.
Results: Depending on the ratio of ion skin depth to system size, our model demonstrates that Hall effects can play a key role in the wave-null interaction. In particular, the initial fast-wave pulse now consists of whistler and ion-cyclotron components; the dispersive nature of the whistler wave leads to (i) earlier interaction with the null; (ii) the creation of multiple additional, transient nulls and, hence, an increased number of energy release sites. In the Hall regime, the relevant timescales (such as the onset of reconnection and the period of the oscillatory relaxation) of the system are reduced significantly, and the reconnection rate is enhanced. Title: A contemporary view of coronal heating Authors: Parnell, C. E.; De Moortel, I. Bibcode: 2012RSPTA.370.3217P Altcode: 2012arXiv1206.6097P Determining the heating mechanism (or mechanisms) that causes the outer atmosphere of the Sun, and many other stars, to reach temperatures orders of magnitude higher than their surface temperatures has long been a key problem. For decades the problem has been known as the coronal heating problem, but it is now clear that `coronal heating' cannot be treated or explained in isolation and that the heating of the whole solar atmosphere must be studied as a highly coupled system. The magnetic field of the star is known to play a key role, but, despite significant advancements in solar telescopes, computing power and much greater understanding of theoretical mechanisms, the question of which mechanism or mechanisms are the dominant supplier of energy to the chromosphere and corona is still open. Following substantial recent progress, we consider the most likely contenders and discuss the key factors that have made, and still make, determining the actual (coronal) heating mechanism (or mechanisms) so difficult. Title: Magnetohydrodynamic waves and coronal seismology: an overview of recent results Authors: De Moortel, I.; Nakariakov, V. M. Bibcode: 2012RSPTA.370.3193D Altcode: 2012arXiv1202.1944D Recent observations have revealed that MHD waves and oscillations are ubiquitous in the solar atmosphere, with a wide range of periods. We give a brief review of some aspects of MHD waves and coronal seismology which have recently been the focus of intense debate or are newly emerging. In particular, we focus on four topics: (i) the current controversy surrounding propagating intensity perturbations along coronal loops, (ii) the interpretation of propagating transverse loop oscillations, (iii) the ongoing search for coronal (torsional) Alfven waves and (iv) the rapidly developing topic of quasi-periodic pulsations (QPP) in solar flares. Title: The Fifth Hinode Science Meeting Authors: Golub, L.; De Moortel, I.; Shimizu, T. Bibcode: 2012ASPC..456.....G Altcode: No abstract at ADS Title: Spatial damping of propagating kink waves due to mode coupling Authors: Pascoe, D. J.; Hood, A. W.; de Moortel, I.; Wright, A. N. Bibcode: 2012A&A...539A..37P Altcode:
Aims: We investigate the damping process for propagating transverse velocity oscillations, observed to be ubiquitous in the solar corona, due to mode coupling.
Methods: We perform 3D numerical simulations of footpoint-driven transverse waves propagating in a low β coronal plasma with a cylindrical density structure. Mode coupling in an inhomogeneous layer leads to the coupling of the kink mode to the Alfvén mode, observed as the decay of the transverse kink oscillations.
Results: We consider the spatial damping profile and find a Gaussian damping profile of the form exp(-z2/Lg2) to be the most congruent with our numerical data, rather than the exponential damping profile of the form exp(- z/Ld) used in normal mode analysis. Our results highlight that the nature of the driver itself will have a substantial influence on observed propagating kink waves.
Conclusions: Our study suggests that this modified damping profile should be taken into account when using coronal seismology to infer local plasma properties from observed damped oscillations. Title: Coupling, damping and dissipation of magnetic waves in the chromosphere and corona Authors: De Moortel, I. Bibcode: 2012decs.confE..46D Altcode: In this talk I will give an overview of current (numerical) modelling of MHD waves and oscillations, emphasising in particular the process of mode coupling. Can models predict the observed damping rates and energy flux? How reliable are the comparisons between theory and observations? As observations of waves and oscillations become increasingly more detailed, it has become clear that the role of wave heating of the solar atmosphere has to be reassessed. I will highlight some of the recent modelling results as well as try to outline where future efforts are needed. Title: What we can and cannot learn from seismology of the solar atmosphere Authors: De Moortel, I. Bibcode: 2012decs.confE..45D Altcode: During the last decade or so, new instruments have revealed a surprisingly large number of observations of oscillatory behaviour in the solar atmosphere. Both standing and propagating waves have now been detected in a variety of different structures with a wide range of instruments. After the initial euphoria in coronal seismology applications, the subject now needs to go through a period of consolidating and verifying results. So, what can we actually learn from coronal seismology? This talk will invite the community to debate future directions for both theoretical modelling and observational campaigns. How robust are the basic MHD waves models? Do they apply in the highly dynamical and structured solar atmosphere? What can we learn from numerical modelling? And what exactly can we deduce from the observations? Title: What can we learn from propagating Alfvenic waves? Authors: Pascoe, D. J.; De Moortel, I.; Hood, A. W.; Wright, A. N. Bibcode: 2012decs.confE..24P Altcode: Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform 3D numerical simulations of footpoint-driven transverse waves propagating in a low beta plasma. When density structuring is present, mode coupling in inhomogeneous regions leads to the coupling of the kink mode to the Alfvén mode. The frequency-dependent decay of the propagating kink wave is observed as energy is transferred to the local Alfvén mode. Modest changes in density are capable of efficiently converting energy from the driving footpoint motion to localised Alfvén modes. Thus, realistic transverse footpoint motions will deposit energy to (azimuthal) Alfvén modes in the corona. Mode coupling is investigated in detail for propagating kink modes as an explanation for the observed wave damping and as a possible seismological tool. The observed strong damping of the Doppler shift oscillations indicates the presence of wide inhomogeneous layers at the edges of the loops. Our simulations (backed up by analytical calculations) show that in this regime, the traditional exp(-z/L) damping rate no longer applies. Hence, care has to be taken when seismologically inferring damping lengths from the observed oscillations. In addition, taking into account line-of-sight integration of multiple loops supporting transverse oscillations, we show that the energy budget present in the 3D coronal volume could be substantially higher than the energy budget derived from the observed Doppler shift oscillations. Title: The Effects of Line-of-sight Integration on Multistrand Coronal Loop Oscillations Authors: De Moortel, I.; Pascoe, D. J. Bibcode: 2012ApJ...746...31D Altcode: Observations have shown that transverse oscillations are present in a multitude of coronal structures. It is generally assumed that these oscillations are driven by (sub)surface footpoint motions. Using fully three-dimensional MHD simulations, we show that these footpoint perturbations generate propagating kink (Alfvénic) modes which couple very efficiently into (azimuthal) Alfvén waves. Using an ensemble of randomly distributed loops, driven by footpoint motions with random periods and directions, we compare the absolute energy in the numerical domain with the energy that is "visible" when integrating along the line of sight (LOS). We show that the kinetic energy derived from the LOS Doppler velocities is only a small fraction of the actual energy provided by the footpoint motions. Additionally, the superposition of loop structures along the LOS makes it nearly impossible to identify which structure the observed oscillations are actually associated with and could impact the identification of the mode of oscillation. Title: Computer Vision for the Solar Dynamics Observatory (SDO) Authors: Martens, P. C. H.; Attrill, G. D. R.; Davey, A. R.; Engell, A.; Farid, S.; Grigis, P. C.; Kasper, J.; Korreck, K.; Saar, S. H.; Savcheva, A.; Su, Y.; Testa, P.; Wills-Davey, M.; Bernasconi, P. N.; Raouafi, N. -E.; Delouille, V. A.; Hochedez, J. F.; Cirtain, J. W.; DeForest, C. E.; Angryk, R. A.; De Moortel, I.; Wiegelmann, T.; Georgoulis, M. K.; McAteer, R. T. J.; Timmons, R. P. Bibcode: 2012SoPh..275...79M Altcode: 2011SoPh..tmp..144M; 2011SoPh..tmp..213M; 2011SoPh..tmp....8M In Fall 2008 NASA selected a large international consortium to produce a comprehensive automated feature-recognition system for the Solar Dynamics Observatory (SDO). The SDO data that we consider are all of the Atmospheric Imaging Assembly (AIA) images plus surface magnetic-field images from the Helioseismic and Magnetic Imager (HMI). We produce robust, very efficient, professionally coded software modules that can keep up with the SDO data stream and detect, trace, and analyze numerous phenomena, including flares, sigmoids, filaments, coronal dimmings, polarity inversion lines, sunspots, X-ray bright points, active regions, coronal holes, EIT waves, coronal mass ejections (CMEs), coronal oscillations, and jets. We also track the emergence and evolution of magnetic elements down to the smallest detectable features and will provide at least four full-disk, nonlinear, force-free magnetic field extrapolations per day. The detection of CMEs and filaments is accomplished with Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric Coronagraph (LASCO) and ground-based Hα data, respectively. A completely new software element is a trainable feature-detection module based on a generalized image-classification algorithm. Such a trainable module can be used to find features that have not yet been discovered (as, for example, sigmoids were in the pre-Yohkoh era). Our codes will produce entries in the Heliophysics Events Knowledgebase (HEK) as well as produce complete catalogs for results that are too numerous for inclusion in the HEK, such as the X-ray bright-point metadata. This will permit users to locate data on individual events as well as carry out statistical studies on large numbers of events, using the interface provided by the Virtual Solar Observatory. The operations concept for our computer vision system is that the data will be analyzed in near real time as soon as they arrive at the SDO Joint Science Operations Center and have undergone basic processing. This will allow the system to produce timely space-weather alerts and to guide the selection and production of quicklook images and movies, in addition to its prime mission of enabling solar science. We briefly describe the complex and unique data-processing pipeline, consisting of the hardware and control software required to handle the SDO data stream and accommodate the computer-vision modules, which has been set up at the Lockheed-Martin Space Astrophysics Laboratory (LMSAL), with an identical copy at the Smithsonian Astrophysical Observatory (SAO). Title: Review Article: MHD Wave Propagation Near Coronal Null Points of Magnetic Fields Authors: McLaughlin, J. A.; Hood, A. W.; de Moortel, I. Bibcode: 2011SSRv..158..205M Altcode: 2010SSRv..tmp..174M; 2010arXiv1004.5568M; 2010SSRv..tmp..157M We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfvén speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfvén wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfvén-speed profile. In a β=0 plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfvén wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfvén wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfvén wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing. Title: Solar physics: Waves galore Authors: Cargill, Peter; de Moortel, Ineke Bibcode: 2011Natur.475..463C Altcode: Wave energy has long been proposed to be a source of the hot solar corona and fast solar wind. Direct measurements made by spacecraft have finally established that coronal waves are ubiquitous and can have the required energy. See Letter p.477 Title: Observed Damping of the Slow Magnetoacoustic Mode Authors: Marsh, M. S.; De Moortel, I.; Walsh, R. W. Bibcode: 2011ApJ...734...81M Altcode: 2011arXiv1104.1100M Spectroscopic and stereoscopic imaging observations of slow magnetoacoustic wave propagation within a coronal loop are investigated to determine the decay length scale of the slow magnetoacoustic mode in three dimensions and the density profile within the loop system. The slow wave is found to have an e-folding decay length scale of 20,000+4000 - 3000 km with a uniform density profile along the loop base. These observations place quantitative constraints on the modeling of wave propagation within coronal loops. Theoretical forward modeling suggests that magnetic field line divergence is the dominant damping factor and thermal conduction is insufficient, given the observed parameters of the coronal loop temperature, density, and wave mode period. Title: Coupled Alfvén and kink oscillations in an inhomogeneous corona Authors: Pascoe, David J.; Wright, Andrew N.; De Moortel, Ineke Bibcode: 2011IAUS..274..129P Altcode: We perform 3D numerical simulations of footpoint-driven transverse waves propagating in a low β plasma. The presence of inhomogeneities in the density profile leads to the coupling of the driven kink mode to Alfvén modes by resonant absorption. The decay of the propagating kink wave as energy is transferred to the local Alfvén mode is in good agreement with a modified interpretation of the analytical expression derived for standing kink modes. This coupling may account for the damping of transverse velocity perturbation waves which have recently been observed to be ubiquitous in the solar corona. Title: Propagating Coupled Alfvén and Kink Oscillations in an Arbitrary Inhomogeneous Corona Authors: Pascoe, D. J.; Wright, A. N.; De Moortel, I. Bibcode: 2011ApJ...731...73P Altcode: Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform three-dimensional numerical simulations of footpoint-driven transverse waves propagating in a low β plasma. We consider the cases of distorted cylindrical flux tubes and a randomly generated inhomogeneous medium. When density structuring is present, mode coupling in inhomogeneous regions leads to the coupling of the kink mode to the Alfvén mode. The decay of the propagating kink wave is observed as energy is transferred to the local Alfvén mode. In all cases considered, modest changes in density were capable of efficiently converting energy from the driving footpoint motion to localized Alfvén modes. We have demonstrated that mode coupling efficiently couples propagating kink perturbations to Alfvén modes in an arbitrary inhomogeneous medium. This has the consequence that transverse footpoint motions at the base of the corona will deposit energy to Alfvén modes in the corona. Title: Phase mixing of nonlinear visco-resistive Alfvén waves Authors: McLaughlin, J. A.; de Moortel, I.; Hood, A. W. Bibcode: 2011A&A...527A.149M Altcode: 2011arXiv1101.5945M
Aims: We investigate the behaviour of nonlinear, nonideal Alfvén wave propagation within an inhomogeneous magnetic environment.
Methods: The governing MHD equations are solved in 1D and 2D using both analytical techniques and numerical simulations.
Results: We find clear evidence for the ponderomotive effect and visco-resistive heating. The ponderomotive effect generates a longitudinal component to the transverse Alfvén wave, with a frequency twice that of the driving frequency. Analytical work shows the addition of resistive heating. This leads to a substantial increase in the local temperature and thus gas pressure of the plasma, resulting in material being pushed along the magnetic field. In 2D, our system exhibits phase mixing and we observe an evolution in the location of the maximum heating, i.e. we find a drifting of the heating layer.
Conclusions: Considering Alfvén wave propagation in 2D with an inhomogeneous density gradient, we find that the equilibrium density profile is significantly modified by both the flow of density due to visco-resistive heating and the nonlinear response to the localised heating through phase mixing. Title: Alfvén wave phase-mixing and damping in the ion cyclotron range of frequencies Authors: Threlfall, J.; McClements, K. G.; De Moortel, I. Bibcode: 2011A&A...525A.155T Altcode: 2010arXiv1007.4752T
Aims: We determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfvén waves in the ion cyclotron range of frequencies in uniform and non-uniform equilibrium plasmas.
Methods: Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient.
Results: The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in k2δ_i^2 where k is wavenumber and δ_i is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit k2δ_i^2 ≫ 1. In a non-uniform plasma it is found that the spatially-integrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispersion, tends to zero in both the weak and strong phase mixing limits. Title: Periodic Spectral Line Asymmetries in Solar Coronal Structures from Slow Magnetoacoustic Waves Authors: Verwichte, E.; Marsh, M.; Foullon, C.; Van Doorsselaere, T.; De Moortel, I.; Hood, A. W.; Nakariakov, V. M. Bibcode: 2010ApJ...724L.194V Altcode: Recent spectral observations of upward moving quasi-periodic intensity perturbations in solar coronal structures have shown evidence of periodic line asymmetries near their footpoints. These observations challenge the established interpretation of the intensity perturbations in terms of propagating slow magnetoacoustic waves. We show that slow waves inherently have a bias toward enhancement of emission in the blue wing of the emission line due to in-phase behavior of velocity and density perturbations. We demonstrate that slow waves cause line asymmetries when the emission line is averaged over an oscillation period or when a quasi-static plasma component in the line of sight is included. Therefore, we conclude that slow magnetoacoustic waves remain a valid explanation for the observed quasi-periodic intensity perturbations. Title: Magnetic reconnection in the solar atmosphere: from proposal to paradigm Authors: Cargill, Peter; Parnell, Clare; Browning, Philippa; de Moortel, Ineke; Hood, Alan Bibcode: 2010A&G....51c..31C Altcode: MEETING REPORT On 13 November 2009, the RAS hosted a discussion meeting to commemorate the formal retirement of Prof. Eric Priest. Here Peter Cargill, Clare Parnell, Philippa Browning, Ineke de Moortel and Alan Hood examine how magnetic reconnection has evolved over the past 50 years from an important but controversial proposal, to a general paradigm. Title: Coupled Alfvén and Kink Oscillations in Coronal Loops Authors: Pascoe, D. J.; Wright, A. N.; De Moortel, I. Bibcode: 2010ApJ...711..990P Altcode: Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. However, there is ongoing discussion regarding their interpretation as kink or Alfvén waves. To investigate the nature of transverse waves propagating in the solar corona and their potential for use as a coronal diagnostic in MHD seismology, we perform three-dimensional numerical simulations of footpoint-driven transverse waves propagating in a low β plasma. We consider the cases of both a uniform medium and one with loop-like density structure and perform a parametric study for our structuring parameters. When density structuring is present, resonant absorption in inhomogeneous layers leads to the coupling of the kink mode to the Alfvén mode. The decay of the propagating kink wave as energy is transferred to the local Alfvén mode is in good agreement with a modified interpretation of the analysis of Ruderman & Roberts for standing kink modes. Numerical simulations support the most general interpretation of the observed loop oscillations as a coupling of the kink and Alfvén modes. This coupling may account for the observed predominance of outward wave power in longer coronal loops since the observed damping length is comparable to our estimate based on an assumption of resonant absorption as the damping mechanism. Title: Automated Feature and Event Detection with SDO AIA and HMI Data Authors: Davey, Alisdair; Martens, P. C. H.; Attrill, G. D. R.; Engell, A.; Farid, S.; Grigis, P. C.; Kasper, J.; Korreck, K.; Saar, S. H.; Su, Y.; Testa, P.; Wills-Davey, M.; Savcheva, A.; Bernasconi, P. N.; Raouafi, N. -E.; Delouille, V. A.; Hochedez, J. F. .; Cirtain, J. W.; Deforest, C. E.; Angryk, R. A.; de Moortel, I.; Wiegelmann, T.; Georgouli, M. K.; McAteer, R. T. J.; Hurlburt, N.; Timmons, R. Bibcode: 2010cosp...38.2878D Altcode: 2010cosp.meet.2878D The Solar Dynamics Observatory (SDO) represents a new frontier in quantity and quality of solar data. At about 1.5 TB/day, the data will not be easily digestible by solar physicists using the same methods that have been employed for images from previous missions. In order for solar scientists to use the SDO data effectively they need meta-data that will allow them to identify and retrieve data sets that address their particular science questions. We are building a comprehensive computer vision pipeline for SDO, abstracting complete metadata on many of the features and events detectable on the Sun without human intervention. Our project unites more than a dozen individual, existing codes into a systematic tool that can be used by the entire solar community. The feature finding codes will run as part of the SDO Event Detection System (EDS) at the Joint Science Operations Center (JSOC; joint between Stanford and LMSAL). The metadata produced will be stored in the Heliophysics Event Knowledgebase (HEK), which will be accessible on-line for the rest of the world directly or via the Virtual Solar Observatory (VSO) . Solar scientists will be able to use the HEK to select event and feature data to download for science studies. Title: Longitudinal Waves in Coronal Loops Authors: de Moortel, I. Bibcode: 2009SSRv..149...65D Altcode: Outwardly propagating intensity disturbances are a common feature in large, quiescent coronal loop structures. In this paper, an overview is given of the observed properties and the theoretical modelling. As a large number of events have been observed and analysed, good statistical results on the estimated parameters have now been obtained. The theoretical modelling mainly focuses on two distinct aspects, namely the observed rapid damping of the perturbations, thought to be due to thermal conduction and the origin of the driver. Leakage of the solar surface p-modes is the main candidate to explain the observed periodicity, due to the strong correlation between loop position and period and the filamentary nature of the observed coronal intensity perturbations. Recent observational results appear to confirm the leakage and subsequent upward propagation of the solar surface 5 minute oscillations into the overlying atmospheric layers. Title: Impulsively generated oscillations in a 3D coronal loop Authors: Pascoe, D. J.; de Moortel, I.; McLaughlin, J. A. Bibcode: 2009A&A...505..319P Altcode: Aims: The effect of changing the attack angle for the interaction of a fast MHD wave with a 3D coronal loop is studied, to investigate to what extent the properties of the excited transverse kink mode oscillations of the loop depend on this angle.
