Magnetohydrodynamic (MHD) seismology uses naturally occurring MHD waves to infer plasma properties that are otherwise hard to measure, especially magnetic field strength and topology, electric currents, fine structuring, transport coefficients, and energy release. Across the solar atmosphere, heliosphere, and planetary magnetospheres, multi-wavelength remote sensing and in-situ observations of waves provide powerful diagnostics that can address major open problems including chromospheric and coronal heating, flare and eruption physics, solar wind acceleration, and space weather impacts. This White Paper sets out the case for a coordinated UK programme that couples high precision observations with advanced theory and numerical modelling, modern time-frequency methods for non-stationary signals, and machine learning approaches for detection, classification, and parameter inference from rapidly growing multi-instrument datasets. It outlines priority needs such as robust mode identification, reliable density and temperature constraints, multi line-of-sight capability, and models that include partial ionisation and non-adiabatic/collisionless effects, alongside enabling instrumentation such as next-generation spectropolarimetry, integral field units, and radio facilities including the Square Kilometre Array. The paper highlights the UK's strong track record and infrastructure, and argues that sustained investment will amplify UK scientific return through international partnerships and mission involvement, delivering transformative plasma diagnostics and downstream benefits for space weather forecasting and related applications.

Small-scale vortical motions in the upper solar atmosphere are abundant and occupy about 2.8% of the photosphere at any given time. Although considerable work has focused on the detection and analysis of individual solar vortices, the interconnected and multi-scale behaviour of these coherent structures remains largely unexplored. We present a methodology for studying this behaviour through vortex interactions, to improve our understanding of how small- and large-scale photospheric flows contribute to energy transfer into the upper solar atmosphere and to the driving of solar activity. We represent vortices as a network of interacting structures. We apply a community detection algorithm to derive an optimal reduced network composed of highly interconnected vortex groups. From the interaction patterns and group structure, we define three roles within each community: peripheral, connector and hub. We then track both vortex communities and their member vortices from the photosphere into the chromosphere and across their lifetimes. On average, vortices assigned to these roles persist to greater heights in the chromosphere and have longer lifetimes than unclassified vortices. This shows that community detection can identify vortices with greater dynamical influence on the upper solar atmosphere. We also find that 32% to 58.6% of vortex communities exhibit global periodic behaviour following a helical path. This collective vortical motion may indicate an enhanced mechanism for wave excitation. Solar vortical community detection, therefore, offers a new framework for studying solar vortices and a new perspective on the importance of collective vortex dynamics.

Using high-resolution observations from the TuMag instrument aboard the Sunrise iii solar observatory balloon mission, we investigate solar vortices in the lower atmosphere. First, we identify vortices by extracting coherent dynamical patterns from intensity data using morphological analysis combined with spectral proper orthogonal decomposition applied to Mg I time series that probe the photosphere and lower chromosphere. We found that ∼8.5 × 10 ^4 vortices may be present on the Sun at any given time, with an average lifetime of $\tau \approx 27\,\mathrm{minutes}$ . To investigate vortex-mediated cross-layer coupling, we apply Granger causality (GC), which tests whether past fluctuations in one atmospheric layer carry statistically significant predictive power for future fluctuations in another, serving as a statistical proxy for directed dynamical coupling potentially associated with energy and momentum transfer. A pixel-to-pixel GC analysis reveals enhanced and spatially organized lower-atmospheric coupling within vortices, with statistically dominant photosphere-to-chromosphere influence in some locations and the reverse in others. This locally enhanced bidirectional spatial pattern of influence presents morphology consistent with the vortex-driven vertical Poynting flux distribution predicted by numerical simulations, suggesting that the coupling inferred from GC traces dynamical interactions associated with vortex-driven energy transport across atmospheric layers. On average, the directional asymmetry favors photosphere-to-chromosphere predictive coupling. Within vortex regions, past photospheric fluctuations provide ≈53% stronger predictive power for future chromospheric fluctuations than in nonvortex regions over a lag of 4.5 minutes. These results provide the first observational evidence of enhanced information transfer between atmospheric layers associated with solar vortices.

