We report a quasi-periodic pulsation (QPP) event simultaneously detected from the spatial displacements of coronal loop at both EUV images and microwave emission during the preflare phase of a C1.1 flare on 2016 March 23. Using the motion magnification technique, a low-amplitude transverse oscillation with the growing period is discovered in a diffuse coronal loop in Atmospheric Imaging Assembly (AIA) image sequences at wavelength of 171 A, and the initial oscillation period is estimated to be ~397 s with a slow growth rate of 0.045. At the same time, a QPP with growing periods from roughly 300 s to nearly 500 s is discovered in the microwave flux in the same active region. Based on the imaging observations measured at EUV wavelengths by the AIA and at microwave 17 GHz by Nobeyama Radioheliograph, the diffuse coronal loop and the microwave radiation source are found to be connected through a hot loop seen in AIA images at wavelength of 94 A. The growing period of the QPP should be related to the modulation of LRC-circuit oscillating process in a current-carrying plasma loop. The existence of electric currents may imply the non-potentialities in the source region during the preflare phase.
Very long-periodic pulsations during preflare phases (preflare-VLPs) have been detected in the full-disk solar soft X-Ray (SXR) flux (see Tan et al. 2016). They may be regarded as precursors to solar flares and may help us better understand the trigger mechanism of solar flares. In this letter, we report a preflare-VLP event before the onset of an M1.1 circular-ribbon flare on 2015 October 16. It was simultaneously observed in Halpha, SXR, and extreme ultraviolet (EUV) wavelengths, which were recorded by the NVST, GOES, EVE, and AIA respectively. The preflare-VLP is identified as the repeat an…
We present a detailed examination on the coronal nonthermal emissions during the preflare phase of the X4.8 flare that occurred on 2002 July 23. The microwave (17 GHz and 34 GHz) data obtained with Nobeyama Radioheliograph, at Nobeyama Solar Radio Observatory and the hard X-ray (HXR) data taken with {\it Reuven Ramaty High Energy Solar Spectroscopic Imager} obviously showed nonthermal sources that are located above the flare loops during the preflare phase. We performed imaging spectroscopic analyses on the nonthermal emission sources both in microwaves and in HXRs, and confirmed that electron…
Solar flares are the most powerful explosions occurring in the solar system, which may lead to disastrous space weather events and impact various aspects of our Earth. So far, it is still a big challenge in modern astrophysics to understand the origin of solar flares and predict their onset. Based on the analysis of soft X-ray emission observed by the Geostationary Operational Environmental Satellite (GOES), this work reported a new discovery of very long-periodic pulsations occurred in the preflare phase before the onset of solar flares (preflare-VLPs). These pulsations are typically with per…
A good observation of preflare activities is important for us to understand the origin and triggering mechanism of solar flares, and to predict the occurrence of solar flares. This work presents the characteristics of microwave spectral fine structures as preflare activities of four solar flares observed by Ondřejov radio spectrograph in the frequency range of 0.8--2.0 GHz. We found that these microwave bursts which occurred 1--4 minutes before the onset of flares have spectral fine structures with relatively weak intensities and very short timescales. They include microwave quasi-periodic pul…
We consider the effects of the heat balance on the structural stability of a preflare current layer. The problem of small perturbations is solved in the piecewise homogeneous MHD approximation taking into account the viscosity, the electrical and thermal conductivity, and the radiative cooling. Solution of the problem allows the formation of an instability of a thermal nature. There is no external magnetic field inside the current layer in equilibrium state, but it can penetrate inside when the current layer is disturbed. Formation of a magnetic field perturbation inside the layer creates a de…
This work investigates the spatial relation between coronal X-ray sources and coherent radio emissions, both generally thought to be signatures of particle acceleration. Two limb events were selected during which the radio emission was well correlated in time with hard X-rays. The radio emissions were of the type of decimetric pulsations as determined from the spectrogram observed by Phoenix-2 of ETH Zurich. The radio positions were measured from observations with the Nancay Radioheliograph between 236 and 432 MHz and compared to the position of the coronal X-ray source imaged with RHESSI. The…
