Solar PhysicsPub Date : 2026-08-11DOI: 10.1007/s11207-026-02718-x
Youcheng Chu, Haoyuan Zhong, Haoyang Zhang, Qingjian Ni
{"title":"An Enhanced MIMO-Unet Model for CHASE High Resolution H(alpha ) Image Deblurring","authors":"Youcheng Chu, Haoyuan Zhong, Haoyang Zhang, Qingjian Ni","doi":"10.1007/s11207-026-02718-x","DOIUrl":"10.1007/s11207-026-02718-x","url":null,"abstract":"<div><p>The Chinese H<span>(alpha )</span> Solar Explorer (CHASE) satellite provided invaluable full-disk H<span>(alpha )</span> spectral data, but images from its initial mission phase (before August 2022) suffered from significant defocus blur, limiting their scientific utility. This paper proposes an enhanced Multi-Input Multi-Output U-Net (MIMO-Unet) model to address this blind deconvolution challenge. Because sharp ground-truth counterparts are unavailable for real early-phase CHASE observations, we constructed a physically constrained dataset by applying a Zernike-polynomial-based defocus model to sharp CHASE/HIS observations acquired after the focusing condition became stable. The proposed model enhances the baseline MIMO-Unet by integrating Squeeze-and-Excitation (SE) blocks into the encoder for adaptive channel-wise feature recalibration and an Atrous Spatial Pyramid Pooling (ASPP) module into the feature fusion stage to capture multi-scale context. On the Zernike-simulated CHASE defocus dataset, the proposed method improves PSNR from 27.0169 dB to 33.8707 dB, corresponding to a 6.85 dB gain, and increases SSIM, FSIM, and the multi-fractal texture-based Perception Evaluation (PE) metric by 45.67%, 27.41%, and 62.96%, respectively, compared with the blurred inputs. Our model achieves the best PSNR (33.8707 dB) and SSIM (0.9282) among the compared deep learning methods, while being exceptionally lightweight with only 7.41M parameters. This work provides a physics-informed deep learning framework for restoring defocus-dominated degradation in CHASE H<span>(alpha )</span> observations, with quantitative validation on Zernike-simulated defocus data and preliminary qualitative tests on real early-phase CHASE observations.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 8","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solar PhysicsPub Date : 2026-08-06DOI: 10.1007/s11207-026-02671-9
Clara Froment, Sophie Masson
{"title":"Thermal Non-equilibrium Cycles in a Non-eruptive Pseudo-Streamer","authors":"Clara Froment, Sophie Masson","doi":"10.1007/s11207-026-02671-9","DOIUrl":"10.1007/s11207-026-02671-9","url":null,"abstract":"<div><p>Thermal non-equilibrium (TNE) is a well-known thermodynamic mechanism, generally studied in coronal loops. These evaporation and condensation cycles are induced by a quasi-steady and stratified heating. Long-period EUV pulsations and coronal rain are two manifestations of TNE. The quasi-periodicity of the cycles is a strong characteristic of TNE as the system dynamically evolves around a thermal equilibrium position that is not reachable. There are recent reports of coronal rain at open-closed boundaries such as fan-spine topologies and pseudo-streamers. However, no definite conclusions were drawn on the physical mechanisms driving these coronal rain events. In this article, we report the detection of long-period EUV pulsations and co-spatial recurring coronal rain showers in a pseudo-streamer observed with the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO). The magnetic topology and evolution of the pseudo-streamer are studied in detail using a combination of potential field source-surface (PFSS) modeling and EUV dynamics. The 2.5-day event exhibits all the characteristic features of previous TNE events reported in coronal loops: periodic EUV pulses appearing sequentially in the different channels, following the ordering of the peaks in their temperature response, and coronal rain showers appearing toward the end of these cycles. We further show that the TNE cycles in the pseudo-streamer occur not only in the closed field but also in the open field. Our observations support the findings of recent numerical studies showing that TNE can also occur in open field regions and at open-closed boundaries. In parallel, interchange reconnection occurs continuously and non-impulsively all along the open-closed boundary as seen in EUV. The interplay between TNE and interchange reconnection may play a role in the release of condensations below the open-closed boundary and should be studied in detail in future works. This observation opens further perspectives for the understanding of TNE in the solar atmosphere and its potential implications for the solar wind.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 8","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02671-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solar PhysicsPub Date : 2026-08-04DOI: 10.1007/s11207-026-02703-4
