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We analyse quasi-periodic pulsations (QPP) detected in the microwave and decimetre radio emission of the 5 September 2017 7:04 UT (SOL2017-09-05T07:04) solar flare, using simultaneous observations by the Siberian Radioheliograph 48 (SRH-48, 4 – 8 GHz) and Mingantu Spectral Radioheliograph (MUSER-I, 0.4 – 2 GHz). The microwave emission was broadband with a typical gyrosynchrotron spectrum, while a quasi-periodic enhancement of the decimetric emission appeared in a narrow spectral band (500 – 700 MHz), consistent with the coherent-plasma-emission mechanism. The periodicity that we found in microwaves is about 30 seconds, coming from a compact loop-like source with a typical height of about 31 Mm. The decimetric emission exhibited a periodicity of about 6 seconds. We suggest a qualitative scenario linking the QPPs observed in both incoherent and coherent spectral bands and their generation mechanisms. The properties of the QPPs found in the microwave signal are typical for perturbations of the flare loop by the standing sausage mode of a fast magnetohydrodynamic (MHD) wave. Our analysis indicated that this sausage-oscillating flare loop was the primary source of oscillations in the discussed event. The suggested scenario is that a fundamental sausage harmonic is the dominant cause for the observed QPPs in the microwave emission. The initiation of oscillations in the decimetric emission is caused by the third sausage harmonic via periodic and nonlinear triggering of the acceleration processes in the current sheets, formed at the interface between the sausage-oscillating flare loop and the external coronal loop that extended to higher altitudes. Our results demonstrate the possible role of MHD wave processes in the release and transport of energy during solar flares, linking coherent and incoherent radio emission mechanisms.

A major, albeit serendipitous, discovery of the SOlar and Heliospheric Observatory mission was the observation by the Extreme Ultraviolet Telescope (EIT) of large-scale extreme ultraviolet (EUV) intensity fronts propagating over a significant fraction of the Sun’s surface. These so-called EIT or EUV waves are associated with eruptive phenomena and have been studied intensely. However, their wave nature has been challenged by non-wave (or pseudo-wave) interpretations and the subject remains under debate. A string of recent solar missions has provided a wealth of detailed EUV observations of these waves bringing us closer to resolving the question of their nature. With this review, we gather the current state-of-the-art knowledge in the field and synthesize it into a picture of an EUV wave driven by the lateral expansion of the CME. This picture can account for both wave and pseudo-wave interpretations of the observations, thus resolving the controversy over the nature of EUV waves to a large degree but not completely. We close with a discussion on several remaining open questions in the field of EUV waves research.

The Hall effect due to weak ionization in the lower solar atmosphere is shown to produce significant coupling between slow magneto-acoustic and Alfvén waves, especially in highly inclined magnetic fields, and even at low frequencies ( ≈ 5  mHz and above). Based on the exact magneto-acoustic linear wave solutions in a 2D isothermal model atmosphere, a perturbation approach is used to calculate the coupling to Alfvén waves polarized in the third dimension. First, a fast wave is injected at the bottom and is partially and often strongly reflected/converted to a down-going slow wave at the Alfvén-acoustic equipartition height, depending on magnetic field inclination, frequency, and wave number. This slow wave then couples strongly to the down-going Alfvén wave via the Hall effect for realistic Hall parameters. The coupling is strongest for horizontal wavenumbers oriented opposite to the field inclination, and magnetic fields around 100 G, for which large values of the Hall parameter are co-spatial with the region where slow and Alfvén waves have almost identical wave forms. Second, a slow wave is injected at the bottom, and found to couple even more strongly to up-going Alfvén waves in certain regions of the wavenumber–frequency plane where acoustic-gravity waves are evanescent. These results contrast with those for Hall-mediated fast-Alfvén coupling, which occurs higher in the atmosphere and is evident only at much higher frequencies.