We studied the characteristic physical properties and behavior of broadband microwave sub-second pulsations observed in an expanding coronal loop during the GOES C2.4 solar flare on 2011 August 10. We found sub-second pulsations and other different burst groups in the complex radio spectrum. The broadband (bandwidth about 1 GHz) sub-second pulsations (temporal period range 0.07-1.49 s, no characteristic dominant period) lasted 70 s in the frequency range 4-7 GHz. These pulsations were not correlated at their individual frequencies, had no measurable frequency drift, and zero polarization. In t…
We investigate quasi-periodic coronal pulsations during the decay phase of an X 3.2 class flare on 14 May 2013, using soft X-ray data from the RHESSI satellite. Periodogram analyses of soft X-ray light curves show that 53 s and 72 s periods co-exist in the 3-6, 6-12 and 12-25 KeV energy bands. Considering the typical length of the flaring loop system and observed periodicities, we find that they are associated with multiple (first two harmonics) of fast magnetoacoustic sausage waves. The phase relationship of soft X-ray emissions in different energy bands using cross-correlation technique show…
In solar coronal loops, thermal non-equilibrium (TNE) is a phenomenon that can occur when the heating is both highly-stratified and quasi-constant. Unambiguous observational identification of TNE would thus permit to strongly constrain heating scenarios. Up to now, while TNE is the standard interpretation of coronal rain, the long-term periodic evolution predicted by simulations has never been observed yet. However, the detection of long-period intensity pulsations (periods of several hours) has been recently reported with SoHO/EIT, and this phenomenon appears to be very common in loops. Moreo…
We report on the discovery of periodic coronal rain in an off-limb sequence of {\it Solar Dynamics Observatory}/Atmospheric Imaging Assembly images. The showers are co-spatial and in phase with periodic (6.6~hr) intensity pulsations of coronal loops of the sort described by Auchere et al. (2014) and Froment et al. (2015, 2017). These new observations make possible a unified description of both phenomena. Coronal rain and periodic intensity pulsations of loops are two manifestations of the same physical process: evaporation / condensation cycles resulting from a state of thermal nonequilibrium …
Context: Thermal non-equilibrium (TNE) produces several observables that can be used to constrain the spatial and temporal distribution of solar coronal heating. Its manifestations include prominence formation, coronal rain, and long-period intensity pulsations in coronal loops. The recent observation of abundant periodic coronal rain associated with intensity pulsations by Auchère et al. allows to unify these two phenomena as the result of TNE condensation and evaporation cycles. On the other hand, many intensity pulsation events observed by Froment et al. show little to no coronal rain forma…
Long-period EUV pulsations, recently discovered to be common in active regions, are understood to be the coronal manifestation of thermal non-equilibrium (TNE). The active regions previously studied with EIT/SOHO and AIA/SDO indicated that long-period intensity pulsations are localized in only one or two loop bundles. The basic idea of this study is to understand why. For this purpose, we tested the response of different loop systems, using different magnetic configurations, to different stratifications and strengths of the heating. We present an extensive parameter-space study using 1D hydrod…
Thermal non-equilibrium (TNE) is a phenomenon that can occur in solar coronal loops when the heating is quasi-constant and highly-stratified. Under such heating conditions, coronal loops undergo cycles of evaporation and condensation. The recent observations of ubiquitous long-period intensity pulsations in coronal loops and their relationship with coronal rain have demonstrated that understanding the characteristics of TNE cycles is an essential step in constraining the circulation of mass and energy in the corona. We report unique observations with the Solar Dynamics Observatory (SDO) and th…
We report on the detection (10 σ) of 917 events of long-period (3 to 16 hours) intensity pulsations in the 19.5 nm passband of the SOHO Extreme ultraviolet Imaging Telescope. The data set spans from January 1997 to July 2010, i.e the entire solar cycle 23 and the beginning of cycle 24. The events can last for up to six days and have relative amplitudes up to 100%. About half of the events (54%) are found to happen in active regions, and 50% of these have been visually associated with coronal loops. The remaining 46% are localized in the quiet Sun. We performed a comprehensive analysis of the p…
