Author name code: browning ADS astronomy entries on 2022-09-14 author:"Browning, Philippa" ------------------------------------------------------------------------ Title: Oscillatory reconnection and waves driven by merging magnetic flux ropes in solar flares Authors: Stewart, J.; Browning, P. K.; Gordovskyy, M. Bibcode: 2022MNRAS.513.5224S Altcode: 2022arXiv220503106S Oscillatory reconnection is a process that has been suggested to underlie several solar and stellar phenomena, and is likely to play an important role in transient events such as flares. Quasi-periodic pulsations in flare emissions may be a manifestation of oscillatory reconnection, but the underlying mechanisms remain uncertain. In this paper, we present 2D magnetohydrodynamic simulations of two current-carrying magnetic flux ropes with an out-of-plane magnetic field undergoing oscillatory reconnection in which the two flux ropes merge into a single flux rope. We find that oscillatory reconnection can occur intrinsically without an external oscillatory driver during flux rope coalescence, which may occur both during large-scale coronal loop interactions and the merging of plasmoids in fragmented current sheets. Furthermore, we demonstrate that radially propagating non-linear waves are produced in the aftermath of flux rope coalescence, due to the post-reconnection oscillations of the merged flux rope. The behaviour of these waves is found to be almost independent of the initial out-of-plane magnetic field. It is estimated that the waves emitted through merging coronal loops and merging plasmoids in loop-top current sheets would have a typical phase speed of 90 and 900 km s-1, respectively. It is possible that the properties of the waves emitted during flux rope coalescence could be used as a diagnostic tool to determine physical parameters within a coalescing region. Title: Pulsations of microwave emission from a solar flare in a twisted loop caused by intrinsic magnetohydrodynamic oscillations Authors: Smith, Christopher; Gordovskyy, M.; Browning, P. K. Bibcode: 2022MNRAS.511.2880S Altcode: 2022arXiv220108419S; 2022MNRAS.tmp..227S 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 70-75 s and amplitude of about 5-10 per cent seen in loops both with and without energetic electrons, and oscillations with a period of about 40 s and amplitude of a few tens of per cent observed only in loops with energetic electrons for about 100 s after the onset of fast energy release. We interpret the longer-period oscillations as the result of a standing kink mode modulating the average magnetic field strength in the loop, whilst the short-period intermittent oscillations associated with energetic electrons are likely to be produced by fast variations of the electric field, which produces energetic electrons in this scenario. The slowly decaying oscillations can explain the quasi-periodic pulsations often observed in the flaring corona. Title: Sizes and Shapes of Sources in Solar Metric Radio Bursts Authors: Gordovskyy, Mykola; Kontar, Eduard P.; Clarkson, Daniel L.; Chrysaphi, Nicolina; Browning, Philippa K. Bibcode: 2022ApJ...925..140G Altcode: 2021arXiv211107777G Metric and decametric radio emissions from the Sun are the only direct source of information about the dynamics of nonthermal electrons in the upper corona. In addition, the combination of spectral and imaging (sizes, shapes, and positions) observations of low-frequency radio sources can be used as a unique diagnostic tool to probe plasma turbulence in the solar corona and inner heliosphere. The geometry of the low-frequency sources and its variation with frequency are still not understood, primarily due to the relatively low spatial resolution available for solar observations. Here we report the first detailed multifrequency analysis of the sizes of solar radio sources observed by the Low Frequency Array. Furthermore, we investigate the source shapes by approximating the derived intensity distributions using 2D Gaussian profiles with elliptical half-maximum contours. These measurements have been made possible by a novel empirical method for evaluating the instrumental and ionospheric effects on radio maps based on known source observations. The obtained deconvolved sizes of the sources are found to be smaller than previous estimations, and often show higher ellipticity. The sizes and ellipticities of the sources inferred using 2D Gaussian approximation, and their variation with frequency are consistent with models of anisotropic radio-wave scattering in the solar corona. Title: The high-energy Sun - probing the origins of particle acceleration on our