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.

The nature of MHD waves within inhomogeneous media is fundamental to understanding and interpreting wave behavior in the solar atmosphere. We investigate fast magnetoacoustic wave behavior within gravitationally stratified, magnetically inhomogeneous media, by studying a magnetic environment containing a simple 2D X-type magnetic null point. The addition of gravitational stratification fundamentally changes the nature of the system, including breaking the symmetry. There are two main governing effects: the stratified density profile acts in combination with the inhomogeneous magnetic field, creating a large gradient in the Alfvén speed and hence a system replete with refraction. The system is investigated using both numerical simulations and a semianalytical WKB solution (via Charpit’s method and a fourth-order Runge–Kutta solver) and we find strong agreement between both. The results show a fundamental difference between the stratification-free and stratified cases, including the formation of caustic surfaces and cusps, and we contextualize these results in the theoretical understanding of fast magnetoacoustic waves.

This work conducts a three-dimensional (3D), nonlinear magnetohydrodynamic (MHD) simulation to investigate wave-generating, time-dependent reconnection around a magnetic null point. A nonperiodic perturbation (in the xz -plane) triggers oscillatory reconnection (OR) at the 3D null, resulting in a self-sustained oscillation with a constant period P . We investigate the response of the system using three distinct wave proxies (compressible parallel, compressible transverse, and incompressible parallel) as well as spectral proper orthogonal decomposition for decoupling and analyzing the resultant MHD wave behavior. We find that OR generates a slow magnetoacoustic wave of period P that propagates outward in all directions along the spine and fan plane of the 3D null point. We also find the generation of a propagating Alfvén wave of period P , exclusively along the y -axis in the fan plane, i.e., in the direction perpendicular to the spine motion. These findings provide new insights into waves generated from a 3D null point and their implications for coronal seismology.

Solar flares are the largest energy-release events in the Solar System, allowing us to study fundamental physical phenomena under extreme conditions. Those include magnetic reconnection, particle acceleration, radiation transport, and various plasma physics processes, all of which occur throughout the heliosphere and rest of the Universe. Flares and eruptive events are also components of geo-effective space weather. Their impacts from a space weather perspective are numerous, such as harm to satellites, disruption to GPS, communications and power systems, and impacts on passenger air travel. A comprehensive understanding of solar flares is therefore not just a compelling science problem, but also important for national security and infrastructure. This white paper (WP) addresses critical open science questions related to solar flares. Key observations and capabilities required to make significant advancements over the coming decade are identified. The UK has a robust and vibrant solar flare community. We are key partners in international collaborations, and also provide instrumentation for existing and upcoming ESA/NASA/JAXA space missions. Continuing this effort over the coming decade is vital to maintain UK leadership in this field, achieve Solar System Advisory Panel roadmap goals, and to work under the UK Space Agency's National Space Strategy Pillars. Several complementary WPs have been submitted that discuss instruments or concepts that would directly address the observational requirements we describe (including: SPARK, solar optimised IFUs, Solar-C/EUVST, and OSIRIS), as well as required numerical modelling efforts and infrastructure.

Magnetic reconnection powers explosive releases of magnetic energy, heating and particle acceleration throughout the plasma universe. Knowledge of this universal process is vital to understanding the Heliosphere, as it plays a key role in solar flares, coronal mass ejections, coronal heating, solar wind acceleration, geomagnetic storms, and interactions between the solar wind and planetary magnetospheres. As such, reconnection underpins multiple science objectives of multiple future space missions. The UK plays a leading role in this international field, through a combination of in situ measurements from Earth's magnetosphere and the solar wind, observations of the solar corona and chromosphere, and world-class numerical simulations and theory. This white paper identifies: Nine priority science objectives for reconnection research in the next decade; Recommendations to guide investment in theory, simulations and infrastructure; Mission priorities and required measurements to ensure the UK maintains and improves its world-class credentials in reconnection science.

Alfvénic waves are known to be prevalent throughout the corona and solar wind. Determining the Poynting flux supplied by the waves is required for constraining their role in plasma heating and acceleration, as well as providing a constraint for Alfvén-wave-driven models that aim to predict coronal and solar wind properties. Previous studies of the Alfvénic waves in polar coronal holes have been able to provide a measure of energy flux for arbitrary case studies. Here, we build upon previous work and take a more systematic approach, examining if there is evidence for any variation in vertical Poynting flux over the course of the solar cycle. We use imaging data from the Solar Dynamics Observatory's Atmospheric Imaging Assembly to measure the displacements of the fine-scale structure present in coronal holes. It is found that the measure for vertical Poynting flux is broadly similar over the solar cycle, implying a consistent contribution from waves to the energy budget of the solar wind. There is variation in energy flux across the measurements (around 30%), but this is suggested to be due to differences in the individual coronal holes rather than a feature of the solar cycle. Our direct estimates are in agreement with recent studies by Z. Huang et al., who constrain the vertical Poynting flux through comparison of predicted wind properties from Alfvénic-wave-driven turbulence models to those observed with OMNI at 1 au. Taken together, both sets of results points toward a lack of correlation between the coronal Poynting flux from waves and the solar cycle.