In this study, we present the observations of extreme-ultraviolet (EUV) waves associated with an M6.5 flare on 2013 April 11. The event was observed by Solar Dynamics Observatory (SDO) in different EUV channels. The flare was also associated with a halo CME and type II radio bursts. We observed both fast and slow components of the EUV wave. The speed of the fast component, which is identified as a fast-mode MHD wave, varies in the range from 600  to  640 km s − 1 , whereas the speed of the slow-component is ≈ 140 km s − 1 . We observed the unusual phenomenon that, as the fast-component EUV wave passes through two successive magnetic quasi-separatrix layers (QSLs), two stationary wave fronts are formed locally. We propose that part of the outward-propagating fast-mode EUV wave is converted into slow-mode magnetohydrodynamic waves, which are trapped in local magnetic field structures, forming successive stationary fronts. Along the other direction, the fast-component EUV wave also creates oscillations in a coronal loop lying ≈ 225 Mm away from the flare site. We have computed the energy of the EUV wave to be of the order of 10 20 J .

Planar acoustically dominated magnetohydrodynamic waves are initiated at the high- β base of a simulated 2D isothermal stratified atmosphere with potential magnetic field exhibiting both open and closed field regions as well as neutral points. They shock on their way upward toward the Alfvén–acoustic equipartition surface a = c , where a and c are the Alfvén and sound speeds, respectively. Expanding on recent 1.5D findings that such shocks mode-convert to fast shocks and slow smoothed waves on passing through a = c , we explore the implications for these more complex magnetic geometries. It is found that the 1.5D behaviour carries over to the more complex case, with the fast shocks strongly attracted to neutral points, which are disrupted producing extensive fine structure. It is also observed that shocks moving in the opposite direction, from a > c to a < c , split into fast and slow components too, and that again it is the slow component that is smoothed.

We have studied the nature of the magnetohydrodynamic (MHD) kink waves in magnetically twisted flux tubes in the presence of plasma flow. To do this, the eigenfunctions of the kink oscillations have been determined using the dispersion relation and the boundary conditions of the tube. Then the components of the magnetic-tension force and the gradient of the pressure force have been obtained to determine the nature of the waves. For the waves with positive azimuthal wavenumber, the magnetic twist and plasma flow have opposite effects on the ratio of restoring forces and the wave has a mixed nature. However, for the waves with negative azimuthal wavenumber the magnetic twist and plasma flow strengthen the effects of each other in increasing the ratio of the magnetic-tension force to the gradient of the pressure force, and they make the nature of the wave more Alfvénic. In the presence of both plasma flow and magnetic twist, in the case of the waves with negative azimuthal wavenumber, for some specific values of the tube parameters, the magnetic-tension force becomes the dominant restoring force both in the radial and azimuthal directions, and the wave can be considered as an Alfvén wave in the internal region of the tube. However, in the case of the waves with positive azimuthal wavenumber, the nature of the wave remains mixed under all circumstances.

We present Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) observation of three types of fast-mode, propagating, magnetosonic waves in a GOES C3.0 flare on 23 April 2013, which was accompanied by a prominence eruption and a broad coronal mass ejection (CME). During the fast-rising phase of the prominence, a large-scale, dome-shaped, extreme-ultraviolet (EUV) wave firstly formed ahead of the CME bubble and propagated at a speed of about 430 km s −1 in the CME’s lateral direction. One can identify the separation process of the EUV wave from the CME bubble. The reflection effect of the on-disk counterpart of this EUV wave was also observed when it interacted with a remote active region. Six minutes after the first appearance of the EUV wave, a large-scale, quasi-periodic EUV train with a period of about 120 seconds, which emanated from the flare epicenter and propagated outward at an average speed up to 1100 km s −1 , appeared inside the CME bubble. In addition, another narrow, quasi-periodic EUV wave train, which also emanated from the flare epicenter, propagated at a speed of about 475 km s −1 and with a period of about 110 seconds, was observed along a closed-loop system connecting two adjacent active regions. We propose that all of the observed waves are fast-mode magnetosonic waves, in which the large-scale, dome-shaped EUV wave ahead of the CME bubble was driven by the expansion of the CME bubble, while the large-scale, quasi-periodic EUV train within the CME bubble and the narrow quasi-periodic EUV wave train along the closed-loop system were excited by the intermittent energy-releasing process in the flare. Coronal seismology application and energy carried by the waves are also estimated based on the measured wave parameters.