nearest star Authors: Matthews, S. A.; Reid, H. A. S.; Baker, D.; Bloomfield, D. S.; Browning, P. K.; Calcines, A.; Del Zanna, G.; Erdelyi, R.; Fletcher, L.; Hannah, I. G.; Jeffrey, N.; Klein, L.; Krucker, S.; Kontar, E.; Long, D. M.; MacKinnon, A.; Mann, G.; Mathioudakis, M.; Milligan, R.; Nakariakov, V. M.; Pesce-Rollins, M.; Shih, A. Y.; Smith, D.; Veronig, A.; Vilmer, N. Bibcode: 2021ExA...tmp..135M Altcode: As a frequent and energetic particle accelerator, our Sun provides us with an excellent astrophysical laboratory for understanding the fundamental process of particle acceleration. The exploitation of radiative diagnostics from electrons has shown that acceleration operates on sub-second time scales in a complex magnetic environment, where direct electric fields, wave turbulence, and shock waves all must contribute, although precise details are severely lacking. Ions were assumed to be accelerated in a similar manner to electrons, but γ-ray imaging confirmed that emission sources are spatially separated from X-ray sources, suggesting distinctly different acceleration mechanisms. Current X-ray and γ-ray spectroscopy provides only a basic understanding of accelerated particle spectra and the total energy budgets are therefore poorly constrained. Additionally, the recent detection of relativistic ion signatures lasting many hours, without an electron counterpart, is an enigma. We propose a single platform to directly measure the physical conditions present in the energy release sites and the environment in which the particles propagate and deposit their energy. To address this fundamental issue, we set out a suite of dedicated instruments that will probe both electrons and ions simultaneously to observe; high (seconds) temporal resolution photon spectra (4 keV - 150 MeV) with simultaneous imaging (1 keV - 30 MeV), polarization measurements (5-1000 keV) and high spatial and temporal resolution imaging spectroscopy in the UV/EUV/SXR (soft X-ray) regimes. These instruments will observe the broad range of radiative signatures produced in the solar atmosphere by accelerated particles. Title: Transport of energetic particles from reconnecting current sheets in flaring corona to the heliosphere Authors: Browning, Philippa; Gordovskyy, Mykola; Inoue, Satashi; Kontar, Eduard; Kusano, Kanya; Vekstein, Gregory Bibcode: 2021EGUGA..2315163B Altcode: In this study, we inverstigate the acceleration of electrons and ions at current sheets in the flaring solar corona, and their transport into the heliosphere. We consider both generic solar flare models and specific flaring events with a data-driven approach. The aim is to answer two questions: (a) what fraction of particles accelerated in different flares can escape into the heliosphere?; and (b) what are the characteristics of the particle populations propagating towards the chromosphere and into the heliosphere?We use a combination of data-driven 3D magnetohydrodynamics simulations with drift-kinetic particle simulations to model the evolution of the magnetic field and both thermal and non-thermal plasma and to forward-model observable characteristics. Particles are accelerated in current sheets associated with flaring reconnection. When applied to a specific flare, the model successfully predicts observed features such as the location and relative intensity of hard X-ray sources and helioseismic source locations. This confirms the viability of the approach.Using these MHD-particle models, we will show how the magnetic field evolution and particle transport processes affect the characteristics of both energetic electrons and ions in the the inner corona and the heliosphere. The implications for interpretation of in situ measurements of energetic particles by Solar Orbiter and Parker Solar Probe will be discussed. Title: Sizes of solar radio sources observed by LOFAR Authors: Gordovskyy, Mykola; Kontar, Eduard; Clarkson, Daniel; Browning, Philippa Bibcode: 2021EGUGA..2315852G Altcode: Decametric radio emission provides a unique insight into the physics of solar and heliospheric plasmas. Along with dynamic spectra, the spatial characteristics of the emission sources observed in solar radio bursts yield important information about the behaviour of high-energy non-thermal electrons, and the state of thermal plasma in the upper solar corona. Recently, it has been shown that sizes and locations of radio sources in the 10-100 MHz range can be used as a diagnostic tool for plasma turbulence in the upper corona and inner heliosphere. However, observations in this spectral range can be strongly affected by limited spatial resolution