Methods: 3D numerical simulations are performed of the interaction of a fast MHD wave, generated by a pressure pulse, with a 3D coronal loop. The loop itself is modelled as a density enhancement (with a finite plasma beta) within a magnetic arcade. The initial pressure pulse has a width comparable to the loop diameter and is situated outside of the loop, at the same height as the loop apex. This height is kept fixed but the (horizontal) angle between the pressure pulse and the loop is varied.
Results: We find that the global, transverse kink mode is efficiently excited for a range of attack angles and qualitatively in agreement with theoretical expectations. The period and damping time are found to be independent of the attack angle. For larger values of the attack angle, the global (longitudinal) slow wave is excited, whereas for intermediate values the second harmonic kink mode is also present. Title: Putting Coronal Seismology Estimates of the Magnetic Field Strength to the Test Authors: De Moortel, I.; Pascoe, D. J. Bibcode: 2009ApJ...699L..72D Altcode: The magnetic field strength inside a model coronal loop is "estimated" using coronal seismology, to examine the reliability of magnetic field strengths derived from observed, transverse coronal loop oscillations. Three-dimensional numerical simulations of the interaction of an external pressure pulse with a coronal loop (modeled as a three-dimensional density enhancement inside a two-dimensional magnetic arcade) are analyzed and the "observed" properties of the excited transverse loop oscillations are used to derive the value of the local magnetic field strength, following the method of Nakariakov & Ofman. Due to the (unexpected) change in periodicity, the magnetic field derived from our "observed" oscillation is substantially different from the actual (input) magnetic field value (approximately 50%). Coronal seismology can derive useful information about the local magnetic field, but the combined effect of the loop curvature, the density ratio, and aspect ratio of the loop appears to be more important than previously expected. Title: Computer Vision for The Solar Dynamics Observatory Authors: Martens, Petrus C.; Angryk, R. A.; Bernasconi, P. N.; Cirtain, J. W.; Davey, A. R.; DeForest, C. E.; Delouille, V. A.; De Moortel, I.; Georgoulis, M. K.; Grigis, P. C.; Hochedez, J. E.; Kasper, J.; Korreck, K. E.; Reeves, K. K.; Saar, S. H.; Savcheva, A.; Su, Y.; Testa, P.; Wiegelmann, T.; Wills-Davey, M. Bibcode: 2009SPD....40.1711M Altcode: NASA funded a large international consortium last year to produce a comprehensive system for automated feature recognition in SDO images. The data we consider are all AIA and EVE data plus surface magnetic field images from HMI. Helioseismology is addressed by another group.

We will produce robust and very efficient software modules that can keep up with the relentless SDO data stream and detect, trace, and analyze a large number of phenomena, including: flares, sigmoids, filaments, coronal dimmings, polarity inversion lines, sunspots, X-ray bright points, active regions, coronal holes, EIT waves, CME's, coronal oscillations, and jets. In addition we will track the emergence and evolution of magnetic elements down to the smallest features that are detectable, and we will also provide at least four full disk nonlinear force-free magnetic field extrapolations per day.

A completely new software element that rounds out this suite is a trainable feature detection module, which employs a generalized image classification algorithm to produce the texture features of the images analyzed. A user can introduce a number of examples of the phenomenon looked and the software will return images with similar features. We have tested a proto-type on TRACE data, and were able to "train" the algorithm to detect sunspots, active regions, and loops. Such a module can be used to find features that have not even been discovered yet, as, for example, sigmoids were in the pre-Yohkoh era.

Our codes will produce entries in the Helio Events Knowledge base, and that will permit users to locate data on individual events as well as carry out statistical studies on large numbers of events, using the interface provided by the Virtual Solar Observatory. Title: Nonlinear fast magnetoacoustic wave propagation in the neighbourhood of a 2D magnetic X-point: oscillatory reconnection Authors: McLaughlin, J. A.; De Moortel, I.; Hood, A. W.; Brady, C. S. Bibcode: 2009A&A...493..227M Altcode: 2009arXiv0901.1781M Context: This paper extends the models of Craig & McClymont (1991, ApJ, 371, L41) and McLaughlin & Hood (2004, A&A, 420, 1129) to include finite β and nonlinear effects.
Aims: We investigate the nature of nonlinear fast magnetoacoustic waves about a 2D magnetic X-point.
Methods: We solve the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Arber et al. 2001, J. Comp. Phys., 171, 151) and consider an initial condition in {v}×{B} \cdot {hat{z}} (a natural variable of the system).
Results: We observe the formation of both fast and slow oblique magnetic shocks. The nonlinear wave deforms the X-point into a “cusp-like” point which in turn collapses to a current sheet. The system then evolves through a series of horizontal and vertical current sheets, with associated changes in connectivity, i.e. the system exhibits oscillatory reconnection. Our final state is non-potential (but in force balance) due to asymmetric heating from the shocks. Larger amplitudes in our initial condition correspond to larger values of the final current density left in the system.
Conclusions: The inclusion of nonlinear terms introduces several new features to the system that were absent from the linear regime.

A movie is available in electronic form at http://www.aanda.org Title: Forward modelling to determine the observational signatures of propagating slow waves for TRACE, SoHO/CDS, and Hinode/EIS Authors: Owen, N. R.; De Moortel, I.; Hood, A. W. Bibcode: 2009A&A...494..339O Altcode: Context: The propagation and damping of slow MHD waves in the solar atmosphere are investigated by numerical simulations and forward modelling, with particular emphasis placed on waves with periodicities of the order of five minutes.
Aims: We extend a coronal model by adding an equilibrium temperature gradient allowing study of wave propagation from the transition region to the corona.
Methods: A 1D model is used that includes gravitational stratification and damping by thermal conduction, optically thin radiation, and compressive viscosity. Forward modelling of the simulation results, for both uniform and non-uniform equilibrium temperature profiles, is undertaken to establish the observational consequences of the physical processes involved for TRACE, SoHO/CDS, and Hinode/EIS.
Results: The presence of thermal conduction causes a phase shift between the wave velocity, energy, and density. This shift may be observable by comparing Doppler velocity and intensity observations. Phase shifts are also seen between intensity observations by different instruments and between different spectral lines. This is an observational effect that arises due to the forward modelling process in which observations are synthesised, but it is not seen in the simulation results. Oscillations from the transition region are found to dominate the coronal emission for TRACE 171 Å by nearly two orders of magnitude. Title: Forward Modelling of Coronal Intensity Perturbations Authors: De Moortel, I.; Bradshaw, S. J. Bibcode: 2008SoPh..252..101D Altcode: 2008SoPh..tmp..139D In this paper, forward modelling is used to investigate the relation between given temperature and density perturbations and the resulting (synthesised) intensity perturbations, as would be observed by, e.g., TRACE and EIS (onboard Hinode). Complex and highly non-linear interactions between the components which make up the intensity (density, ionisation balance and emissivity) mean that it is non-trivial to reverse this process, i.e., obtain the density and temperature perturbations associated with observed intensity oscillations. In particular, it is found that the damping rate does not often `survive' the forward modelling process, highlighting the need for a very careful interpretation of observed (intensity) damping rates. With a few examples, it is demonstrated that in some cases even the period of the oscillations can be altered and that it is possible for two different sets of input temperature and density to lead to very similar intensities (the well-known `ill-posed' inversion process). Title: Coronal Seismology Authors: De Moortel, I. Bibcode: 2008ESPM...12.3.26D Altcode: The idea of exploiting observed oscillations as a diagnostic tool for determining the physical conditions of the coronal plasma was first suggested several decades ago. During the last few years, high quality space-based observations have shown evidence for waves and oscillations in a wide variety of solar structures, such as coronal loops, polar plumes and prominences. I will (very) briefly summarise MHD wave theory, which forms the basis for coronal seismology, as well as present some of the recent theoretical models. In particular, I will focus on how observations and theoretical modelling are intrinsically linked, both guided and constrained by each other. Title: The way forward for coronal heating Authors: De Moortel, Ineke; Browning, Philippa; Bradshaw, Stephen J.; Pintér, Balázs; Kontar, Eduard P. Bibcode: 2008A&G....49c..21D Altcode: Ineke De Moortel, Philippa K Browning, Stephen J Bradshaw, Balázs Pintér and Eduard P Kontar consider approaches to the longstanding and enigmatic problem of coronal heating, as presented at the RAS discussion meeting on 11 January 2008. Title: Coronal Loop Seismology: Selective Examples Authors: De Moortel, I. Bibcode: 2008ASPC..383..266D Altcode: The idea of exploiting observed oscillations as a diagnostic tool for determining the physical conditions of the coronal plasma was first suggested several decades ago. During the last few years, high quality space-based observations have shown evidence for waves and oscillations in a wide variety of solar structures, such as coronal loops, polar plumes and prominences. In this review, observations of propagating, slow waves and standing, fast modes in the solar corona are summarized and examples are given of how these observations can be used to deduce information about different physical properties of the solar corona. A few suggestions are made as to how the relatively large uncertainties in the derived parameters could be reduced. Title: An Estimate of P-Mode Damping by Wave Leakage Authors: De Moortel, I.; Rosner, R. Bibcode: 2007SoPh..246...53D Altcode: High-cadence TRACE observations show that outward-propagating intensity disturbances are a common feature in large, quiescent coronal loops. Analysis of the frequency distribution of these modes shows peaks at both three- and five-minute periods, indicating that they may be driven by the solar surface oscillations (p modes). The energy flux contained within the coronal intensity disturbances is of the order of (1.1±0.4)×103 ergs cm−2 s−1. A simple order-of-magnitude estimate of the damping rate of the relevant p modes allows us to put an observational constraint on the damping of p modes and shows that leakage into the overlying coronal atmosphere might be able to account for a significant fraction of p-mode damping. Title: Magnetic reconnection in flux-tubes undergoing spinning footpoint motions Authors: Wilmot-Smith, A. L.; De Moortel, I. Bibcode: 2007A&A...473..615W Altcode: Aims:Photospheric motions acting on the coronal magnetic field have the potential to build up huge amounts of magnetic energy. The energy may be released through magnetic reconnection, and so a detailed understanding of the 3D process is crucial if its implications for coronal heating are to be fully addressed.