Spatio-temporal Characteristics of Very Long-periodic Pulsations in Solar Metrewave Bursts: Implications for their Origins
Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心）；Institute of Space Sciences, Shandong University（山东大学空间科学研究院）
Quasi-constant heating at the footpoints of loops leads to evaporation and condensation cycles of the plasma: thermal non-equilibrium (TNE). This phenomenon is believed to play a role in the formation of prominences and coronal rain. However, it is often discarded to be involved in the heating of warm loops as the models do not reproduce observations. Recent simulations have shown that these inconsistencies with observations may be due to oversimplifications of the geometries of the models. In addition, our recent observations reveal that long-period intensity pulsations (several hours) are co…
Using the ULTRASPEC instrument mounted on the 2.4-m Thai National Telescope, we observed two large flares, each with a total energy close to 10^34 erg with sub-second cadence. A combination of a wavelet analysis, a Fourier transform plus an empirical mode decomposition, reveals quasi-period pulsations (QPP) which exhibit an apparent doubling of the oscillation period. Both events showed oscillations of a few minutes over a interval of several minutes, and despite the availability of sub-second cadence, there was no evidence of sub-minute oscillations. The doubling of the QPP periods and shorte…
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 quas…
Standing long-period (with the periods longer than several minutes) oscillations in large hot (with the temperature higher than 3 MK) coronal loops have been observed as the quasi-periodic modulation of the EUV and microwave intensity emission and the Doppler shift of coronal emission lines, and have been interpreted as standing slow magnetoacoustic (longitudinal) oscillations. Quasi-periodic pulsations of shorter periods, detected in thermal and non-thermal emissions in solar flares could be produced by a similar mechanism. We present theoretical modelling of the standing slow magnetoacoustic…
A phenomenological relationship between oscillations in a sunspot and quasi-periodic pulsations in flaring energy releases at an active region above the sunspot, is established. The analysis of the microwave emission recorded by the Nobeyama Radioheliograph at 17 GHz shows a gradual increase in the power of the 3-min oscillation train in the sunspot associated with AR 10756 before flares in this active region. The flaring light curves are found to be bursty with a period of 3 min. Our analysis of the spatial distribution of the 3-min oscillation power implies that the oscillations follow from …
We present results revealing microwave pulsations produced in a model of a flaring twisted solar coronal loop, without any external oscillatory driver. Two types of oscillations are identified: slowly-decaying oscillations with a period of about 70-75s and amplitude of about 5-10% seen in loops both with and without energetic electrons, and oscillations with period of about 40s and amplitude of a few tens of percent observed only in loops with energetic electrons for about 100s after onset of fast energy release. We interpret the longer-period oscillations as the result of a standing kink mode…
Context: Long-period intensity pulsations were recently detected in the EUV emission of coronal loops, and have been attributed to cycles of plasma evaporation and condensation driven by thermal non-equilibrium (TNE). Numerical simulations that reproduce this phenomenon also predict the formation of periodic flows of plasma at coronal temperatures along some of the pulsating loops. Aims: In this paper, we aim at detecting these predicted flows of coronal-temperature plasma in pulsating loops. Methods: To this end, we use time series of spatially resolved spectra from the EUV imaging spectromet…
We recently detected variations in extreme ultraviolet intensity in coronal loops repeating with periods of several hours. Models of loops including stratified and quasi-steady heating predict the development of a state of thermal non-equilibrium (TNE): cycles of evaporative upflows at the footpoints followed by falling condensations at the apex. Based on Fourier and wavelet analysis, we demonstrate that the observed periodic signals are indeed not signatures of vibrational modes. Instead, superimposed on the power law expected from the stochastic background emission, the power spectra of the …