of the instrument, as well as by the effect of the Earth's ionosphere on radio wave propagation.We describe a new method for correcting radio intensity maps for instrumental and ionospheric effects using observations of a known radio source at an arbitrary location in the sky. Based on this method, we derive sizes and areas of the emission sources in the solar radio bursts observed by the Low-Frequency Array (LOFAR) in 30-45 MHz range. It is shown that the sizes of sources are of the order of ten arcminutes and decrease with increasing frequency. Overall, we find that the sizes and their variation, as well as the shapes of the sources in the considered events are consistent with the theoretical models of turbulent radio-wave scattering in the solar corona developed by Kontar et al. 2019 (Astrophys.J., 884, 122). Title: Forward Modeling of Particle Acceleration and Transport in an Individual Solar Flare Authors: Gordovskyy, Mykola; Browning, Philippa K.; Inoue, Satoshi; Kontar, Eduard P.; Kusano, Kanya; Vekstein, Grigory E. Bibcode: 2020ApJ...902..147G Altcode: 2020arXiv200910130G The aim of this study is to generate maps of the hard X-ray emission produced by energetic electrons in a solar flare and compare them with observations. The ultimate goal is to test the viability of the combined MHD/test-particle approach for data-driven modeling of active events in the solar corona and their impact on the heliosphere. Based on an MHD model of X-class solar flare observed on 2017 September 8, we calculate trajectories of a large number of electrons and protons using the relativistic guiding-center approach. Using the obtained particle trajectories, we deduce the spatial and energy distributions of energetic electrons and protons, and calculate bremsstrahlung hard X-ray emission using the "thin-target" approximation. Our approach predicts some key characteristics of energetic particles in the considered flare, including the size and location of the acceleration region, energetic particle trajectories and energy spectra. Most importantly, the hard X-ray bremsstrahlung intensity maps predicted by the model are in good agreement with those observed by RHESSI. Furthermore, the locations of proton and electron precipitation appear to be close to the sources of helioseismic response detected in this flare. Therefore, the adopted approach can be used for observationally driven modeling of individual solar flares, including manifestations of energetic particles in the corona, as well as the inner heliosphere. Title: Predicting the time variation of radio emission from MHD simulations of a flaring T-Tauri star Authors: Waterfall, C. O. G.; Browning, P. K.; Fuller, G. A.; Gordovskyy, M.; Orlando, S.; Reale, F. Bibcode: 2020MNRAS.496.2715W Altcode: 2020MNRAS.tmp.1811W; 2020arXiv200605570W We model the time-dependent radio emission from a disc accretion event in a T-Tauri star using 3D, ideal magnetohydrodynamic simulations combined with a gyrosynchrotron emission and radiative transfer model. We predict for the first time, the multifrequency (1-1000 GHz) intensity and circular polarization from a flaring T-Tauri star. A flux tube, connecting the star with its circumstellar disc, is populated with a distribution of non-thermal electrons that is allowed to decay exponentially after a heating event in the disc and the system is allowed to evolve. The energy distribution of the electrons, as well as the non-thermal power-law index and loss rate, are varied to see their effect on the overall flux. Spectra are generated from different lines of sight, giving different views of the flux tube and disc. The peak flux typically occurs around 20-30 GHz and the radio luminosity is consistent with that observed from T-Tauri stars. For all simulations, the peak flux is found to decrease and move to lower frequencies with elapsing time. The frequency-dependent circular polarization can reach 10 $-30{{\ \rm per\ cent}}$ but has a complex structure that evolves as the flare evolves. Our models show that observations of the evolution of the spectrum and its polarization can provide important constraints on physical properties of the flaring environment and associated accretion event. Title: Using the Stokes V widths of Fe I lines for diagnostics of the intrinsic solar photospheric magnetic field Authors: Gordovskyy, M.; Shelyag, S.; Browning, P. K.; Lozitsky, V. G. Bibcode: 2020A&A...633A.136G Altcode: 2019arXiv191203340G
Aims: The goal of this study is to explore a novel method for the solar photospheric magnetic field diagnostics using Stokes V widths of different magnetosensitive Fe I spectral lines.