Marco Marongiu, Giulia Murtas, Alberto Pellizzoni, Sara Mulas, Maria Noemi Iacolina, Simona Righini, Elise Egron, Abimael Xavier Barbosa Amaro, Adriana Marcucci, Massimiliano Oranges, Davide Napolitano, Maddalena Sirigu, Mauro Messerotti, Salvatore Luigi Guglielmino, Alessandra Zanichelli, Vincenzo Andretta, Serena Maria Lezzi, Luca Schirru, Adelaide Ladu, Pierluigi Ortu, Giuseppe Valente, Mauro Pili, Tonino Pisanu, Giampaolo Serra, Alessandro Cabras, Andrea Melis, Pasqualino Marongiu, Alessandro Navarrini, Giuseppe Pupillo, Mattia Mancini, Pietro Zucca
{"title":"Exploring Coronal Holes Through K-Band Radio Observations (18 – (26text{ GHz})) with INAF Radio Telescopes","authors":"Marco Marongiu, Giulia Murtas, Alberto Pellizzoni, Sara Mulas, Maria Noemi Iacolina, Simona Righini, Elise Egron, Abimael Xavier Barbosa Amaro, Adriana Marcucci, Massimiliano Oranges, Davide Napolitano, Maddalena Sirigu, Mauro Messerotti, Salvatore Luigi Guglielmino, Alessandra Zanichelli, Vincenzo Andretta, Serena Maria Lezzi, Luca Schirru, Adelaide Ladu, Pierluigi Ortu, Giuseppe Valente, Mauro Pili, Tonino Pisanu, Giampaolo Serra, Alessandro Cabras, Andrea Melis, Pasqualino Marongiu, Alessandro Navarrini, Giuseppe Pupillo, Mattia Mancini, Pietro Zucca","doi":"10.1007/s11207-026-02703-4","DOIUrl":"10.1007/s11207-026-02703-4","url":null,"abstract":"<div><p>Coronal holes (CHs) are low-density regions in the solar atmosphere, characterised by open magnetic field lines driving the high-speed solar wind. While appearing dark in EUV/X-rays, their radio signatures are complex and frequency-dependent, showing either brightness depressions or enhancements relative to the quiet-Sun (QS). This variability reflects the complex inner temperature, density and magnetic structures of the solar atmosphere.</p><p>Within the SunDish project, we investigate the CH phenomenology using the National Institute for Astrophysics (INAF) large single-dish radio telescopes (Medicina ‘Gavril Grueff’ 32-m and Sardinia Radio Telescope ‘SRT’ 64-m), aiming to bridge the observational gap between the chromosphere and corona by exploring the under-investigated K-band (18 – <span>(26text{ GHz})</span>). This study analyses three representative scenarios: expected brightness temperature (<span>(T_{b})</span>) depressions, radio-enhanced CHs, and radio-dark regions (RDRs) unrelated to standard CHs.</p><p>Our analysis reveals a non-uniform phenomenology where radio-enhanced CHs and RDRs identify deep-penetrating structures affecting the upper chromosphere, including the first radio counterpart to a dark halo. Spectral indices and weak circular polarisation confirm thermal free-free emission as the primary mechanism, excluding significant gyro-magnetic contributions. However, magnetic field estimates suggest that a purely thermal model in a simple stratified atmosphere cannot fully describe these regions, where radio enhancements likely arise from unresolved structures like coronal bright points and magnetic flux tubes. These results highlight multi-frequency diagnostics as an essential tool for probing the coupling between different layers of the solar atmosphere, demonstrating that CHs are dynamic environments where complex magnetic activity drives their vertical structure and evolution.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 8","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02703-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solar PhysicsPub Date : 2026-08-04DOI: 10.1007/s11207-026-02713-2
Antonio Campos-Jara, Alberto Álvarez-Herrero, Pilar García Parejo, Daniel Garranzo-García, Pablo Santamarina Guerrero, Francisco Javier Bailén, Alex Feller, Achim Gandorfer, David Orozco Suárez, Jose Carlos del Toro Iniesta
{"title":"Polarimetric Calibration of the Tunable Magnetograph for the Sunrise III Mission","authors":"Antonio Campos-Jara, Alberto Álvarez-Herrero, Pilar García Parejo, Daniel Garranzo-García, Pablo Santamarina Guerrero, Francisco Javier Bailén, Alex Feller, Achim Gandorfer, David Orozco Suárez, Jose Carlos del Toro Iniesta","doi":"10.1007/s11207-026-02713-2","DOIUrl":"10.1007/s11207-026-02713-2","url":null,"abstract":"<div><p>The Tunable Magnetograph (TuMag) onboard Sunrise III is an imaging spectropolarimeter designed to ultimately infer the solar vector magnetic field and line-of-sight velocity. It includes Liquid Crystal Variable Retarders for polarimetric modulation and hence requires accurate polarimetric calibration to achieve its scientific goals. This work reports on the pre-flight calibration carried out on ground at different stages during the TuMag assembly, integration and verification phase. It includes the polarization modulator characterization, the verifications at instrument level, and, finally, the full system calibration after its integration in SUNRISE within the Post-Focus Instrumentation platform. The calibration includes determining the field-dependent demodulation matrices (pixel-by-pixel calibration) and evaluating polarimetric efficiencies, ensuring compliance with the mission sensitivity requirements. The results of this work provide the calibrated demodulation matrices that will be used for the scientific exploitation of the mission data.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 8","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02713-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solar PhysicsPub Date : 2026-07-28DOI: 10.1007/s11207-026-02712-3