Methods: A 3D MHD experiment is described in which misaligned magnetic flux tubes are subjected to simple spinning boundary motions.
Results: The resulting shear between adjacent flux systems generates a twisted central separator current sheet that extends vertically throughout the domain. Current density is amplified to a sufficient extent that reconnection begins, and occurs everywhere along the separator current sheet, while the separatrix current sheets that exist in the early stages of the experiment are found to be unimportant in the systems dynamical evolution. In 2D cross-sections, the reconnection process exhibits many similarities to the regime of flux pile-up reconnection. Title: Observation of Higher Harmonic Coronal Loop Oscillations Authors: De Moortel, I.; Brady, C. S. Bibcode: 2007ApJ...664.1210D Altcode: A sequence of TRACE 171 Å observations taken on 2001 May 13 shows evidence of flare-induced, transverse coronal loop oscillations. We revisit this particular data set and present evidence of the presence of spatially resolved higher harmonics in the transverse loop displacements. The oscillations are identified as the second-harmonic, fast MHD kink waves (periods of 577-672 s), with higher harmonics (250-346 s) also present. The apparent absence of the fundamental mode and the fact that it is the second harmonic (P2) that dominates the oscillatory behavior of this particular loop may shed more light on either the excitation and/or the damping mechanism(s) of flare-induced, transverse loop oscillations. Title: Magnetic Field Extrapolations And Current Sheets Authors: Welsch, Brian; De Moortel, I.; McTiernan, J. M. Bibcode: 2007AAS...210.9101W Altcode: 2007BAAS...39Q.204W Solar flares and coronal mass ejections (CMEs) --- phenomena which impact our society, but are scientifically interesting in themselves --- are driven by free magnetic energy in the coronal magnetic field. Since the coronal magnetic field cannot be directly measured, modelers often extrapolate the coronal field from the photospheric magnetograms --- the only field measurements routinely available. The best extrapolation techniques assume that the field is force free (coronal currents parallel the magnetic field), but that currents are not simply a linear function of the magnetic field. Recent tests, however, suggest that such non-linear force-free field (NLFFF) extrapolation techniques often underestimate free magnetic energy. We hypothesize that, since relaxation-based NLFFF techniques tend to smooth field discontinuities, such approaches will fail when current sheets are present. Here, we test this hypothesis by applying the Optimization NLFFF method to two configurations from an MHD simulation --- one with strong current concentrations, and one with weak concentrations. This work is supported by a NASA Sun-Earth Connections Theory grant to UC-Berkeley. Title: Numerical modelling of 3D reconnection. II. Comparison between rotational and spinning footpoint motions Authors: De Moortel, I.; Galsgaard, K. Bibcode: 2006A&A...459..627D Altcode: The coronal magnetic field is constantly subjected to a variety of photospheric, footpoint motions, leading to the build up, and subsequent release, of magnetic energy. Two different types of footpoint motions are considered here, namely (large scale) rotating and (small scale) spinning, using 3D numerical MHD simulations. The initial model consists of two aligned, thin flux tubes, which are forced to interact due to the boundary driving of the footpoints. Two variations of this setup are studied, namely with and without an additional, constant, background magnetic field. The nature of the boundary motions determines the shape of the central current sheet, the driving force of the reconnection process, as well as the efficiency of the build up of quasi-separatrix layers (when B_bg ≠ 0). The reconnection process is more efficient for the rotating of the flux sources and when a background magnetic field is added. In general, heating due to large and small scale motions is of comparable magnitude when no background field is present. However, with an additional background magnetic field, heating due to small scale footpoint motions seems substantially more efficient. Title: Understanding Magnetic Structures in the Solar Corona Through Topological Analysis Authors: Maclean, R. C.; Parnell, C. E.; De Moortel, I.; Büchner, J.; Priest, E. R. Bibcode: 2006ESASP.617E.156M Altcode: 2006soho...17E.156M No abstract at ADS Title: Numerical modelling of 3D reconnection due to rotational footpoint motions Authors: De Moortel, I.; Galsgaard, K. Bibcode: 2006A&A...451.1101D Altcode: The rapid dynamical evolution of the photospheric magnetic carpet provides a large energy source for the solar corona. In this context, the role of 3D magnetic reconnection is crucial in releasing the free magnetic energy, build up due to the continuous footpoint motions. To understand the processes by which this can take place, we have to obtain a better understanding of the basic reconnection process that can take place in 3D magnetic field configurations. In this paper, we investigate magnetic reconnection, driven by rotational footpoint motions, using 3D numerical MHD simulations. The model consists of two positive and two negative sources, which are placed symmetrically on opposite boundaries of the cubic domain. The initially potential fluxtubes are forced to interact by the rotational driving of the flux concentrations on the boundaries. We consider two variations of this setup, namely with and without an additional, constant, background magnetic field. In the no-background case, the magnetic connectivity is divided into independent regions by separatrix surfaces, while the case with a background field is represented by one global connectivity region. The dynamical evolution is followed and found to differ significantly from the comparable potential evolution. Strong currents are concentrated along separatrix surfaces or rapidly developing quasi-separatrix layers (QSLs). Investigating the reconnection rates of the systems shows that the stronger the background field is, the more efficient the reconnection process of the flux in the respective fluxtubes. Title: Longitudinal intensity oscillations observed with TRACE: evidence of fine-scale structure Authors: McEwan, M. P.; de Moortel, I. Bibcode: 2006A&A...448..763M Altcode: The aim of this paper is two-fold: to increase the number of examples of observed longitudinal oscillations in coronal loops and to find evidence of the small temporal and spatial scales of these loop oscillations. Increasing the number of observed longitudinal oscillations allows for improvement in the statistics of the measured parameters, providing more accurate values for numerical and theoretical models. Furthermore, the small temporal and spatial scales of these loop oscillations could give indication of a driving force, symptomatic of coupling with the global p-modes. We found evidence that individual loop strands of wide coronal loop footpoints oscillate independently for short time periods. These strands have a diameter of the order of a few Mm, and the timescales on which the oscillations exist are typically less than an hour. We suggest that this is indicative of the oscillating strands being driven by the leakage of the global 5 min p-modes up into the corona, as simulated by De Pontieu et al. (2005, ApJ, 624, L61). Additionally, we find 25 further examples, added to those of De Moortel et al. (2002a, Sol. Phys., 209, 89), of outwardly propagating slow MHD waves in coronal loop footpoints. The datasets are taken from JOP83, observed between April 21st 2003 and May 3rd 2003, in the TRACE 171 Å bandpass. The intensity oscillations travel outwards with a propagation speed of order v = 99.7 ± 3.9 km s-1 and they are of small amplitude, with variations of approximately 3.7 ± 0.2 % of the background intensity. These disturbances are only detected for short distances, around 8.3 ± 0.6 Mm along the loops, and the main period of oscillation is around 300 s. A second peak of period was found at around 200 s, however no correlation with the presence of a sunspot was observed within this study. Using these measured parameters we have estimated the energy flux to be of order 313 ± 26 erg cm-2 s-1. Title: Propagating magnetohydrodynamics waves in coronal loops Authors: De Moortel, I. Bibcode: 2006RSPTA.364..461D Altcode: No abstract at ADS Title: 3D Numerical Simulations of Coronal Tectonics Authors: De Moortel, I.; Galsgaard, K. Bibcode: 2006IAUS..233..149D Altcode: We present the results of numerical simulations of 3D magnetic reconnection driven by photospheric footpoint motions. The model consists of two positive and two negative sources, which are placed on opposite boundaries of the cubic domain. Two different types of photospheric motions are then considered, namely rotating and twisting of the sources. These different footpoint motions result in a difference in the evolution of the magnetic skeleton and the location and efficiency of the energy build up. Both the dynamical evolution and the corresponding potential evolution of each system is investigated and a comparison is made between the energy storage and release that occurs at separators and separatrix surfaces. Title: An overview of coronal seismology Authors: De Moortel, I. Bibcode: 2005RSPTA.363.2743D Altcode: No abstract at ADS Title: D Numerical Simulations of Magnetic Reconnection Driven by Rotational Footpoint Motions Authors: De Moortel, I.; Galsgaard, K. Bibcode: 2005ESASP.600E..22D Altcode: 2005dysu.confE..22D; 2005ESPM...11...22D No abstract at ADS Title: Numerical Simulations of 3d Magnetic Reconnection due to Rotational Driving Authors: De Moortel, I.; Galsgaard, K. Bibcode: 2005ESASP.596E..31D Altcode: 2005ccmf.confE..31D No abstract at ADS Title: Tracing Coronal Waves Back to the Photosphere Authors: De Pontieu, B.; Erdelyi, R.; De Moortel, I.; Metcalf, T. Bibcode: 2005AGUSMSH11C..03D Altcode: There are now many observations of waves with periods around 5 minutes in the outer atmosphere of the Sun. We provide an observational overview of 5 minute periodicity in chromospheric spicules in active region plage, upper transition region moss and the low legs of coronal loops. Using a numerical model, we show that all of these phenomena are connected: normally evanescent photospheric oscillations can propagate into the low atmosphere as long as they are guided along magnetic field lines that are inclined away from the vertical. The leaked photospheric oscillations develop into shocks and lead to periodic upward chromospheric flows, which we have identified as active region spicules. These shocks continue upwards and enter into the corona. We suggest that TRACE observations of propagating acoustic waves in the corona are shocked and tunneled photospheric oscillations. Using SOHO/MDI, TRACE and Imaging Vector Magnetograph (Hawaii) data we explore how these coronal waves can be exploited to determine the connectivity between photosphere and corona,and thus allow seismology of the lower solar atmosphere. Title: How to Channel Photospheric Oscillations into the Corona Authors: De Pontieu, B.; Erdélyi, R.; De Moortel, I. Bibcode: 2005ApJ...624L..61D Altcode: There are now many observations of waves in the solar corona with periods around 5 minutes. The source of these waves is uncertain, although global p-modes in the photosphere are an obvious candidate, given the similarity of the dominant periods. However, p-modes are traditionally