Methods: We calculate Stokes I and V profiles of several Fe I lines based on a one-dimensional photospheric model VAL C using the NICOLE radiative transfer code. These profiles are used to produce calibration curves linking the intrinsic magnetic field values with the widths of blue peaks of Stokes V profiles. The obtained calibration curves are then tested using the Stokes profiles calculated for more realistic photospheric models based on magnetohydrodynamic of magneto-convection.
Results: It is shown that the developed Stokes V widths method can be used with various optical and near-infrared lines. Out of six lines considered in this study, Fe I 6301 line appears to be the most effective: it is sensitive to fields over ∼200 G and does not show any saturation up to ∼2 kG. Other lines considered can also be used for the photospheric field diagnostics with this method, however, only in narrower field value ranges, typically from about 100 G to 700-1000 G.
Conclusions: The developed method can be a useful alternative to the classical magnetic line ratio method, particularly when the choice of lines is limited. Title: Determining whether the squashing factor, Q, would be a good indicator of reconnection in a resistive MHD experiment devoid of null points Authors: Reid, J.; Parnell, C. E.; Hood, A. W.; Browning, P. K. Bibcode: 2020A&A...633A..92R Altcode: The squashing factor of a magnetic field, Q, is commonly used as an indicator of magnetic reconnection, but few studies seek to evaluate how reliable it is in comparison with other possible reconnection indicators. By using a full, self-consistent, three-dimensional, resistive magnetohydrodynamic experiment of interacting magnetic strands constituting a coronal loop, Q and several different quantities are determined. Each is then compared with the necessary and sufficient condition for reconnection, namely the integral along a field line of the component of the electric field parallel to the magnetic field. Among the reconnection indicators explored, we find the squashing factor less successful when compared with alternatives, such as Ohmic heating. In a reconnecting magnetic field devoid of null points, our work suggests that Q, being a geometric measure of the magnetic field, is not a reliable indicator of the onset or a diagnostic of the location of magnetic reconnection in some configurations. Title: Anisotropic Radio-wave Scattering and the Interpretation of Solar Radio Emission Observations Authors: Kontar, Eduard P.; Chen, Xingyao; Chrysaphi, Nicolina; Jeffrey, Natasha L. S.; Emslie, A. Gordon; Krupar, Vratislav; Maksimovic, Milan; Gordovskyy, Mykola; Browning, Philippa K. Bibcode: 2019ApJ...884..122K Altcode: 2019arXiv190900340K The observed properties (i.e., source size, source position, time duration, and decay time) of solar radio emission produced through plasma processes near the local plasma frequency, and hence the interpretation of solar radio bursts, are strongly influenced by propagation effects in the inhomogeneous turbulent solar corona. In this work, a 3D stochastic description of the propagation process is presented, based on the Fokker-Planck and Langevin equations of radio-wave transport in a medium containing anisotropic electron density fluctuations. Using a numerical treatment based on this model, we investigate the characteristic source sizes and burst decay times for Type III solar radio bursts. Comparison of the simulations with the observations of solar radio bursts shows that predominantly perpendicular density fluctuations in the solar corona are required, with an anisotropy factor of ∼0.3 for sources observed at around 30 MHz. The simulations also demonstrate that the photons are isotropized near the region of primary emission, but the waves are then focused by large-scale refraction, leading to plasma radio emission directivity that is characterized by a half width at half maximum of about 40° near 30 MHz. The results are applicable to various solar radio bursts produced via plasma emission. Title: Frequency-Distance Structure of Solar Radio Sources Observed by LOFAR Authors: Gordovskyy, Mykola; Kontar, Eduard; Browning, Philippa; Kuznetsov, Alexey Bibcode: 2019ApJ...873...48G Altcode: Low-frequency radio observations make it possible to study the solar corona at distances up to 2-3 R . Frequency of plasma emission is a proxy for electron density of the emitting plasma and, therefore, observations of solar radio bursts can be used to probe the density