Abstract We propose to employ the framework of information geometry to detect anomalies in Very Low Frequency (VLF) and Low Frequency (LF) signal propagation, measured globally across amplitude and phase channels. Using a sliding‐window approach, the probability distributions of signal data are compared over adjacent intervals, defining a statistical measure of distinguishability, named information velocity. Information velocity enables the identification of anomalies in VLF/LF signals and connect them to various atmospheric, geophysical, and space weather phenomena. We have shown the effectiveness of information geometry in quantifying signal variability, offering a powerful framework for anomaly detection in VLF data and wider in the geophysical and atmospheric sciences context. The results demonstrate its potential for uncovering insights into ionospheric behavior, atmospheric disturbances, and their interplay with Earth's electromagnetic environment.

Solar vortices are fundamental components of solar atmospheric dynamics, serving as natural laboratories for magnetic field twisting, energy concentration and transport, wave guidance, and plasma coupling across atmospheric layers. Numerical and observational studies show that solar vortices are intimately connected to key physical processes including magnetic reconnection, atmospheric heating, turbulence, and wave generation. This white paper, prepared for the UK Space Frontiers 2035 call, outline five high-priority scientific questions addressing vortex generation mechanisms, cross-layer coupling, magnetic restructuring, collective wave-guidance structures, and their role in triggering explosive events and modulating the solar wind. Key observations and capabilities required to make significant advancements over the coming decade are identified. The UK solar physics community has established world-leading expertise in vortex dynamics, combining strengths in high-resolution observations, MHD turbulence theory, numerical modelling, and space instrumentation. UK researchers have made foundational contributions to Solar Orbiter, delivered critical systems for DKIST, and maintain active involvement in MUSE and SOLAR-C EUVST missions. Our technical approach centres on developing next-generation instrumentation: a multi-band, space-qualified system employing four tunable Fabry-Pérot Interferometers providing diffraction-limited, high-cadence spectropolarimetric coverage from the deep photosphere to the low corona. This capability will be validated through a staged mission architecture beginning with balloon-borne demonstrators. Continuing this effort over the coming decade is vital to maintain UK leadership in this field and achieve the goals of roadmap for solar system research.

We investigate the oscillatory behaviour of the footpoints of twisted magnetic flux tubes in the solar photosphere. We identify the dominant magnetohydrodynamic (MHD) wave modes present in these waveguides and assess their role in energy transport. Using vector magnetograms from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager Space-weather HMI Active Region Patches (SDO/HMI SHARP) series of active region 11158, the footpoints of twisted flux tubes are identified as convex local maxima of the Integrated Average Current Deviation (IACD) field, which highlights regions of enhanced magnetic twist and current concentration. To study the waves propagating in these structures, we apply the Spectral Proper Orthogonal Decomposition (SPOD) method, which separates complex spatio-temporal data into oscillatory patterns and their characteristic frequencies. Our analysis shows that the footpoints of the twisted flux tubes support both kink and sausage MHD modes, with oscillations detected across multiple diagnostics, including IACD, the vertical magnetic field, and the vertical Poynting flux. The coexistence of these modes suggests nonlinear interactions or mode coupling within the twisted magnetic structures. These twisted flux tubes act as magnetic waveguides that modulate the vertical transport of energy between the photosphere and higher atmospheric layers. The inferred upward Poynting fluxes ( 10^5 – 10^6 W m^-2 ) indicate that such twisted magnetic features may contribute to localised chromospheric heating.