Slow magnetoacoustic oscillations in stellar coronal loops with gravitational stratification are analyzed with a numerical solution of the boundary-value problem for eigenvalues and eigen functions. In this study, we only focus on the resonant periods. The effects of the gravitational stratification, star mass, loop temperature, and loop length on the properties of slow magnetoacoustic oscillations are investigated. It is shown that the discrepancy between stratified and non-stratified loops is higher in density perturbations than velocity perturbations. When the star has larger mass, higher c…
We present a case study of the solar flare (SOL2001-10-02T17:31) that showed quasi-periodic pulsations (QPPs) in hard X-rays with two simultaneously excited periods, P_1 = 26-31 s and P_2 = 110 s. Complete evolution of the flare recorded by the Yohkoh telescopes, together with the patrol SOHO/EIT images, allowed us to identify magnetic structures responsible for particular periods and to propose an overall scenario which is consistent with the available observations. Namely, we suggest that emerging magnetic flux initiated the reconnection with legs of a large arcade of coronal loops that had …
We present systematic analysis of spatio-temporal evolution of sources of hard X-ray (HXR) pulsations in solar flares. We concentrate on disk flares whose impulsive phase are accompanied by a series of more than three peaks (pulsations) of HXR emission detected in the RHESSI 50-100 keV channel with 4-second cadence. 29 such flares observed from February 2002 to June 2015 with time differences between successive peaks of 8-270 s are studied. The main observational result is that sources of HXR pulsations in all flares are not stationary, they demonstrate apparent displacements from pulsation to…
Fast sausage modes (FSMs) in flare loops have long been invoked to account for rapid quasi-periodic pulsations (QPPs) with periods of order seconds in flare lightcurves. However, most theories of FSMs in solar coronal cylinders assume a perfectly axisymmetric equilibrium, an idealized configuration apparently far from reality. In particular, it remains to examine whether FSMs exist in coronal cylinders with fine structures. Working in the framework of ideal magnetohydrodynamics (MHD), we numerically follow the response to an axisymmetric perturbation of a coronal cylinder for which a considera…
We explore the Quasi-Periodic Pulsations (QPPs) in a solar flare observed by Fermi Gamma-ray Burst Monitor (GBM), Solar Dynamics Observatory (SDO), Solar Terrestrial Relations Observatory (STEREO), and Interface Region Imaging Spectrograph (IRIS) on 2014 September 10. QPPs are identified as the regular and periodic peaks on the rapidly-varying components, which are the light curves after removing the slowly-varying components. The QPPs display only three peaks at the beginning on the hard X-ray (HXR) emissions, but ten peaks on the chromospheric and coronal line emissions, and more than seven …
In this Letter, we perform a detailed analysis of the M5.5-class eruptive flare occurring in active region 12929 on 2022 January 20. The eruption of a hot channel generates a fast coronal mass ejection (CME) and a dome-shaped extreme-ultraviolet (EUV) wave at speeds of 740$-$860 km s$^{-1}$. The CME is associated with a type II radio burst, implying that the EUV wave is a fast-mode shock wave. During the impulsive phase, the flare shows quasi-periodic pulsations (QPPs) in EUV, hard X-ray, and radio wavelengths. The periods of QPPs range from 18 s to 113 s, indicating that flare energy is relea…
Modeling the Excitation, Propagation and Damping of Quasi-Periodic Fast Magnetosonic Waves in Realistic Coronal Active Region Magnetic Field Structures
Catholic University of America（美国天主教大学）；NASA Goddard Space Flight Center（NASA戈达德太空飞行中心）；Tel Aviv University（特拉维夫大学）；University of Hawaii at Mānoa（夏威夷大学马诺阿分校）；Lockheed Martin Solar and Astrophysics Laboratory（洛克希德·马丁太阳与天体物理实验室）
Solar flares often display pulsating and oscillatory signatures in the emission, known as quasi-periodic pulsations (QPP). QPP are typically identified during the impulsive phase of flares, yet in some cases, their presence is detected late into the decay phase. Here, we report extensive fine structure QPP that are detected throughout the large X8.2 flare from 2017 September 10. Following the analysis of the thermal pulsations observed in the GOES/XRS and the 131 A channel of SDO/AIA, we find a pulsation period of ~65 s during the impulsive phase followed by lower amplitude QPP with a period o…