Istvan Ballai, Patrick Antolin, Alessandro Bemporad
{"title":"Advances in the Physics of the Sun and the Solar-Heliosphere Connection – Editorial","authors":"Istvan Ballai, Patrick Antolin, Alessandro Bemporad","doi":"10.1007/s11207-026-02712-3","DOIUrl":"10.1007/s11207-026-02712-3","url":null,"abstract":"","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 7","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solar PhysicsPub Date : 2026-07-28DOI: 10.1007/s11207-026-02698-y
Anna Manou, Miho Janvier, Deborah Baker, Pascal Démoulin, Lidia van Driel-Gesztelyi, Stephanie L. Yardley
{"title":"On the Relation Between Upflow Velocities and Coronal Non-thermal Velocities as Measured by Hinode/EIS","authors":"Anna Manou, Miho Janvier, Deborah Baker, Pascal Démoulin, Lidia van Driel-Gesztelyi, Stephanie L. Yardley","doi":"10.1007/s11207-026-02698-y","DOIUrl":"10.1007/s11207-026-02698-y","url":null,"abstract":"<div><p>Upflows at coronal temperatures are typically present at the edges of active regions, where plasma escapes into the upper atmosphere. This study focuses on NOAA Active Regions 12665 and 12685 which are in different evolutionary stages, they display varying activity levels, and have a large difference in their magnetic field structure. Our targets were followed by Hinode/EIS as the ARs crossed the solar disk, and we used Fe <span>XII</span> maps to track their evolution. We separated time periods with nearly stationary flows from the non-stationary ones, in order to isolate the effects of solar rotation and activity on both the line-of-sight and non-thermal velocities. We confirmed the presence of a strong positive correlation between the Doppler and non-thermal velocity during both time periods and with different levels of activity. These results help us differentiate the physical origin of non-thermal velocities, such as Alfvén waves, MHD turbulence, magnetic reconnection, and multi-stream components. Our results favour the latter.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 7","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02698-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solar PhysicsPub Date : 2026-07-23DOI: 10.1007/s11207-026-02708-z
Trestan F. Simon, Ryan J. French
{"title":"SADCat: A Catalog of Supra-Arcade Downflow Events in Solar Flares","authors":"Trestan F. Simon, Ryan J. French","doi":"10.1007/s11207-026-02708-z","DOIUrl":"10.1007/s11207-026-02708-z","url":null,"abstract":"<div><p>Supra-arcade downflows (SADs) are sunward-traveling features routinely observed in hot fan structures above magnetic loop arcades during eruptive solar flares. We manually compiled a catalog (SADCat) of 178 SAD-productive flares imaged by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory (SDO) during solar cycle 24 as a resource for the wider solar flare community. We conducted a preliminary analysis of the SADCat, comparing the flare X-ray and CME properties between eruptive solar flares with and without SADs. We found that peak GOES X-ray flux, flare duration, CME speed, and CME mass have a strong influence on whether a flare produces visible SADs, whereas flare impulsivity and CME acceleration have little effect.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 7","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02708-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solar PhysicsPub Date : 2026-07-22DOI: 10.1007/s11207-026-02705-2
Anant Telikicherla, Jessica Hamilton, A. A. Shmies, Malik H. Walker, Fatima Yousuf
{"title":"Advancing Solar Flare Nowcasting with Machine Learning Based Detection of Hot Onset Precursor Events","authors":"Anant Telikicherla, Jessica Hamilton, A. A. Shmies, Malik H. Walker, Fatima Yousuf","doi":"10.1007/s11207-026-02705-2","DOIUrl":"10.1007/s11207-026-02705-2","url":null,"abstract":"<div><p>This manuscript is part of the Heliophysics Summer School Machine Learning Special Collection. Predicting solar flares remains a major challenge in space-weather forecasting. Large eruptive flares can trigger coronal mass ejections and energetic particle events that threaten satellites, endanger astronauts, and degrade High Frequency (HF) communications. Current flare alerts rely on Soft X-ray measurements from the X-ray Sensor onboard Geostationary Operational Environmental Satellite (GOES-XRS) crossing fixed flux thresholds, and therefore are issued only once the flare is already in its impulsive phase. This