Small-scale vortices in the solar photosphere play a central role in transporting mass, energy, and momentum into the upper solar atmosphere, yet reliably detecting these structures remains rather challenging. We address this problem by introducing a simple preprocessing step that normalizes the velocity field by its magnitude. Our method preserves flow streamlines while suppressing shear-induced artifacts that lead to spurious detections in nonuniform, high-rotation environments. For validation, we apply this approach to high-resolution Bifrost simulations and evaluate vortex detection using four commonly employed methods: instantaneous vorticity deviation, the lambda 2 criterion, the Q criterion, and the Gamma method. We assess which structures exhibit physically consistent rotation by using the d criterion to automatically detect rotational plasma-flow features, which we use as an approximate ground truth. We find that, in the unnormalized field, a substantial fraction of detections made by the first three methods are false positive detections. Normalization removes most of these. The Gamma method detects true vortices but misses a large number of vortical flows. The normalization step yields better-defined and more realistic vortex boundaries. As the Gamma method underpins most observational analyses, current studies likely capture only a subset of vortical flows. By comparison, the other three methods detect 4 to 5 times more vortices after normalization, suggesting that the true photospheric vortex coverage may be underestimated by a similar factor. Overall, this physically motivated preprocessing step enhances the accuracy and physical realism of vortex detection and offers a practical enhancement for analyzing vortical flows in turbulent flows.

Magnetic pores are compact, strongly magnetised waveguides in the lower solar atmosphere and therefore provide favourable conditions for identifying magnetohydrodynamic (MHD) wave modes. Earlier seeing-free observations revealed concurrent sausage, kink, and fluting modes in photospheric pores, but only at a single sampled layer. In this Letter, we exploit the dense spectral sampling of the near-ultraviolet 327-329 nm window observed by the Sunrise-III UV Spectropolarimeter and Imager (SUSI) to investigate how pore wave modes behave across multiple photospheric and low-chromospheric heights spanning roughly 500 km. We analyse 75 min of a Sunrise-III/SUSI time series containing a small solar pore. From eight selected spectral lines sampling different estimated formation heights, we identify the pore boundary at each line and time step and apply proper orthogonal decomposition (POD) to the boundary oscillations. In all eight lines, the first POD mode is consistently identified as an axisymmetric sausage mode, with dominant power at 1-2 mHz, and carries the dominant normalised eigenvalue fraction, typically about 66-86

Analysing high-resolution solar atmospheric observations requires robust techniques to recover plasma flow features across different scales, especially in active regions. Current methodologies often fall short in capturing subgranular-scale flows, and there is limited research on the errors introduced by velocity estimation techniques and analysing the properties of recovered flows in the presence of kG magnetic flux density. This study concentrates on validating the effectiveness of the DeepVel neural network in recovering subgranular to mesogranular-scale topological plasma flow features throughout the total evolution of a simulated active region by tracking tracers, and reproducing coherent patterns. The neural network was trained on the R2D2 radiative MHD simulation depicting the emergence and decay of a magnetic flux tube. DeepVel achieved strong correlations (exceeding 0.7) with flows from an unseen MURaM simulation, despite being trained on a model with a simpler radiative transfer and lacking thermal resistivity. DeepVel was able to capture the detailed topology well, e.g., the structure of vortical and diverging structures across all scales present in the flows. DeepVel performed slightly less well in the umbra, this is likely explained by magnetic field suppression and reduced contrast. Differences in velocities introduced by DeepVel did not affect Lagrangian analysis; consequently, we demonstrate for the first time that the DeepVel-recovered velocities accurately reflected the flow’s transport barriers. These findings highlight the precision and reliability of the DeepVel and its ability to emulate plasma flows surrounding and within active regions.