We analyse the phase shifts of standing, slow magnetohydrodynamic (MHD) waves in solar coronal loops using a linear MHD model taking into account the role of thermal conductivity, compressive viscosity, radiative losses, and heating–cooling misbalance. We estimate the phase shifts in time and space of density and temperature perturbations with respect to velocity perturbations and also calculate the phase difference between density and temperature perturbations. The overall significance of compressive viscosity is found to be negligible for most of the loops considered in the study. For loops with high background density and/or low background temperature, the role of radiative losses (with heating–cooling misbalance) is found to be more significant. Also, the effect of heating–cooling misbalance with a temperature- and density-dependent heating function is found to be more significant in the case of longer loop lengths ( L = 500  Mm). We derived a general expression for the polytropic index [ γ eff ] and found that under linear MHD the effect of compressive viscosity on the polytropic index is negligible. The radiative losses with constant heating lead to a monotonic increase of γ eff with increasing density, whereas the consideration of an assumed heating function [ H ( ρ , T ) ∝ ρ a T b , where a = − 0.5 and b = − 3 ] makes the γ eff peak at a certain loop density. We also explored the role of different heating functions by varying the free parameters a and b for a fixed loop of ρ 0 = 10 − 11  kg m −3 , T 0 = 6.3  MK, and loop length L = 180  Mm. We find that the consideration of different heating functions [ H ( ρ , T ) ] leads to a significant variation of the phase difference between density and temperature perturbations; however, the polytropic index remains close to a value of 1.66.

We investigate the transverse coronal-loop oscillations induced by the eruption of a prominence-carrying flux rope on 7 December 2012. The flux rope, originating from NOAA Active Region (AR) 11621, was observed in extreme-ultraviolet (EUV) wavelengths by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) spacecraft and in the H α line center by the ground-based telescope at the Big Bear Solar Observatory (BBSO). The early evolution of the flux rope is divided into two steps: a slow-rise phase at a speed of ≈ 230 km s −1 and a fast-rise phase at a speed of ≈ 706 km s −1 . The eruption generates a C5.8 flare and the onset of the fast rise is consistent with the hard X-ray (HXR) peak time of the flare. The embedded prominence has a lower speed of ≈ 452 km s −1 . The eruption is significantly inclined from the local solar normal by ≈ 60 ∘ , suggesting a typical non-radial eruption. During the early eruption of the flux rope, the nearby coronal loops are disturbed and experience independent kink-mode oscillations in the horizontal and vertical directions. The oscillation in the horizontal direction has an initial amplitude of ≈ 3.1 Mm, a period of ≈ 294 seconds, and a damping time of ≈ 645 seconds. It is most striking in 171 Å and lasts for three to four cycles. The oscillations in the vertical directions are observed mainly in 171, 193, and 211 Å. The initial amplitudes are in the range of 3.4 – 5.2 Mm, with an average value of 4.5 Mm. The periods are between 407 seconds and 441 seconds, with an average value of 423 seconds. The oscillations are damping and last for nearly four cycles. The damping times are in the range of 570 – 1012 seconds, with an average value of 741 seconds. Assuming a semi-circular shape of the vertically oscillating loops, we calculate the loop lengths according to their heights. Using the observed periods, we carry out coronal seismology and estimate the internal Alfvén speeds (988 – 1145 km s −1 ) and the magnetic-field strengths (12 – 43 G) of the oscillating loops.

Slow magnetoacoustic waves observed in the solar corona are used as seismological probes of plasma parameters. It has been shown that the dispersion properties of such waves can vary significantly under the influence of the wave-induced thermal misbalance. In the current research, we study the effect of misbalance on waves inside the magnetic-flux tube under the second-order thin-flux-tube approximation. Using the parameters of active-region-fan coronal loops, we calculated wave properties such as the phase speed and decrement. It is shown that neglecting thermal misbalance may be the reason for the substantial divergence between seismological and spectrometric estimations of plasma parameters. We also show that the frequency dependence of the phase speed is affected by two features, namely the geometric dispersion and the dispersion caused by the thermal misbalance. In contrast to the phase speed, the wave decrement primarily is affected by the thermal misbalance only. The dependencies of the phase speed and decrement of the slow wave on the magnetic field and tube cross-section are also analysed.