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.

Solar flares are explosive releases of magnetic energy stored in the solar corona, driven by magnetic reconnection. These events accelerate electrons, generating hard X-ray emissions, and often display quasi-periodic pulsations (QPPs) across the energy spectra. However, the energy transfer process remains poorly constrained, with competing theories proposing different acceleration mechanisms. We investigate electron acceleration and transport in a flaring coronal loop by solving a time-dependent Fokker–Planck equation. Our model incorporates transient turbulent acceleration, simulating the effects of impulsive energy input to emulate the dynamics of time-dependent reconnection processes. We compute the density-weighted electron flux, a diagnostic directly comparable to observed X-ray emissions, across the energy and spatial domains from the corona to the chromosphere. We investigate different time-dependent functional forms of the turbulent acceleration, finding that the functional form of the acceleration source maintains its signature across energy bands (1–100 keV) with a response time that is energy dependent (with higher-energy bands displaying longer response times). In addition, we find that (a) for a square pulse the switch on and off response time is different; (b) for a sinusoidal input the periodicity is preserved; and (c) for a damped sinusoidal the decay rate increases with density and higher-energy bands lose energy faster. This work presents a novel methodology for analyzing electron acceleration and transport in flares driven by time-dependent sources.

Oscillatory reconnection is a dynamic, magnetic relaxation mechanism in which a perturbed null point reverts to equilibrium via time-dependent reconnection. In this paper, we investigate the long-term periodic signal generated by a 3D magnetic null point when it is perturbed by a nonperiodic driver for a variety of driving amplitudes. We solve the 3D nonlinear magnetohydrodynamic equations using a bespoke numerical boundary condition (a sponge region) that damps wave reflections and thus allows the long-term periodic signal at the 3D null point to be investigated. We observe multiple cycles of the 3D oscillatory reconnection mechanism for the first time. We find that the periodicity is both constant and independent of the choice of driving amplitude. Furthermore, the resultant time-dependent current density at the null point, normalized by the driving amplitude, is invariant. We extract a single period for oscillatory reconnection at a 3D null point, opening the future possibility of using this characteristic period as a diagnostic tool to reveal indirectly the fundamental plasma properties of 3D null points.

The oscillatory reconnection mechanism is investigated for a parameter study of eight orders of magnitude of resistivity, with a particular interest in the evolution of the oscillating current density at the null point and its associated periodicity. The resistive, nonlinear MHD simulations are solved in 2.5D for different levels of resistivity. Three methods (wavelet analysis, Fourier transform, and ANOVA) are used to investigate the effect of resistivity versus resultant period. It is found that there is an independence between the level of background resistivity and the period of the oscillatory reconnection mechanism. Conversely, it is found that resistivity has a significant effect on the maximum amplitude of the current density and the nature of its decay rate, as well as the magnitude of ohmic heating at the null.

Oscillatory reconnection is a specific type of time-dependent reconnection which involves periodic changes in the magnetic topology of a null point. The mechanism has been reported for a variety of magnetic field strengths and configurations, background temperatures, and densities. All these studies report an oscillation in the current density at the null point, but also report a variety of periods, amplitudes, and overall behaviors. We conduct a parametric study for equilibrium magnetic field strength and initial background temperature, solving two-dimensional resistive magnetohydrodynamic equations around a magnetic X-point. We introduce a parameter space for the ratio of internal to magnetic energy and find self-similar solutions for simulations where this ratio is below 0.1 (which represents a magnetically dominated environment or, equivalently, a low-beta plasma). Self-similarity can be seen in oscillations in the current density at the null (including amplitude and period), ohmic heating, and the temperature generated via reconnection jets. The parameter space of energy ratios also allows us to contextualize previous studies of the oscillatory reconnection mechanism and bring those different studies together into a single unified understanding.

Solar pores are ideal magnetic structures for wave propagation and transport of energy radially outwards across the upper layers of the solar atmosphere. We aim to model the excitation and propagation of magnetohydrodynamic waves in a pore with a light bridge modeled as two interacting magnetic flux tubes separated by a thin, weaker-field layer. We solve the three-dimensional magnetohydrodynamic equations numerically and calculate the circulation as a measure of net torsional motion. We find that the interaction between flux tubes results in the natural excitation of propagating torsional Alfv & eacute;n waves but find no torsional waves in the model with a single flux tube. The torsional Alfv & eacute;n waves propagate with wave speeds matching the local Alfv & eacute;n speed where wave amplitude peaks.