structure of the outer corona. In this study, positions of solar radio sources are investigated using the Low-Frequency Array (LOFAR) spectral imaging in the frequency range 30-50 MHz. We show that there are events where apparent positions of the radio sources cannot be explained using the standard coronal density models. Namely, the apparent heliocentric positions of the sources are 0.1-0.7 R further from the Sun compared with the positions predicted by the Newkirk model, and these shifts are frequency-dependent. We discuss several possible explanations for this effect, including enhanced plasma density in the flaring corona, as well as scattering and refraction of the radio waves. Title: Forced magnetic reconnection and plasmoid coalescence. I. Magnetohydrodynamic simulations Authors: Potter, M. A.; Browning, P. K.; Gordovskyy, M. Bibcode: 2019A&A...623A..15P Altcode: 2019arXiv190102392P Context. Forced magnetic reconnection, a reconnection event triggered by external perturbation, should be ubiquitous in the solar corona. Energy released during such cases can be much greater than that which was introduced by the perturbation. The exact dynamics of magnetic reconnection events are determined by the structure and complexity of the reconnection region: the thickness of reconnecting layers, the field curvature; the presence, shapes and sizes of magnetic islands. It is unclear how the properties of the external perturbation and the initial current sheet affect the reconnection region properties, and thereby the reconnection dynamics and energy release profile.
Aims: We investigate the effect of the form of the external perturbation and initial current sheet on the evolution of the reconnection region and the energy release process. Chiefly we explore the non-linear interactions between multiple, simultaneous perturbations, which represent more realistic scenarios. Future work will use these results in test particle simulations to investigate particle acceleration over multiple reconnection events.
Methods: Simulations are performed using Lare2d, a 2.5D Lagrangian-remap solver for the visco-resistive MHD equations. The model of forced reconnection is extended to include superpositions of sinusoidal driving disturbances, including localised Gaussian perturbations. A transient perturbation is applied to the boundaries of a region containing a force-free current sheet. The simulation domain is sufficiently wide to allow multiple magnetic islands to form and coalesce.
Results: Island coalescence contributes significantly to energy release and involves rapid reconnection. Long wavelength modes in perturbations dominate the evolution, without the presence of which reconnection is either slow, as in the case of short wavelength modes, or the initial current sheet remains stable, as in the case of noise perturbations. Multiple perturbations combine in a highly non-linear manner: reconnection is typically faster than when either disturbance is applied individually, with multiple low-energy events contributing to the same total energy release. Title: Combining MHD and kinetic modelling of solar flares Authors: Gordovskyy, Mykola; Browning, Philippa; Pinto, Rui F. Bibcode: 2019AdSpR..63.1453G Altcode: 2018arXiv180905751G Solar flares are explosive events in the solar corona, representing fast conversion of magnetic energy into thermal and kinetic energy, and hence radiation, due to magnetic reconnection. Modelling is essential for understanding and predicting these events. However, self-consistent modelling is extremely difficult due to the vast spatial and temporal scale separation between processes involving thermal plasma (normally considered using magnetohydrodynamic (MHD) approach) and non-thermal plasma (requiring a kinetic approach). In this mini-review we consider different approaches aimed at bridging the gap between fluid and kinetic modelling of solar flares. Two types of approaches are discussed: combined MHD/test-particle (MHDTP) models, which can be used for modelling the flaring corona with relatively small numbers of energetic particles, and hybrid fluid-kinetic methods, which can be used for modelling stronger events with higher numbers of energetic particles. Two specific examples are discussed in more detail: MHDTP models of magnetic reconnection and particle acceleration in kink-unstable twisted coronal loops, and a novel reduced-kinetic model of particle transport in converging magnetic fields. Title: Modelling the radio