A quantitative study of the observable radio signatures of the sausage, kink, and torsional MHD oscillation modes in flaring coronal loops is performed. Considering first non-zero order effect of these various MHD oscillation modes on the radio source parameters such as magnetic field, line of sight, plasma density and temperature, electron distribution function, and the source dimensions, we compute time dependent radio emission (spectra and light curves). The radio light curves (of both flux density and degree of polarization) at all considered radio frequencies are than quantified in both t…
Quasi-periodic pulsations (QPP) are common in solar flares and are now regularly observed in stellar flares. We present the detection of two different types of QPP signals in the thermal emission light curves of the X9.3 class solar flare SOL2017-09-06T12:02, which is the most powerful flare of Cycle 24. The period of the shorter-period QPP drifts from about 12 to 25 seconds during the flare. The observed properties of this QPP are consistent with a sausage oscillation of a plasma loop in the flaring active region. The period of the longer-period QPP is about 4 to 5 minutes. Its properties are…
Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provies a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence & Compo cannot, in most cases, adequately represent the power spe…
Being directly observed in the Doppler shift and imaging data and indirectly as quasi-periodic pulsations in solar and stellar flares, slow magnetoacoustic waves offer an important seismological tool for probing many vital parameters of the coronal plasma. A recently understood active nature of the solar corona for magnetoacoustic waves, manifested through the phenomenon of wave-induced thermal misbalance, led to the identification of new natural mechanisms for the interpretation of observed properties of waves. A frequency-dependent damping of slow waves in various coronal plasma structures r…
Solar flares are one of the most energetic events in the solar atmosphere. It is widely accepted that flares are powered by magnetic reconnection in the corona. An eruptive flare is usually accompanied by a coronal mass ejection, both of which are probably driven by the eruption of a magnetic flux rope (MFR). Here we report an eruptive flare on 2016 March 23 observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The extreme-ultraviolet imaging observations exhibit the clear rise and eruption of an MFR. In particular, the observations reveal solid evidence for mag…
Quasi-periodic pulsations (QPP) seen in the time derivative of the GOES soft X-ray light curves are analyzed for the near-limb X3.2 event on 14 May 2013. The pulsations are apparent for a total of at least two hours from the impulsive phase to well into the decay phase, with a total of 163 distinct pulses evident to the naked eye. A wavelet analysis shows that the characteristic time scale of these pulsations increases systematically from $\sim$25 s at 01:10 UT, the time of the GOES peak, to $\sim$100 s at 02:00 UT. A second ridge in the wavelet power spectrum, most likely associated with flar…
We study the relationship between implosive motions in a solar flare, and the energy redistribution in the form of oscillatory structures and particle acceleration. The flare SOL2012-03-09T03:53 (M6.4) shows clear evidence for an irreversible (stepwise) coronal implosion. Extreme-ultraviolet (EUV) images show at least four groups of coronal loops at different heights overlying the flaring core undergoing fast contraction during the impulsive phase of the flare. These contractions start around a minute after the flare onset, and the rate of contraction is closely associated with the intensity o…
The reflection, refraction, and transmission of large-scale extreme ultraviolet (EUV) waves (collectively, secondary waves) have been observed during their interactions with coronal structures such as active regions (ARs) and coronal holes (CHs). However, the effect of the total reflection of EUV waves has not been reported in the literature. Here, we present the first unambiguous observational evidence of the total reflection of a quasi-periodic EUV wave train during its interaction with a polar CH. The event occurred in NOAA AR 12473, located close to the southeast limb of the solar disk, an…
Rapidly decaying long-period oscillations often occur in hot coronal loops of active regions associated with small (or micro-) flares. This kind of wave activity was first discovered with the SOHO/SUMER spectrometer from Doppler velocity measurements of hot emission lines, thus also often called "SUMER" oscillations. They were mainly interpreted as global (or fundamental mode) standing slow magnetoacoustic waves. In addition, increasing evidence has suggested that the decaying harmonic type of pulsations detected in light curves of solar and stellar flares are likely caused by standing slow-mo…