Magnetic flux tubes in the presence of background rotational flows are abundant throughout the solar atmosphere and may act as conduits for MHD waves to transport energy throughout the solar atmosphere. Here we investigate the contribution from MHD waves to the Poynting flux in a 3D numerical simulation of a realistic solar atmosphere, modelling a structure resembling a solar vortex tube, using the PLUTO code in the presence of different plasma flow configurations. These simulations feature a closed magnetic loop system where a rotational flow is imposed at one foot-point in addition to photospheric perturbations acting as a wave driver mimicking those of p-modes. We find that a variety of MHD waves exist within the vortex tube, including sausage, kink and torsional Alfvén waves, owing to the photospheric wave driver and the nature of the rotational flow itself. We demonstrate how the visual interpretation of different MHD modes becomes non-trivial when a background rotational flow is present compared to a static flux tube. By conducting a simulation both with and without the rotational plasma flow, we demonstrate how the perturbed Poynting flux increases in the presence of the rotational flow as the waves transport increased magnetic energy. We attribute this increase to the dynamical pressure from the rotational flow increasing the plasma density at the tube boundary, which acts to trap the wave energy more effectively inside the vortex. Moreover, we demonstrate how the Poynting flux is always directed upwards in weakly twisted magnetic flux tubes.

Magnetic flux tubes in the presence of background rotational flows are abundant throughout the solar atmosphere and may act as conduits for MHD waves to transport energy throughout the solar atmosphere. Here we investigate the contribution from MHD waves to the Poynting flux in a 3D numerical simulation of a realistic solar atmosphere, modeling a structure resembling a solar vortex tube, using the PLUTO code in the presence of different plasma flow configurations. These simulations feature a closed magnetic loop system where a rotational flow is imposed at one footpoint in addition to photospheric perturbations acting as a wave driver mimicking those of p -modes. We find that a variety of MHD waves exist within the vortex tube, including sausage, kink, and torsional Alfvén waves, owing to the photospheric wave driver and the nature of the rotational flow itself. We demonstrate how the visual interpretation of different MHD modes becomes nontrivial when a background rotational flow is present compared to a static flux tube. By conducting a simulation both with and without the rotational plasma flow, we demonstrate how the perturbed Poynting flux increases in the presence of the rotational flow as the waves transport increased magnetic energy. We attribute this increase to the dynamical pressure from the rotational flow increasing the plasma density at the tube boundary, which acts to trap the wave energy more effectively inside the vortex. Moreover, we demonstrate how the Poynting flux is always directed upward in weakly twisted magnetic flux tubes.

This Primer provides an overview of a fundamental set of analysis methods for studying waves, vibrations and related oscillatory phenomena — including instabilities, turbulence and shocks — across diverse scientific fields. These phenomena are ubiquitous, from astrophysics to complex systems in terrestrial environments, and understanding them requires careful selection of techniques. Misapplication of analysis tools can introduce misleading results. In this Primer, the fundamental principles of various wave analysis methods are first reviewed, along with adaptations to address complexities such as nonlinear, non-stationary and transient signal behaviour. These techniques are applied to identical synthetic datasets to provide a quantitative comparison of their strengths and limitations. Details are provided to help select the most appropriate analysis tools based on specific data characteristics and scientific goals, promoting reliable interpretations and ensuring reproducibility. Additionally, the Primer highlights best ethical practices for data deposition and the importance of open-code sharing. Finally, the broad applications of these techniques are explored in various research fields, current challenges in wave analysis are discussed, and an outlook on future directions is provided, with an emphasis on potential transformative discoveries that could be made by optimizing and developing cutting-edge analysis methods. Waves are ubiquitous in nature and occur across various scales and settings. In this Primer, Jafarzadeh et al. discuss techniques for preprocessing and analysing waves, including information on choosing the appropriate methods based on wave properties, and present worked examples using synthetic datasets.