and X-ray emission from T-Tauri flares Authors: Waterfall, C. O. G.; Browning, P. K.; Fuller, G. A.; Gordovskyy, M. Bibcode: 2019MNRAS.483..917W Altcode: 2018MNRAS.tmp.2737W T-Tauri stars are known for their high levels of magnetic activity and variability. Both classical and weak-line T-Tauri stars are overluminous in the radio compared with the well-established Güdel-Benz relation between radio and X-ray luminosity for solar and main sequence stellar flares. We show that there is little difference in the observational properties of classical T-Tauri stars and weak-line T-Tauri stars. We then model a typical T-Tauri - circumstellar disc system magnetosphere to predict the radio emission from flares associated with the circumstellar disc and accretion events. We assume that energetic electrons are generated in a large-scale magnetic flux tube due to a reconnection event with the accretion disc field at 4 R. Our standard model, with a dipolar magnetic field with a strength of 2 kG at the stellar surface and non-thermal and thermal densities of 2.5 × 1011 cm-3 and 5.0 × 1011 cm-3 respectively, produces both X-ray and radio emission consistent with observations (logLX = 30.5, logLR = 16.3). Varying the model parameters, we can reproduce the observed range of radio and X-ray emission. The peak radio luminosity and the frequency of this peak (which occurs at >10 GHz and possibly beyond 100 GHz for some sets of parameters) depend on the fraction of non-thermal particles and may be used as a diagnostic of this quantity. The surface field strength was varied from 0.5 to 7 kG, with the peak flux increasing by over three orders of magnitude. The models provide a framework for constraining the properties of these sources and to guide and interpret future observations. Title: Analysis of unresolved photospheric magnetic field structure using Fe I 6301 and 6302 lines Authors: Gordovskyy, M.; Shelyag, S.; Browning, P. K.; Lozitsky, V. G. Bibcode: 2018A&A...619A.164G Altcode: 2018arXiv180806862G Context.Early magnetographic observations indicated that the magnetic field in the solar photosphere has an unresolved small-scale structure. Near-infrared and optical data with extremely high spatial resolution show that these structures have scales of a few tens of kilometres, which are not resolved in the majority of solar observations. Aims.The goal of this study is to establish the effect of the unresolved photospheric magnetic field structure on Stokes profiles observed with relatively low spatial resolution. Ultimately, we aim to develop methods for fast estimation of the photospheric magnetic filling factor and line-of-sight gradient of the photospheric magnetic field, which can be applied to large observational data sets. Methods.We exploit 3D magnetohydrodynamic models of magneto-convection developed using the MURAM code. Corresponding profiles of Fe I 6301.5 and 6302.5 Å spectral lines are calculated using the NICOLE radiative transfer code. The resulting I and V Stokes [x, y, λ] cubes with a reduced spatial resolution of 150 km are used to calculate magnetic field values as they would be obtained in observations with the Solar Optical Telescope (SOT) onboard Hinode or the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamic Observatory (SDO) mission.
Results: Three different methods of magnetic filling factor estimation are considered: the magnetic line ratio method, the Stokes V width method, and a simple statistical method. We find that the statistical method and the Stokes V width method are sufficiently reliable for fast filling factor estimations. Furthermore, we find that the Stokes I ± V bisector splitting gradient can be used for fast estimation of the line-of-sight gradient of the photospheric magnetic field. Title: Three-dimensional magnetic reconnection in a collapsing coronal loop system Authors: O'Flannagain, Aidan M.; Maloney, Shane A.; Gallagher, Peter T.; Browning, Philippa; Refojo, Jose Bibcode: 2018A&A...617A...9O Altcode: 2018arXiv180609365O Context. Magnetic reconnection is believed to be the primary mechanism by which non-potential energy stored in coronal magnetic fields is rapidly released during solar eruptive events. Unfortunately, owing to the small spatial scales on which reconnection is thought to occur, it is not directly observable in the solar corona. However, larger scale processes, such as associated inflow and outflow, and signatures of accelerated particles have been put forward as evidence of reconnection.