study focuses on solar-flare nowcasting using the Hot Onset Precursor Event (HOPE), a recently identified pre-flare phenomenon. In this study we extend existing HOPE trigger algorithms by applying a simple multilayer perceptron model to estimate flare peak magnitude and peak time. The method consists of detecting HOPE plasma temperature and emission measure signatures, and then using the time-histories of these variables to predict flare magnitude and time. The system is optimized to detect <span>(mathrm{>M5.0})</span> flares. The model was trained using 180 flares from GOES-14 through GOES-19 XRS instrument dataset, and tested over 46 independent flares. A 1-week proof-of-concept validation was performed during which all four <span>(mathrm{>M5.0})</span> flares were successfully detected, with an average lead time of 17.9 minutes relative to the NOAA R3 radio-blackout alert. These results show that HOPE-based machine learning models can deliver early warnings for high-impact flares.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 7","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02705-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solar PhysicsPub Date : 2026-07-22DOI: 10.1007/s11207-026-02706-1
Glenn T. Laurent, Craig E. DeForest, Matt N. Beasley, Nicholas F. Erickson, Roy R. Graham, Mary H. Hanson, J. Marcus Hughes, Derek A. Lamb, Reith Nolan, Steve Osterman, Trent Peterson, Michael Shoffner, Kelly D. Smith, Travis Smith, Todd Veach, William L. Wells, Alexander J. Wilson
{"title":"The Wide Field Imager (WFI) Instruments for the Polarimeter to Unify the Corona and Heliosphere (PUNCH)","authors":"Glenn T. Laurent, Craig E. DeForest, Matt N. Beasley, Nicholas F. Erickson, Roy R. Graham, Mary H. Hanson, J. Marcus Hughes, Derek A. Lamb, Reith Nolan, Steve Osterman, Trent Peterson, Michael Shoffner, Kelly D. Smith, Travis Smith, Todd Veach, William L. Wells, Alexander J. Wilson","doi":"10.1007/s11207-026-02706-1","DOIUrl":"10.1007/s11207-026-02706-1","url":null,"abstract":"<div><p>We describe the design, hardware, and calibration performance of the Wide-Field Imager (WFI) instruments for the Polarimeter to Unify the Corona and Heliosphere (PUNCH) mission. The WFI instruments are a trio of visible-light heliospheric imagers that, together, view the outer corona and solar wind from under 3.5<sup>∘</sup> to over 47<sup>∘</sup> from the Sun, via sunlight that is Thomson-scattered from free electrons. In flight, the WFIs are arranged so that their collective fields of view form an approximately symmetric trefoil on the sky, comprising three circular-truncated square fields spaced 120° apart in position angle. The WFIs work with the NFI instrument, described elsewhere, to implement the full PUNCH field spanning all solar position angles, at elongations from 1.5° to 47° from disk center. WFI is implemented using dioptric (lens) optics and deep multi-stage baffles that attenuate solar, planetary, and lunar stray light sufficiently for ground processing to reveal the faint signal for the primary science. WFI measures both total brightness (tB) and polarized brightness (pB), via an on-board polarizing filter wheel (PFW) and charge-coupled device (CCD) camera that share a common design with those of the NFI instrument.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 7","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02706-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solar PhysicsPub Date : 2026-07-22DOI: 10.1007/s11207-026-02709-y
Shao-Xia Chen, Bo Li, Mijie Shi
{"title":"Fast Sausage Waves in Twisted Coronal Loops with Continuous Equilibrium Distribution","authors":"Shao-Xia Chen, Bo Li, Mijie Shi","doi":"10.1007/s11207-026-02709-y","DOIUrl":"10.1007/s11207-026-02709-y","url":null,"abstract":"<div><p>There are observational evidences supporting the existence of twisted magnetic fields in the solar corona. The dispersive properties and resonant absorption of the fast sausage modes (FSMs) in a twisted coronal loop are investigated. The coronal loop is modeled as a structured straight magnetic cylinder with an azimuthal magnetic field throughout in addition to an axis-aligned longitudinal magnetic field. The dispersion relation (DR) of FSMs is derived by numerically solving the eigenvalue problem (EVP) resulting from the one-dimensional resistive magnetohydrodynamic (MHD) equations. Our results confirm the previous conclusion that the principal FSM exhibits no cutoff, implying that this mode can propagate with arbitrary wavelengths. The dependencies of the oscillation frequency and damping rates of FSMs on the magnetic twist and longitudinal wavenumber are examined. For the flux tube parameters considered in this paper, we find that the damping of FSMs is too weak to produce observable signals in actual observations.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 7","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}