considered evanescent in the upper photosphere, and it has been unclear how they could propagate through the chromosphere into the corona. Using a numerical model, we show that photospheric oscillations with periods around 5 minutes can actually propagate into the corona so long as they are guided along an inclined magnetic flux tube. The nonverticality of the flux tube increases the acoustic cutoff period to values closer to the dominant periods of the photospheric oscillations, thus allowing tunneling or even direct propagation into the outer atmosphere. The photospheric oscillations develop into shocks, which drive chromospheric spicules and reach the corona. We suggest that Transition Region and Coronal Explorer (TRACE) observations of propagating magnetoacoustic waves in the corona represent these shocked and tunneled photospheric oscillations. We also explore how seismology of these waves could be exploited to determine the connectivity between photosphere and corona. Title: Coronal Seismology and the Propagation of Acoustic Waves along Coronal Loops Authors: Klimchuk, J. A.; Tanner, S. E. M.; De Moortel, I. Bibcode: 2004ApJ...616.1232K Altcode: 2004astro.ph.12085K We use a combination of analytical theory, numerical simulation, and data analysis to study the propagation of acoustic waves along coronal loops. We show that the intensity perturbation of a wave depends on a number of factors, including dissipation of the wave energy, pressure and temperature gradients in the loop atmosphere, work action between the wave and a flow, and the sensitivity properties of the observing instrument. In particular, the scale length of the intensity perturbation varies directly with the dissipation scale length (i.e., damping length) and the scale lengths of pressure, temperature, and velocity. We simulate wave propagation in three different equilibrium loop models and find that dissipation and pressure and temperature stratification are the most important effects in the low corona where the waves are most easily detected. Velocity effects are small and cross-sectional area variations play no direct role for lines of sight that are normal to the loop axis. The intensity perturbation scale lengths in our simulations agree very well with the scale lengths we measure in a sample of loops observed by TRACE. The median observed value is 4.35×109 cm. In some cases the intensity perturbation increases with height, which is likely an indication of a temperature inversion in the loop (i.e., temperature that decreases with height). Our most important conclusion is that thermal conduction, the primary damping mechanism, is accurately described by classical transport theory. There is no need to invoke anomalous processes to explain the observations. Title: Photospheric Oscillations in the Solar Atmosphere: Driving Chromospheric Spicules and Coronal Waves Authors: De Pontieu, B.; Erdelyi, R.; De Moortel, I.; Metcalf, T. Bibcode: 2004AGUFMSH13A1142D Altcode: There are now many observations of oscillations and waves with periods around 5 minutes in the solar transition region and corona. We provide an observational overview of 5 minute periodicity in upper transition region moss, the low legs of coronal loops, and chromospheric spicules in active region plage. The source of the 5 minute periodicity is unclear, since photospheric p-modes are evanescent in the upper photosphere which should prevent them from propagating into the chromosphere, transition region and corona. Using a numerical model we show that photospheric oscillations can propagate into the low atmosphere as long as they are guided along a magnetic flux tube that is inclined away from the vertical. The leaked photospheric oscillations develop non-linearly into shocks at low chromospheric heights because of the density decrease with height. The upward traveling shocks and resulting rebound shocks of the chromosphere lead to periodic upward chromospheric flows, which in a recent paper we have identified as the periodic spicules that we observe in active region plage. After passage through the spicule, these shocked photospheric oscillations propagate into the corona. We suggest that TRACE observations of propagating acoustic waves in the corona are shocked and tunneled photospheric oscillations. We also explore whether these coronal waves can be exploited to determine the connectivity between photosphere and corona, and thus perform seismology of the lower solar atmosphere. Title: Coronal Seismology and the Propagation of Acoustic Waves Along Coronal Loops Authors: Klimchuk, J. A.; Tanner, S. E.; De Moortel, I. Bibcode: 2004AGUFMSH24A..06K Altcode: We use a combination of analytical theory, numerical simulation, and data analysis to study the propagation of acoustic waves along coronal loops. We show that the intensity perturbation of a wave depends on a number of factors, including dissipation of the wave energy, pressure and temperature gradients in the loop atmosphere, work action between the wave and a flow, and the sensitivity properties of the observing instrument. In particular, the scale length of the intensity perturbation varies directly with the dissipation scale length (i.e., damping length) and the scale lengths of pressure, temperature, and velocity. We simulate wave propagation in three different equilibrium loop models and find that dissipation and pressure and temperature stratification are the most important effects in the low corona where the waves are most easily detected. Velocity effects are small, and cross-sectional area variations play no direct role for lines-of-sight that are normal to the loop axis. The intensity perturbation scale lengths in our simulations agree very well with the scale lengths we measure in a sample of loops observed by TRACE. The median observed value is 4.35×109 cm. In some cases the intensity perturbation increases with height, which is likely an indication of a temperature inversion in the loop (i.e., temperature that decreases with height). Our most important conclusion is that thermal conduction, the primary damping mechanism, is accurately described by classical transport theory. There is no need to invoke anomalous processes to explain the observations. Title: The damping of slow MHD waves in solar coronal magnetic fields. III. The effect of mode coupling Authors: De Moortel, I.; Hood, A. W.; Gerrard, C. L.; Brooks, S. J. Bibcode: 2004A&A...425..741D Altcode: The properties of slow MHD waves in a two dimensional model are investigated, in a low-beta plasma. Including a horizontal density variation causes ``phase mixing'' and coupling between slow and fast MHD waves. The effects of different density profiles, different driving frequencies, different values for the viscosity coefficient and plasma beta (<1) are studied. Using numerical simulations, it was found that the behaviour of the perturbed velocity was strongly dependent on the values of the parameters. From analytical approximations, a strong interaction with the fundamental, normal modes of the system was found to play an important role. The coupling to the fast wave proved to be an inefficient way to extract energy from the driven slow wave and is unlikely to be responsible for the rapid damping of propagating slow MHD waves, observed by TRACE. The ``phase mixing'' of the slow waves due to the (horizontal) density inhomogeneity does cause a significant amount of damping, but is again unlikely to be sufficiently strong to explain the rapid observed damping. Title: Waves and wavelets: An automated detection technique for solar oscillations Authors: De Moortel, I.; McAteer, R. T. J. Bibcode: 2004SoPh..223....1D Altcode: 2004SoPh..223....1M This paper investigates the possibility of automating the detection of propagating intensity perturbations in coronal loops using wavelet analysis. Two different sets of TRACE 171 Å images are studied using the automated wavelet routine presented by McAteer et al. (2004). Both localised, short-lived periodicities and sustained, periodic, oscillations are picked up by the routine, with the results dependent to a large extent on the signal-to-noise ratio of the dataset. At present, the automation is only partial; the relevance of the detected periodicity and the identification of the coronal structure supporting it still have to be determined by the user, as does the judging of the accuracy of the results. Care has to be taken when interpreting the results of the wavelet analysis, and a good knowledge of all possible factors that might influence or distort the results is a necessity. Despite these limitations, wavelet analysis can play an important role in automatically identifying a variety of phenomena and in the analysis of the ever-growing (observational or simulated) datasets. Title: Wavelet Analysis: the effect of varying basic wavelet parameters Authors: De Moortel, I.; Munday, S. A.; Hood, A. W. Bibcode: 2004SoPh..222..203D Altcode: The most commonly used methods to analyse (observed) quasi-periodic signals are standard techniques such as Fourier and wavelet analysis. Whereas a Fourier transform provides information on the dominant frequencies, wavelet analysis has the added advantage of providing the time localisation of the various frequency components. The usefulness and robustness of wavelet analysis is investigated by varying the different parameters which characterise the `mother' wavelet. We examine the effect of varying these parameters on the temporal and frequency resolution and the damping profile, which can be obtained from the wavelet transform. Additionally, the effect of a changing periodicity on the wavelet transform is investigated. Both simple harmonic functions and intensity oscillations observed by TRACE are used to demonstrate the various advantages and disadvantages of the different methods. In general, using the Paul wavelet or a smaller value of the wavelet parameter k provides a better time resolution, whereas the Morlet wavelet or a larger value of k improves the frequency resolution. Overall, our results indicate that great care is needed when using a wavelet analysis and that all the possible factors that could affect the transform should be taken into consideration. Title: Acoustic Wave Interpretation of Propagating Intensity Disturbances in Coronal Loops Authors: Klimchuk, J. A.; Tanner, S. E. M.; De Moortel, I. Bibcode: 2004AAS...204.9503K Altcode: 2004BAAS...36..826K Intensity disturbances have been observed by TRACE and EIT to propagate upward along the legs of long active region coronal loops. The periodic nature and speed of these disturbances suggest that they are traveling acoustic waves. It is being debated, however, whether the damping of the perturbations is consistent with the acoustic wave interpretation. We here examine this issue in detail with a combination of numerical simulation, analytical theory, and improved analysis of the observations. Using our state-of-the-art 1D hydro code, we simulate the propagation of waves generated at the base of model coronal loops. We consider static equilibrium loops having constant and expanding cross-section, and an equilibrium loop with steady flow. We show that the amplitude of the intensity perturbation is affected by a number of factors: wave dissipation (direct plasma heating), work done by the wave on the flow, pressure stratification, nonuniform temperature, and temperature-dependent sensitivity of the observing instrument. We compare our theoretical results with intensity scale lengths measured in a sample of loops observed by TRACE.