Standing sausage modes are important in interpreting quasi-periodic pulsations in the lightcurves of solar flares. Their periods and damping times play an important role in seismologically diagnosing key parameters like the magnetic field strength in regions where flare energy is released. Usually such applications are based on theoretical results neglecting unresolved fine structures in magnetized loops. However, the existence of fine structuring is suggested on both theoretical and observational grounds. Adopting the framework of cold magnetohydrodynamics (MHD), we model coronal loops as mag…
The soft X-ray emissions of solar flares come mainly from the bright coronal loops at the highest temperatures normally achieved in the flare process. Their ubiquity has led to their use as a standard measure of flare occurrence and energy, although the overwhelming bulk of the total flare energy goes elsewhere. Recently Dolla et al. (2012) noted quasi-periodic pulsations (QPP) in the soft X-ray signature of the X-class flare SOL2011-02-15, as observed by the standard photometric data from the GOES (Geostationary Operational Environmental Satellite) spacecraft. In this paper we analyze the sui…
Characterized by cyclic axisymmetric perturbations to both the magnetic and fluid parameters, magnetohydrodynamic fast sausage modes (FSMs) have proven useful for solar coronal seismology given their strong dispersion. This review starts by summarizing the dispersive properties of the FSMs in the canonical configuration where the equilibrium quantities are transversely structured in a step fashion. With this preparation we then review the recent theoretical studies on coronal FSMs, showing that the canonical dispersion features have been better understood physically, and further exploited seis…
The reason for the occurrence of different elements of the fine structure of solar radio bursts in the decimeter and centimeter wavelength ranges has been determined based on all available data from terrestrial and satellite observations. In some phenomena, fast pulsations, a zebra structure, fiber bursts, and spikes have been observed almost simultaneously. Two phenomena have been selected to show that the pulsations of radio emission are caused by particles accelerated in the magnetic reconnection region and that the zebra structure is excited in a source, such as a magnetic trap for fast pa…
QFP wave trains in the corona have been studied intensively in the past decade, thanks to the full-disk, high spatiotemporal resolution, and wide-temperature coverage observations taken by the SDO/AIA. In AIA observations, QFP wave trains are seen to consist of multiple coherent and concentric wavefronts emanating successively near the epicenter of the accompanying flares; they propagate outwardly either along or across coronal loops at fast-mode magnetosonic speeds from several hundred to more than 2000 km/s, and their periods are in the range of tens of seconds to several minutes. Based on t…
A universal scaling between damping time and period of quasi-periodic pulsations from solar EUV brightenings to X-ray stellar flares
Solar-Terrestrial Centre of Excellence – SIDC, Royal Observatory of Belgium（太阳-星际卓越中心–SIDC，比利时皇家天文台）；Centre for mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven（KU鲁汶大学数学系数学等离子体天体物理学中心）；University of Exeter（埃克塞特大学）；Centre for Fusion, Space and Astrophysics, Physics Department, University of Warwick（华威大学物理部聚变、空间与天体物理学中心）；Engineering Research Institute “Ventspils International Radio Astronomy Centre (VIRAC)”, Ventspils University of Applied Sciences（文茨皮尔斯应用科学大学“文茨皮尔斯国际射电天文中心（VIRAC）”工程研究所）；Centro de Investigacion en Astronomía, Universidad Bernardo O’Higgins（贝尔纳多·奥希金斯大学天文学研究中心）；Aryabhatta Research Institute of Observational Sciences (ARIES)（阿亚玻塔观测科学研究所（ARIES））
We analyse quasi-periodic pulsations (QPP) detected in the microwave and decimeter radio emission of the 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 s, coming from …
Recurrent Coronal Jets and QPPs: Periodic Reconnection and Localized Heating Across Quiet-Sun to Active Regions
Astronomical Observatory, Kyoto University（京都大学天文观测所）；Key Laboratory of Solar Activity and Space Weather, School of Aerospace, Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳）航天学院太阳活动与空间天气重点实验室）；Division of Mathematics, School of Science and Engineering, University of Dundee（邓迪大学科学与工程学部数学系）；Department of Physics, Indian Institute of Technology (BHU), Varanasi（瓦拉纳西印度技术学院（贝拿勒斯 Hindu 大学）物理系）