Aims: Using a combination of observations we explore the origin of a persistent Type I radio source that accompanies a coronal X-shaped structure during its passage across the disk. Of particular interest is the time range around a partial collapse of the structure that is associated with inflow, outflow, and signatures of particle acceleration.
Methods: Imaging radio observations from the Nançay Radioheliograph were used to localise the radio source. Solar Dynamics Observatory (SDO) AIA extreme ultraviolet (EUV) observations from the same time period were analysed, looking for evidence of inflows and outflows. Further mpole magnetic reconstructions using SDO HMI observations allowed the magnetic connectivity associated with the radio source to be determined.
Results: The Type I radio source was well aligned with a magnetic separator identified in the extrapolations. During the partial collapse, gradual (1 km s-1) and fast (5 km s-1) inflow phases and fast (30 km s-1) and rapid (80-100 km s-1) outflow phases were observed, resulting in an estimated reconnection rate of ∼0.06. The radio source brightening and dimming was found to be co-temporal with increased soft X-ray emission observed in both Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and Geostationary Operational Environmental Satellite (GOES).
Conclusions: We interpret the brightening and dimming of the radio emission as evidence for accelerated electrons in the reconnection region responding to a gradual fall and rapid rise in electric drift velocity, in response to the inflowing and outflowing field lines. These results present a comprehensive example of 3D null-point reconnection.

The movies associated to Figs. 2 and 3 are available at https://www.aanda.org/ Title: Coronal energy release by MHD avalanches: continuous driving Authors: Reid, J.; Hood, A. W.; Parnell, C. E.; Browning, P. K.; Cargill, P. J. Bibcode: 2018A&A...615A..84R Altcode: Previous work has confirmed the concept of a magnetohydrodynamic (MHD) avalanche in pre-stressed threads within a coronal loop. We undertook a series of full, three-dimensional MHD simulations in order to create three threads by twisting the magnetic field through boundary motions until an instability ensues. We find that, following the original instability, one unstable thread can disrupt its neighbours with continued driving. A "bursty" heating profile results, with a series of ongoing energy releases, but no evident steady state. For the first time using full MHD, we show that avalanches are a viable mechanism for the storing and release of magnetic energy in the solar corona, as a result of photospheric motions. Title: Spatial and frequency structure of solar LOFAR radio sources Authors: Gordovskyy, Mykola; Browning, Philippa; Kontar, Eduard; Kuznetsov, Alexey Bibcode: 2018EGUGA..2013823G Altcode: We investigate frequency-position structure of radio sources in solar type III and type IV bursts in the frequency range 30-50 MHz observed by LOFAR. These sources are produced by fundamental and harmonic plasma emission induced by propagating suprathermal electrons. Therefore, the frequency is a proxy for the electron density in the emitting plasma, and these observations can be used to estimate the plasma density in the outer corona. Our analysis indicates that coronal plasma, which produces the emission, is denser and has larger hydrodynamic scale height (i.e., it is less stratified or more uniform) compared to Newkirk's density model. We interpret this as the result of local plasma gradients induced by plasma motion in the corona above solar active regions. Title: Flare particle acceleration resulting from the interaction of twisted coronal flux ropes Authors: Threlfall, James; Hood, Alan; Browning, Philippa Bibcode: 2018EGUGA..20.5145T Altcode: Solar flares are highly explosive events which release significant quantities of energy (upto 10^32 ergs) from specific magnetic configurations in the solar atmosphere. As part of this process, flares produce unique signatures across the entire electromagnetic spectrum, from radio to ultra-violet (UV) and X-ray wavelengths, over extremely short length and timescales. Many of the observed signals are indicative of strong particle acceleration, where highly energised electron and proton populations rapidly achieve MeV/GeV energies and therefore form a significant fraction of the energy budget of each event. It is almost universally accepted that magnetic reconnection plays a fundamental role (on some level) in the acceleration of particles to such incredible energies. I will briefly summarise a recent investigation of non-thermal particle behaviour in a three-dimensional (3D) magnetohydrodynamical (MHD) model of unstable multi-threaded flaring coronal loops. Using the test-particle approach, I will describe how particle orbits respond to the reconnection and fragmentation in MHD simulations wherein the onset of the kink instability in a single loop thread can lead to the destabilisation and fragmentation of other loop threads. I will also compare the test particle energy distributions and final positions with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares. Title: Flare particle acceleration in the interaction of twisted coronal flux ropes Authors: Threlfall, J.; Hood, A. W.; Browning, P. K. Bibcode: 2018A&A...611A..40T Altcode: 2018arXiv180102907T Aim. The aim of this work is to investigate and characterise non-thermal particle behaviour in a three-dimensional (3D) magnetohydrodynamical (MHD) model of unstable multi-threaded flaring coronal loops.