Research supported by NASA and ONR. Title: Observations and theory of slow waves in coronal loops Authors: De Moortel, I.; Hood, A. W. Bibcode: 2004AAS...204.9502D Altcode: 2004BAAS...36..826D High cadence TRACE observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops, close to active regions. An overview is given of measured parameters of such longitudinal oscillations in coronal loops. The observed oscillations are interpreted as propagating slow magneto-acoustic waves and are unlikely to be flare-driven. A theoretical model of slow magneto-acoustic waves, incorporating the effects of gravitational stratification, the magnetic field geometry, thermal conduction and compressive viscosity is presented to explain the very short observed damping lengths. The results of these numerical simulations are compared with the TRACE observations. Preliminary results indicate that thermal conduction and the magnetic field geometry play an important role. Title: The damping of slow MHD waves in solar coronal magnetic fields. II. The effect of gravitational stratification and field line divergence Authors: De Moortel, I.; Hood, A. W. Bibcode: 2004A&A...415..705D Altcode: This paper continues the study of De Moortel & Hood (\cite{Moortelh03}) into the propagation of slow MHD waves in the solar corona. Firstly, the damping due to optically thin radiation is investigated and compared to the effect of thermal conduction. In a second stage, gravitational stratification is included in the model and it is found that this increases the damping length significantly. Finally, the effect of different magnetic field geometries on the damping of the slow waves is investigated. As a first approximation, a purely radial magnetic field is considered and although the amplitudes of the perturbations decrease due to the divergence of the field, the effect is small compared to the effect of thermal conduction. A more realistic local geometry, estimated from the observations, is investigated and it is demonstrated that a general area divergence can cause a significant, additional, decrease of the amplitudes of the perturbations. The results of numerical simulations, incorporating the effects of gravitational stratification, the magnetic field geometry and thermal conduction are compared with TRACE observations of propagating waves in coronal loops. It is found that a combination of thermal conduction and (general) area divergence yields detection lengths that are in good agreement with observed values. Title: Time-Frequency Analysis of Quasi-Periodic Signals Authors: De Moortel, I.; Munday, S.; Hood, A. W. Bibcode: 2004ESASP.547..501D Altcode: 2004soho...13..501D In recent years, the analysis of quasi-periodic signals observed by satellites such as SOHO and TRACE has become increasingly important. So far, mostly standard methods have been used, such as Fourier analysis to identify the dominant frequencies and wavelet analysis to provide the time localisation of the various frequency components. We compare the temporal and frequency resolution of different `time-frequency' methods. In particular, the usefulness and robustness of wavelet analysis is investigated by varying the different parameters which characterise the `mother' wavelet. Both simple harmonic functions and intensity oscillations observed by TRACE are used to demonstrate the various advantages and disadvantages of the different methods. Title: A Search for Photospheric Sources of Coronal Longitudinal Oscillations Authors: Ireland, J.; De Moortel, I.; Walsh, R. W.; Moretti, P. F. Bibcode: 2004ESASP.547...57I Altcode: 2004soho...13...57I It has recently been shown that longitudinal intensity fluctuations observed in TRACE 171 Å loops come in what appear to be two separate populations. These populations are differentiated by their period, and are clustered distinctly around 3 and 5 minute periods. The 3 minute fluctuations appear to be rooted in sunspots, whereas the 5 minute sunspots are not. This study presents two test cases in the search for a photospheric source to these oscillations. A wavelet analysis is presented in the search for a fluctuating magnetic component since previous studies show that a magnetic fluctuation may be intermittent. A Fourier analysis is used to look in the intensity and Doppler regions of the same area of interest. Some comments are made on the photosphere in relation to the search for the driver of the as yet unobserved driver of longitudinal coronal oscillations. Title: Longitudinal Oscillations in Coronal Loops - Joint Observations with SOHO/CDS and TRACE Authors: Marsh, M. S.; Walsh, R. W.; De Moortel, I.; Ireland, J. Bibcode: 2004ESASP.547..519M Altcode: 2004soho...13..519M Joint Observing Program (JOP) 83 Solar and Heliospheric Observatory/Coronal Diagnostic Spectrometer (SOHO/CDS) and Transition Region and Coronal Explorer (TRACE) data is analysed for evidence of propagating intensity oscillations along loop structures in the solar corona. A propagating intensity oscillation with a minimum estimated speed of 50-195 km s is observed within a TRACE 171 Å coronal loop using a running difference method. Co-spatial and co-temporal CDS and TRACE observations of this loop are analysed using a wavelet analysis method. The TRACE data shows a propagating oscillation with a period of 300 s. This period is also observed with CDS suggesting propagating oscillations at chromospheric, transition region and coronal temperatures in the He I, O V and Mg IX lines. Title: Observations and Theory of Longitudinal Waves in Coronal Loops Authors: De Moortel, I.; Hood, A. W.; De Pontieu, B. Bibcode: 2004ESASP.547..427D Altcode: 2004soho...13..427D High cadence TRACE observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops, close to active regions. An overview is given of measured parameters of such longitudinal oscillations in coronal loops. The observed oscillations are interpreted as propagating slow magnetoacoustic waves and are unlikely to be flare-driven. A basic magnetic field extrapolation is used to estimate the local geometry of the magnetic field. A theoretical model of slow magneto-acoustic waves, incorporating the effects of gravitational stratification, the magnetic field geometry, thermal conduction and compressive viscosity is presented to explain the very short observed damping lengths. The results of these numerical simulations are compared with the TRACE observations. Preliminary results indicate that the magnetic field geometry plays an important role. Title: The damping of slow MHD waves in solar coronal magnetic fields Authors: De Moortel, I.; Hood, A. W. Bibcode: 2003A&A...408..755D Altcode: A theoretical description of slow MHD wave propagation in the solar corona is presented. Two different damping mechanisms, namely thermal conduction and compressive viscosity, are included and discussed in detail. We revise the properties of the ``thermal'' mode, which is excited when thermal conduction is included. The thermal mode is purely decaying in the case of standing waves, but is oscillatory and decaying in the case of driven waves. When thermal conduction is dominant, the waves propagate largely undamped, at the slower, isothermal sound speed. This implies that there is a minimum damping time (or length) that can be obtained by thermal conduction alone. The results of numerical simulations are compared with TRACE observations of propagating waves, driven by boundary motions, and standing waves observed by SUMER/SOHO, excited by an initial impulse. For typical coronal conditions, thermal conduction appears to be the dominant damping mechanism. Title: Determination of coronal loop properties from trace observations Authors: De Moortel, I.; Parnell, C. E.; Hood, A. W. Bibcode: 2003SoPh..215...69D Altcode: In this paper, we determine the temperature profile along the footpoints of large coronal loops observed by TRACE in both the 171 Å and 195 Å passbands. The temperature along the lower part of these coronal loops only shows small variations and can probably be considered to be isothermal. Using the obtained temperature profile T(s) and an estimate of the column depth along the loop, we then determine the pressure along the lower part of the observed coronal loops and hence the value of the pressure scale length. The obtained scale lengths correspond in order-of-magnitude with the theoretically predicted gravitational scale height. We show that the differences between the observed and predicted scale heights are unlikely to be caused by (significant) flows along the loops but could possibly be a consequence of the inclination of the loops. This implies that the quasi-periodic intensity oscillations observed in the loops are most probably caused by compressive waves propagating upward at the coronal sound speed. Title: Joint observations of propagating oscillations with SOHO/CDS and TRACE Authors: Marsh, M. S.; Walsh, R. W.; De Moortel, I.; Ireland, J. Bibcode: 2003A&A...404L..37M Altcode: Joint Observing Program (JOP) 83 Solar and Heliospheric Observatory/Coronal Diagnostic Spectrometer (SOHO/CDS) and Transition Region and Coronal Explorer (TRACE) data is analysed for evidence of propagating intensity oscillations along loop structures in the solar corona. A propagating intensity oscillation with a minimum estimated speed of 50-195 km s-1 is observed within a TRACE 171 Å coronal loop using a running difference method. Co-spatial and co-temporal CDS and TRACE observations of this loop are analysed using a wavelet analysis method. The TRACE data shows a propagating oscillation with a period of ~300 s. This period is also observed with CDS suggesting propagating oscillations at chromospheric, transition region and coronal temperatures in the He I, O V and Mg Ix lines. Title: Hydrodynamic Simulations of Longitudinal Intensity Oscillations Observed in Coronal Loops by TRACE Authors: Tanner, S. E.; Klimchuk, J. A.; Hood, A. W.; De Moortel, I. Bibcode: 2003SPD....34.0406T Altcode: 2003BAAS...35..811T Propagating intensity disturbances are often observed by TRACE in large coronal loops located at the perimeters of active regions (e.g., De Moortel et al., 2002, Solar Phys., 209, 61). On average, the disturbances have periods of 280 s, propagation speeds of 120 km s-1, intensity amplitudes of 4%, and surprisingly small damping (detection) lengths of 9000 km. In addition, there is a positive correlation between damping length and period. The preliminary interpretation of these disturbances is that they are rapidly dissipating slow magneto-acoustic waves.