Solar pores are ideal magnetic structures for wave propagation and transport of energy radially-outwards across the upper layers of the solar atmosphere. We aim to model the excitation and propagation of magnetohydrodynamic waves in a pore with a lightbridge modelled as two interacting magnetic flux tubes separated by a thin, weaker field, layer. We solve the three-dimensional MHD equations numerically and calculate the circulation as a measure of net torsional motion. We find that the interaction between flux tubes results in the natural excitation of propagating torsional Alfvén waves, but find no torsional waves in the model with a single flux tube. The torsional Alfvén waves propagate with wave speeds matching the local Alfvén speed where wave amplitude peaks.

Solar flares are among the most powerful and disruptive events in our solar system, however the physical mechanisms driving and transporting this energetic release are not fully understood. An important signature associated with flare energy release is highly variable emission on timescales of sub-seconds to minutes which often exhibit oscillatory behaviour, features collectively known as quasi-periodic pulsations (QPPs). To fully identify the driving mechanism of QPPs, exploit their potential as a diagnostic tool, and incorporate them into our understanding of solar and stellar flares, new observational capabilities and initiatives are required. There is a clear community need for flare-focused, rapid cadence, high resolution, multi-wavelength imaging of the Sun, with high enough sensitivity and dynamic range to observe small fluctuations in intensity in the presence of a large overall intensity. Furthermore, multidisciplinary funding and initiatives are required to narrow the gap between numerical models and observations. QPPs are direct signatures of the physics occurring in flare magnetic reconnection and energy release sites and hence are critical to include in a unified flare model. Despite significant modelling and theoretical work, no single mechanism or model can fully explain the presence of QPPs in flares. Moreover, it is also likely that QPPs fall into different categories that are produced by different mechanisms. At present we have insufficient information to observationally distinguish between mechanisms. The motivation to understand QPPs is strengthened by the geo-effectiveness of flares on the Earth's ionosphere, and by the fact that stellar flares exhibit similar QPP signatures. QPPs present a golden opportunity to better understand flare physics and exploit the solar-stellary analogy, benefiting both astrophysics, heliophysics, and the solar-terrestrial connection.

Oscillatory reconnection is a relaxation process in magnetized plasma, with an inherent periodicity that is exclusively dependent on the properties of the background plasma. This study focuses on the seismological prospects of oscillatory reconnection in the solar corona. We perform three sets of parameter studies (for characteristic coronal values of the background magnetic field, density, and temperature) using the PLUTO code to solve the fully compressive, resistive MHD equations for a 2D magnetic X-point. From each parameter study, we derive the period of the oscillatory reconnection. We find that this period is inversely proportional to the characteristic strength of the background magnetic field and the square root of the initial plasma temperature, while following a square root dependency upon the equilibrium plasma density. These results reveal an inverse proportionality between the magnitude of the Alfvén speed and the period, as well as the background speed of sound and the period. Furthermore, we note that the addition of anisotropic thermal conduction only leads to a small increase in the mean value for the period. Finally, we establish an empirical formula that gives the value for the period in relation to the background magnetic field, density, and temperature. This gives us a quantified relation for oscillatory reconnection, to be used as a plasma diagnostic in the solar corona, opening up the possibility of using oscillatory reconnection for coronal seismology.

For many years it has been an ambition of the solar and heliophysics communities to obtain a 3-D view of the entire Sun as this is critical for understanding many fundamental processes acting within and around our star; these are key questions to address for all stars, but particularly our own.To understand solar activity, we must study the structure and evolution of the seats of such activity, the so-called active regions that are regions defined by complex and highly dynamic magnetic structure.Currently we do that from a limited set of measurement and view-points constraining the science we can do.The majority of our solar observations are made near or from the Earth, but there have been notable exceptions.Steps towards measuring different views of the Sun were carried out by the Ulysses mission.Despite plans to carry remote sensing instrumentation, the spacecraft only carried in-situ instruments, but flew an extremely successful mission providing the first measurements over the Sun's poles.The NASA STEREO mission provided 2 views of the Sun in the equatorial region, from widely separated platforms but was limited due to the lack of magnetic field data and visibility of the poles.The recent ESA/NASA Solar Orbiter mission will gradually reach out of the equatorial plane and observe from 33 degrees with both remote sensing and in situ instruments providing a major step forward in studies of our star's polar regions.In recent reviews such as the JAXA/NASA/ESA next generation solar physics mission report in 2017, 5 multi spacecraft mission to provide an extended view of the Sun were proposed.In the ESA Voyage 2050 call, polar solar mission concepts were proposed to provide extensive measurements of the mysterious polar regions that have not yet been observed with imaging instruments [1] -this paper describes different technologies that allow an extended view of the poles.ESA's Vigil mission will be stationed at the Lagrange L5 point and will carry both remote sensing and in situ instruments.This white paper indicates the support of the European and Japanese communities for the Firefly mission concept (see white paper led by Nour Raouafi).These communities have expertise from probing the interior of the Sun using helioseismology methods to solar activity and how it feeds the heliosphere.An ambitious mission such as Firefly provides extensive opportunities to answer scientific questions that remain unanswered due to our restricted views of the Sun.There are 4 science questions probing the fundamental processes of what drives the Sun's magnetic activity from the inside of the star to activity in the heliosphere.These topics are of significant consequence to the impact our understanding of every star and hence the understanding of habitability and impacts of space weather on planets.