Solar vortex regions show enhanced Poynting flux and favourable heating conditions, but how the vortices reorganize and influence their surroundings remains unclear. Here we apply information-theoretic diagnostics to a Bifrost simulation to quantify the dynamics of a long-lived vortex. By combining Shannon Entropy and Normalized Mutual Information, we track how the vortex reshapes plasma-magnetic couplings and modifies local thermodynamics. The vortex originates in the upper photosphere and extends into the chromosphere, where it suppresses the background p-mode-like organisation seen in the neighbouring magnetic flux tube. Shannon Entropy analysis shows that magnetic complexity rises sharply as the vortex develops, which is consistent with the build-up of currents and stored energy. At the same time, temperature becomes more strongly linked to magnetic shear, pointing to heating associated with current dissipation. The way temperature responds to different heating processes also changes with height: in the photosphere and lower chromosphere, it follows local compressional and expansion motions, while in the upper atmosphere, it is influenced mainly by viscous and current-driven effects. During this phase, the usual temperature-density relationship weakens, indicating that the plasma departs from purely adiabatic behaviour. Applying the same diagnostics to a nearby non-vortical flux tube yields only weak, uniform couplings, which confirms that the enhanced links are vortex-driven. Together, these results demonstrate that a coherent solar vortex not only drives heating but also reconfigures the local atmosphere, replacing periodic pressure-driven behaviour with magnetically dominated dynamics.

The Sun's atmosphere hosts swirling plasma structures, known as solar vortices, which have long been thought to channel wave energy into higher layers. Until now, no direct observations have confirmed their role in the heating of the atmosphere. Here, we present the first direct evidence that solar vortices act as structured waveguides, carrying magnetoacoustic modes (waves that behave like sound waves but travel through magnetized plasma) that leave clear wave-heating signatures. By mapping vortex regions at multiple heights and analysing the waves they contain, we show that magnetoacoustic waves efficiently transfer energy, offset losses from radiation, and dominate energy transport in the lower chromosphere. These results challenge the long-standing assumption that vortices primarily support twisting disturbances traveling along magnetic field lines (Alfven waves), revealing instead that magnetoacoustic modes play the leading role in the lower atmosphere. This redefines the role of vortices in magnetized plasmas and has broader implications for wave-plasma interactions in regions of strong magnetic fields.

Phase mixing has long been understood to be a viable mechanism for expediting the dissipation of Alfvén wave energy resulting in the subsequent heating of the solar atmosphere. To fulfill the conditions necessary for phase mixing to occur, we consider the cross-field gradient in the Alfvén speed as a free parameter in our model. Using a single-fluid description of a partially ionized chromospheric plasma, we explore the efficiency of damping of shear Alfvén waves subject to phase mixing when a pulse wave driver is employed. Our results demonstrate a strong dependence of the dissipation length of shear Alfvén waves on both the ionization degree of the plasma and the gradient of the Alfvén speed. When assessing the efficiency of phase mixing across various inhomogeneities, our findings indicate that waves originating from a pulse driver initially exhibit heating rates identical to those generated by a continuous wave driver. One key difference observed was that Alfvén pulses possess a lower overall decay rate, due to a change in damping profile from exponential to algebraic. This discrepancy arises from the absence of a consistent injection of energy into the base of the domain, which preserves longitudinal gradients of the magnetic field perturbations more effectively. These findings demonstrate the importance of understanding the relations between the wave driver, damping mechanisms, and propagation dynamics in resolving the atmospheric heating problem.

Our study investigates the properties of Alfvén waves in partially ionised solar plasmas in the presence of steady, field-aligned, flows of charged and neutral particles. Our work aims to understand how such flows modify wave propagation and damping in environments where ion-neutral collisions are significant. We employ a two-fluid model that treats ions and neutrals as separate colliding fluids and incorporates background steady flows for both species. Using a combination of analytical dispersion analysis and numerical solutions, we examine the impact of these flows on the behaviour of Alfvén waves. Our results show that steady flows lead to substantial modifications of wave properties, including Doppler shifts, propagation direction reversal, flow-dependent changes in damping rates, and the appearance of a new mode associated with neutral flow and collisional coupling. We also identify conditions under which flow-driven mode conversion can arise. Our results offer new insights into the interplay between plasma flows and particle collisions in the regions of the solar atmosphere where partial ionisation is relevant.