To investigate this interpretation more rigorously, we have performed a series of detailed coronal loop simulations using our 1D hydrodynamic code, ARGOS. We generate waves in the loop by imposing a spatially localized oscillating force at the loop footpoint, using a range of different oscillation periods. We here report on the results of our study and, in particular, whether the damping lengths have the properties observed by TRACE.

This work was supported by NASA and ONR. Title: Thermal conduction damping of longitudinal waves in coronal loops Authors: De Moortel, I.; Hood, A. W. Bibcode: 2003PADEU..13..127D Altcode: High cadence TRACE observations show that outward propagating intensity disturbances are a common feature in large coronal loops. An overview is given of measured parameters of such longitudinal waves in coronal loops. We found that loops that are situated above sunspot regions display intensity oscillations with periods centred around 3 minutes, whereas oscillations in `non-sunspot' loops show periods centred around 5 minutes. The observed longitudinal waves are interpreted as propagating slow magneto-acoustic waves and we show that the disturbances are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. We found that (slightly enhanced) thermal conduction could account for the observed damping lengths. Title: An overview of longitudinal oscillations in coronal loops Authors: De Moortel, I.; Hood, A. W.; Ireland, J.; Walsh, R. W. Bibcode: 2002ESASP.506..509D Altcode: 2002svco.conf..509D; 2002ESPM...10..509D High cadence TRACE observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops. An overview is given of geometric and physical parameters of such propagating disturbances observed in 38 coronal loops. We found that loops that are situated above sunspot regions display intensity oscillations with periods centred around 3 minutes, whereas oscillations in 'non-sunspot' loops show periods centred around 5 minutes. The observed longitudinal oscillations are interpreted as propagating slow magneto-acoustic waves and we show that the disturbances are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. We present a simple theoretical model to explain the observed features. Title: Observational evidence of underlying driving of longitudinal oscillations in coronal loops Authors: De Moortel, I.; Ireland, J.; Hood, A. W.; Walsh, R. W. Bibcode: 2002ESASP.505..211D Altcode: 2002IAUCo.188..211D; 2002solm.conf..211D We give an overview of both geometric and physical parameters of propagating disturbances in coronal loops, using high cadence TRACE data (JOP83 & JOP144). The majority of these outward propagating oscillations are found in the footpoints of large diffuse coronal loop structures, close to active regions. The disturbances travel outward with a propagation speed v = 122±43 km s-1. The variations in intensity are estimated to be of the order of 4.1±1.5%, compared to the background brightness and are found to be damped very quickly, within 8.9±4.4 Mm along the loop. Using a wavelet analysis, periods in the 282±93 seconds range are obtained. However, it was found that loops that are situated above sunspot regions display intensity oscillations with a period smaller than 200 seconds, whereas oscillations in 'non-sunspot' loops show periods larger than 200 seconds. This result provides evidence that the underlying oscillations can propagate through the transition region and into the corona. We conclude that the observed longitudinal oscillations are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. Title: Examination of the photospheric magnetic field underlying longitudinally oscillating coronal loops Authors: Ireland, J.; Walsh, R. W.; De Moortel, I.; Moretti, P. F. Bibcode: 2002ESASP.505..429I Altcode: 2002IAUCo.188..429I; 2002solm.conf..429I Longitudinally oscillating coronal loops have been seen in TRACE 171 Å data in many different quiescent active regions. The oscillation is thought to be an example of an outwardly propagating slow magneto-acoustic wave. However, the source of these waves is as yet unknown. In the context of SOHO Joint Observing Program 144, we search for a possible photospheric driver to these waves. We examine the photospheric longitudinal magnetic flux underlying an oscillating loop observed between 1200-1300 UT on June 7th 2001. The field was imaged using the Kanzelhöhe Magneto-Optical Filter instrument and the SOHO Michelson Doppler Imager (MDI). The dynamics of the photospheric magnetic field underlying these loops is discussed in the context of possible mechanisms causing the observed coronal oscillations. Title: Longitudinal intensity oscillations in coronal loops observed with TRACE II. Discussion of Measured Parameters Authors: De Moortel, I.; Hood, A. W.; Ireland, J.; Walsh, R. W. Bibcode: 2002SoPh..209...89D Altcode: In this paper, we give a detailed discussion of the parameters of longitudinal oscillations in coronal loops, described in Paper I. We found a surprising absence of correlations between the measured variables, with the exception of a relation between the estimated damping length and the period of the intensity variations. Only for 2 out of the 38 cases presented in Paper I did we find a significant perturbation in the 195 Å TRACE data. The loops supporting the propagating disturbances were typically stable, quiescent loops and the total luminosity of the analyzed structures generally varied by no more than 10%. The observed density oscillations are unlikely to be flare-driven and are probably caused by an underlying driver exciting the loop footpoints. It was demonstrated that the rapid damping of the perturbations could not simply be explained as a consequence of the decreasing intensity along the loops. However, we found that (slightly enhanced) thermal conduction alone could account for the observed damping lengths and wavelengths, and, additionally, explain the correlation between propagation period and damping length. Title: Longitudinal intensity oscillations in coronal loops observed with TRACE I. Overview of Measured Parameters Authors: De Moortel, I.; Ireland, J.; Walsh, R. W.; Hood, A. W. Bibcode: 2002SoPh..209...61D Altcode: In this paper we aim to give a comprehensive overview of geometric and physical properties of longitudinal oscillations in large coronal loops. The 38 examples of propagating disturbances were obtained from the analysis of high cadence, 171 Å TRACE data (JOP 83 and JOP 144). The majority of these outward propagating oscillations are found in the footpoints of large diffuse coronal loop structures, close to active regions. The disturbances travel outward with a propagation speed of the order of v≈122±43 km s−1. The variations in intensity are estimated to be roughly 4.1±1.5% of the background loop brightness. The propagating disturbances are found to be damped very quickly and are typically only detected in the first 8.9±4.4 Mm along the loop. Using a wavelet analysis, periods of the order of 282±93 s are found and the energy flux was estimated as 342±126 erg cm−2 s−1. We found highly filamentary behavior in the lower part of the coronal loops and showed that the intensity oscillations can be present for several consecutive hours, with a more or less constant period. It is evident that the longitudinal oscillations are a widespread, regularly occurring coronal phenomena. A companion paper is devoted to the interpretation and discussion of the results. Title: Application of wavelet analysis to transversal coronal loop oscillations Authors: Ireland, J.; De Moortel, I. Bibcode: 2002A&A...391..339I Altcode: There as yet remain few examples of well observed, transversal oscillations in coronal loops. Such oscillations have the potential to yield much information on the nature of the solar corona, as demonstrated by the analysis of Nakariakov et al. (\cite{nak}) of a transversely oscillating loop observed in the TRACE 171 Å passband on 14th July, 1998. Their analysis extracts a decaying loop oscillation signal from the data which is then considered in the light of the substantial body of theoretically and computationally derived knowledge of the dynamics of coronal loops. The analysis presented in this paper approaches the reduction of the same dataset using wavelet techniques described by De Moortel & Hood (\cite{demhood}) and De Moortel et al. (\cite{dhi}). The authors show that the value of the decay exponent N in a decaying oscillating time series of the form exp (-ktN) is measurable from a wavelet transform of the time series (for some decay constant k and time t). The application of these techniques shows that the value of the decay exponent in the 14th July, 1998 event is not well determined by the data, i.e., the associated error is very large. Since the value of the decay exponent implies the presence of particular decay mechanisms and not others, the large error associated with the exponent value implies that a wide range of mechanisms should be considered when discussing the physics behind this event. Comments are also made on the time dependence of the oscillation wavelet scale. Two additional examples of transversal coronal loop oscillations are also analysed. Title: Preliminary description of Kanzelhöhe/MDI magnetograms and the search for sources of coronal oscillations Authors: Ireland, J.; Walsh, R. W.; De Moortel, I.; Moretti, P. F. Bibcode: 2002ESASP.508..299I Altcode: 2002soho...11..299I Many examples of transverse (Schrijver et al., 2002; Aschwanden et al., 2002) and longitudinal coronal loop oscillations have now been observed in TRACE 171 Å data (see De Moortel et al., 2002 at this meeting for examples of longitudinal oscillations). These oscillations hold the promise of telling us much about the physics of the corona. However, the mechanisms describing these distinct phenomena are as yet unclear. Magnetogram data from MDI and Kanzelhöhe taken as part of SOHO Joint Observing 144 allows us to use the spatial resolution of MDI and temporal resolution of Kanzelhöhe to probe the photospheric magnetic field at likely footpoint sources of coronal loop oscillations at length and time scales not available to either instrument separately. Variations in the photospheric magnetic field are analysed in conjunction with co-temporally observed TRACE 171 Å derived time series. Title: Trace observations of propagating slow magneto-acoustic disturbances in coronal loops Authors: De