Solar flares are efficient particle accelerators with a large fraction of released magnetic energy (10%–50%) converted into energetic particles such as hard X-ray producing electrons. This energy transfer process is not well constrained, with competing theories regarding the acceleration mechanism(s), including MHD turbulence. We perform a detailed parameter study examining how various properties of the acceleration region, including its spatial extent and the spatial distribution of turbulence, affect the observed electron properties, such as those routinely determined from X-ray imaging and spectroscopy. Here, a time-independent Fokker–Planck equation is used to describe the acceleration and transport of flare electrons through a coronal plasma of finite temperature. Motivated by recent nonthermal line broadening observations that suggested extended regions of turbulence in coronal loops, an extended turbulent acceleration region is incorporated into the model. We produce outputs for the density-weighted electron flux, a quantity directly related to observed X-rays, modeled in energy and space from the corona to chromosphere. We find that by combining several spectral and imaging diagnostics (such as spectral index differences or ratios, energy or spatial-dependent flux ratios, and electron depths into the chromosphere) the acceleration properties, including the timescale and velocity dependence, can be constrained alongside the spatial properties. Our diagnostics provide a foundation for constraining the properties of acceleration in an individual flare from X-ray imaging spectroscopy alone, and can be applied to past, current, and future observations including those from RHESSI and Solar Orbiter.

Oscillatory reconnection can manifest through the interaction between the ubiquitous MHD waves and omnipresent null points in the solar atmosphere and is characterized by an inherent periodicity. In the current study, we focus on the relationship between the period of oscillatory reconnection and the strength of the wave pulse initially perturbing the null point, in a hot coronal plasma. We use the PLUTO code to solve the fully compressive, resistive MHD equations for a 2D magnetic X-point. Using wave pulses with a wide range of amplitudes, we perform a parameter study to obtain values for the period, considering the presence and absence of anisotropic thermal conduction separately. In both cases, we find that the resulting period is independent of the strength of the initial perturbation. The addition of anisotropic thermal conduction only leads to an increase in the mean value for the period, in agreement with our previous study. We also consider a different type of initial driver and we obtain an oscillation period matching the independent trend previously mentioned. Thus, we report for the first time on the independence between the type and strength of the initializing wave pulse and the resulting period of oscillatory reconnection in a hot coronal plasma. This makes oscillatory reconnection a promising mechanism to be used within the context of coronal seismology.

Oscillatory reconnection (a relaxation mechanism with periodic changes in connectivity) has been proposed as a potential physical mechanism underpinning several periodic phenomena in the solar atmosphere, including, but not limited to, quasi-periodic pulsations (QPPs). Despite its importance, however, the mechanism has never been studied within a hot, coronal plasma. We investigate oscillatory reconnection in a one million Kelvin plasma by solving the fully-compressive, resistive MHD equations for a 2D magnetic X-point under coronal conditions using the PLUTO code. We report on the resulting oscillatory reconnection including its periodicity and decay rate. We observe a more complicated oscillating profile for the current density compared to that found for a cold plasma, due to mode-conversion at the equipartition layer. We also consider, for the first time, the effect of adding anisotropic thermal conduction to the oscillatory reconnection mechanism, and we find this simplifies the spectrum of the oscillation profile and increases the decay rate. Crucially, the addition of thermal conduction does not prevent the oscillatory reconnection mechanism from manifesting. Finally, we reveal a relationship between the equilibrium magnetic field strength, decay rate, and period of oscillatory reconnection, which opens the tantalising possibility of utilizing oscillatory reconnection as a seismological tool.

We review novel data analysis techniques developed or adapted for the field of coronal seismology. We focus on methods from the last ten years that were developed for extreme ultraviolet (EUV) imaging observations of the solar corona, as well as for light curves from radio and X-ray. The review covers methods for the analysis of transverse and longitudinal waves; spectral analysis of oscillatory signals in time series; automated detection and processing of large data sets; empirical mode decomposition; motion magnification; and reliable detection, including the most common pitfalls causing artefacts and false detections. We also consider techniques for the detailed investigation of MHD waves and seismological inference of physical parameters of the coronal plasma, including restoration of the three-dimensional geometry of oscillating coronal loops, forward modelling and Bayesian parameter inference.