This study investigates the properties of waves that propagate along a density interface in partially ionised plasmas, separating two regions of different properties, including ionisation degree. Our analysis covers frequencies that are much smaller than the collisional frequency of particles, so we are using a single-fluid approximation, where the partial ionisation aspect of the plasma appears through the ambipolar diffusion in the generalised Ohm’s law. The derived dispersion relation is solved numerically. Our results show that guided waves along a density interface undergo very little change in their propagation speed (frequency); however, their damping rate shows variation with the ionisation degree and plasma- β parameter. We find that waves can only propagate when plasma- β >1.2 , indicating pressure-driven dynamics relevant to photospheric structures with moderate magnetic fields. The damping rate increases with higher neutral particle content but decreases with higher plasma- β values. For ionisation degrees close to fully ionised plasma, the damping is minimal but becomes more significant as the neutral particle concentration increases. These findings provide important insights into wave behaviour in partially ionised plasma interfaces and lay the groundwork for future studies of wave propagation in partially ionised plasma slab waveguides.

Coronal mass ejections (CMEs) are known drivers of large-scale waves in the low corona. However, wave dynamics in the extended corona and inner heliosphere remain largely unexplored. Here, we report the first observational and numerical evidence of coherent global compressive oscillations in the outer corona and inner heliosphere, revealed by white-light SOHO/LASCO C3 data and an MHD simulation. Analyzing the CME event of 2012 July 23 using Spectral Proper Orthogonal Decomposition (SPOD), we isolate two distinct wave signatures: (1) a directional fast-mode shock-like compressive wave that dissipates completely within ~3 hours, and (2) a large-scale global circular wavefront consistent with fast-mode MHD behavior, lasting ~7 hours and extending across the LASCO C3 field of view, marking the first detection of such a global oscillation. Our findings reveal a previously unrecognized component of CME-driven wave activity, providing new constraints on the dynamics of the extended corona and inner heliosphere.

Coronal mass ejections are known drivers of large-scale waves in the low corona. However, wave dynamics in the extended corona and inner heliosphere remain largely unexplored. Here, we report the first observational and numerical evidence of coherent global compressive oscillations in the outer corona and inner heliosphere, revealed by white-light Solar and Heliospheric Observatory Large Angle and Spectrometric Coronagraph (LASCO) C3 data and an MHD simulation. Analyzing the coronal mass ejection event of 2012 July 23 using spectral proper orthogonal decomposition, we isolate two distinct wave signatures: (1) a directional fast-mode shock-like compressive wave that dissipates completely within 3 hr, and (2) a large-scale global circular wave front consistent with fast-mode MHD behavior, lasting 7 hr and extending across the LASCO C3 field of view, marking the first detection of such a global oscillation. Our findings reveal a previously unrecognized component of coronal mass ejection–driven wave activity, providing new constraints on the dynamics of the extended corona and inner heliosphere.

This study investigated the mechanisms of vorticity generation and the role of vortex tubes in plasma heating and energy transport. Vortex tubes were identified using the instantaneous vorticity deviation technique in the MURaM data set of a simulated solar plage region of the solar photosphere. Within 3D kinetic vortex tubes, the misalignment of the magnetic pressure and the inverse of the density gradient, rather than baroclinic effects, primarily drive vorticity within the tubes. During their lifetime, vortices become less dense as the Lorentz force pushes plasma outwards against pressure gradients. In the simulated upper photosphere, the Lorentz force contributes to adiabatic cooling and heating by expanding or compressing the plasma around the vortex tubes. In turn, vortex motion affects the magnetic field, enhancing current generation and intensifying the Lorentz force, which may further increase adiabatic cooling and heating. Moreover, our results confirm that vortices can significantly boost viscous and ohmic heating on intergranular scales in the photosphere. They generate more magnetic than kinetic energy, with energy transport by Poynting flux notably nonuniform and dominant at the vortex boundaries. This creates energy circulation in which the net upwards Poynting flux can enhance chromospheric plasma heating and support chromospheric temperatures.