Moortel, I.; Ireland, J.; Walsh, R. W. Bibcode: 2002ESASP.508..275D Altcode: 2002soho...11..275D We study propagating disturbances in 38 coronal loops and give an overview of their properties using high cadence, 171 Å, TRACE data (JOP 83 & JOP 144). The majority of these outward propagating oscillations are found in the footpoints of large diffuse coronal loop structures, close to active regions. The disturbances travel outward with a propagation speed of the order of v ≍ 119+/-39 km/s. The variations in intensity are estimated to be roughly 4.1+/-1.6% of the background brightness and the propagating disturbances are found to be damped very quickly, within 8.6+/-3.8 Mm along the loop. Using a wavelet analysis, periods of the order of 282+/-93 seconds are found and the energy flux was estimated as 346+/-132 ergs/cm2s. It is suggested that these oscillations are slow magneto-acoustic waves propagating along the lower part of large, quiescent, coronal loops. Title: The detection of 3 & 5 min period oscillations in coronal loops Authors: De Moortel, I.; Ireland, J.; Hood, A. W.; Walsh, R. W. Bibcode: 2002A&A...387L..13D Altcode: High cadence, 171 Alfvén A, TRACE observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops. These oscillations are interpreted as propagating slow magneto-acoustic waves. Using a wavelet analysis, we found periods of the order of 282 +/- 93 s. However, a careful study of the location of the footpoints revealed a distinct separation between those loops that support oscillations with periods smaller than 200 s and periods larger than 200 s. It was found that loops that are situated above sunspot regions display intensity oscillations with a period of the order of 172 +/- 32 s, whereas oscillations in ``non-sunspot'' loops show periods of the order of 321 +/- 74 s. We conclude that the observed longitudinal oscillations are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. This result suggests that the underlying oscillations can propagate through the transition region and into the corona. Title: Coronal seismology through wavelet analysis Authors: De Moortel, I.; Hood, A. W.; Ireland, J. Bibcode: 2002A&A...381..311D Altcode: This paper expands on the suggestion of De Moortel & Hood (\cite{DeMoortel00}) that it will be possible to infer coronal plasma properties by making a detailed study of the wavelet transform of observed oscillations. TRACE observations, taken on 14 July 1998, of a flare-excited, decaying coronal loop oscillation are used to illustrate the possible applications of wavelet analysis. It is found that a decay exponent n ~ 2 gives the best fit to the double logarithm of the wavelet power, thus suggesting an e-varepsilon t^2 damping profile for the observed oscillation. Additional examples of transversal loop oscillations, observed by TRACE on 25 October 1999 and 21 March 2001, are analysed and a damping profile of the form e-varepsilon t^n, with n ~ 0.5 and n ~ 3 respectively, is suggested. It is demonstrated that an e-varepsilon t^n damping profile of a decaying oscillation survives the wavelet transform, and that the value of both the decay coefficient varepsilon and the exponent n can be extracted by taking a double logarithm of the normalised wavelet power at a given scale. By calculating the wavelet power analytically, it is shown that a sufficient number of oscillations have to be present in the analysed time series to be able to extract the period of the time series and to determine correct values for both the damping coefficient and the decay exponent from the wavelet transform. Title: Wavelet analysis and the determination of coronal plasma properties Authors: De Moortel, I.; Hood, A. W. Bibcode: 2000A&A...363..269D Altcode: The usefulness of wavelet analysis is demonstrated by considering analytical expressions for phase mixed Alfvén waves in different physical circumstances. The wavelet analysis is briefly introduced, using the complex-valued Morlet wavelet, consisting of a plane wave modulated by a Gaussian, as the basic wavelet. The time and scale resolution of the wavelet transform are then discussed in more detail, by working out the transform of simple harmonic functions analytically. As an illustration of the power of wavelet analysis, phase mixed Alfvén waves are investigated. A comparison is made between a truly finite harmonic wave and an Alfvén wave, dissipated by phase mixing and, using the wavelet transform, it is demonstrated that it is possible to distinguish between these two `finite' signals. It is also possible to extract the value of the dissipation coefficient from the wavelet transform. When considering phase mixing of Alfvén waves in a gravitationally stratified atmosphere, the lengthening of the wavelengths is clearly evident in the transform, which provides an independent estimate of the value of the pressure scale height. In a radially diverging atmosphere, the shortening of the wavelengths is also apparent in the wavelet transform, showing how the Alfvén speed varies along the loop and thus providing information on the coronal density and magnetic field. When applying wavelet analysis to observed wave-like oscillations, it should be possible to infer properties of the coronal plasma by making a detailed study of the wavelet transform. Title: Observation of oscillations in coronal loops Authors: De Moortel, I.; Walsh, R. W.; Ireland, J. Bibcode: 2000AIPC..537..216D Altcode: 2000wdss.conf..216D High cadence TRACE data (JOP 83) in the 171 Å bandpass are used to report on several examples of outward propagating oscillations in the footpoints of large diffuse coronal loop structures close to active regions. The disturbances travel outward with a propagation speed between 70 and 160 km s-1. The variations in intensity are of the order of 2%-4%, compared to the background brightness and these get weaker as the disturbance propagates along the structure. From a wavelet analysis at different positions along the structures, periods in the 200-400 seconds range are found. It is suggested that these oscillations are slow magneto-acoustic waves propagating along the loop, carrying an estimated energy flux of 4×102 ergs cm-2 s-1. . Title: Phase mixing of Alfvén waves in an open and stratified atmosphere Authors: De Moortel, I.; Hood, A. W.; Arber, T. D. Bibcode: 2000AIPC..537..224D Altcode: 2000wdss.conf..224D Phase mixing was introduced by Heyvaerts and Priest [1] as a mechanism for heating plasma in open magnetic field regions. Here we include a stratified density and a diverging background magnetic field. We present numerical and WKB solutions to describe the effect of stratification and divergence on phase mixing of Alfvén waves. It is shown that the decrease in density lengthens the oscillation wavelengths and thereby reduces the generation of transverse gradients. However, the divergence of the field lines shortens the wavelengths and thus enhances the generation of gradients. Furthermore we found that in a stratified atmosphere, ohmic heating is spread out over a greater height range whereas viscous heating is not strongly influenced by the stratification. A wavelet analysis indicated that the wavelet transform could provide us with information about the medium the waves are traveling through. . Title: Observation of oscillations in coronal loops Authors: De Moortel, I.; Ireland, J.; Walsh, R. W. Bibcode: 2000A&A...355L..23D Altcode: On March 23rd 1999, a set of TRACE observations in the 171 Alfvén A (Fe Ix) bandpass was made of active region AR 8496. A wavelet analysis of a bright loop-footpoint to the south west of this active region displays outward propagating perturbations with periods 180-420 seconds at approximately 70-165 km s-1. We suggest that these oscillations are slow magneto-acoustic waves propagating along the loop, carrying an estimated energy flux of 4 x 102 ergs cm-2 s-1. Title: Phase mixing of Alfvén waves in a stratified and radially diverging, open atmosphere Authors: De Moortel, I.; Hood, A. W.; Arber, T. D. Bibcode: 2000A&A...354..334D Altcode: Phase mixing was proposed by Heyvaerts and Priest (1983) as a mechanism for heating the plasma in open magnetic field regions of coronal holes. Here the basic model is modified to include a gravitationally stratified density and a diverging background magnetic field. We present WKB solutions and use a numerical code to describe the effect of dissipation, stratification and divergence on phase mixing of Alfvén\ waves. It is shown that the wavelengths of an Alfvén\ wave is shortened as it propagates outwards which enhances the generation of gradients. Therefore, the convection of wave energy into heating the plasma occurs at lower heights than in a uniform model. The combined effect of a stratified density and a radially diverging background magnetic field on phase mixing of Alfvén\ waves depends strongly on the particular geometry of the configuration. Depending on the value of the pressure scale height, phase mixing can either be more or less efficient than in the uniform case. Title: Phase Mixing of Alfvén Waves in an Open and Stratified Atmosphere Authors: De Moortel, I.; Hood, A. W.; Arber, T. D. Bibcode: 1999ESASP.448..257D Altcode: 1999ESPM....9..257D; 1999mfsp.conf..257D No abstract at ADS Title: Phase mixing of Alfvén waves in a stratified and open atmosphere Authors: De Moortel, I.; Hood, A. W.; Ireland, J.; Arber, T. D. Bibcode: 1999A&A...346..641D Altcode: Phase mixing was introduced by Heyvaerts and Priest (1983) as a mechanism for heating the plasma in the open magnetic field regions of coronal holes. Here the basic process is modified to include a stratified atmosphere in which the density decreases with height. We present an analytical solution in the case of zero dissipation and use a numerical code in the non-zero dissipation case to describe the effect of stratification on phase mixing. The exponential damping behaviour derived by Heyvaerts and Priest is largely confirmed in the non stratified limit. However, it is shown that the decrease in density lengthens the oscillation wavelengths and thereby reduces the generation of transverse gradients. Furthermore we found that in a stratified atmosphere the perturbed magnetic field and velocity behave quite differently depending on whether we consider resistivity or viscosity. Ohmic heating is spread out over a greater height range in a stratified medium whereas viscous heating is not strongly influenced by the stratification.