Methods: We have used a numerical scheme which solves the relativistic guiding centre approximation to study the motion of electrons and protons. The scheme uses snapshots from high resolution numerical MHD simulations of coronal loops containing two threads, where a single thread becomes unstable and (in one case) destabilises and merges with an additional thread.
Results: The particle responses to the reconnection and fragmentation in MHD simulations of two loop threads are examined in detail. We illustrate the role played by uniform background resistivity and distinguish this from the role of anomalous resistivity using orbits in an MHD simulation where only one thread becomes unstable without destabilising further loop threads. We examine the (scalable) orbit energy gains and final positions recovered at different stages of a second MHD simulation wherein a secondary loop thread is destabilised by (and merges with) the first thread. We compare these results with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares. Title: Comparison of methods for modelling coronal magnetic fields Authors: Goldstraw, E. E.; Hood, A. W.; Browning, P. K.; Cargill, P. J. Bibcode: 2018A&A...610A..48G Altcode: 2017arXiv171107458G
Aims: Four different approximate approaches used to model the stressing of coronal magnetic fields due to an imposed photospheric motion are compared with each other and the results from a full time-dependent magnetohydrodynamic (MHD) code. The assumptions used for each of the approximate methods are tested by considering large photospheric footpoint displacements.
Methods: We consider a simple model problem, comparing the full non-linear MHD, determined with the Lare2D numerical code, with four approximate approaches. Two of these, magneto-frictional relaxation and a quasi-1D Grad-Shafranov approach, assume sequences of equilibria, whilst the other two methods, a second-order linearisation of the MHD equations and Reduced MHD, are time dependent.
Results: The relaxation method is very accurate compared to full MHD for force-free equilibria for all footpoint displacements, but has significant errors when the plasma β0 is of order unity. The 1D approach gives an extremely accurate description of the equilibria away from the photospheric boundary layers, and agrees well with Lare2D for all parameter values tested. The linearised MHD equations correctly predict the existence of photospheric boundary layers that are present in the full MHD results. As soon as the footpoint displacement becomes a significant fraction of the loop length, the RMHD method fails to model the sequences of equilibria correctly. The full numerical solution is interesting in its own right, and care must be taken for low β0 plasmas if the viscosity is too high. Title: Polarisation of microwave emission from reconnecting twisted coronal loops Authors: Gordovskyy, M.; Browning, P. K.; Kontar, E. P. Bibcode: 2017A&A...604A.116G Altcode: 2016arXiv161102237G Context. Magnetic reconnection and particle acceleration due to the kink instability in twisted coronal loops can be a viable scenario for confined solar flares. Detailed investigation of this phenomenon requires reliable methods for observational detection of magnetic twist in solar flares, which may not be possible solely through extreme UV and soft X-ray thermal emission. Polarisation of microwave emission in flaring loops can be used as one of the detection criteria.
Aims: The aim of this study is to investigate the effect of magnetic twist in flaring coronal loops on the polarisation of gyro-synchrotron microwave (GSMW) emission, and determine whether it could provide a means for magnetic twist detection.
Methods: We consider time-dependent magnetohydrodynamic and test-particle models developed using the LARE3D and GCA codes to investigate twisted coronal loops that relax after kink instability. Synthetic GSMW emission maps (I and V Stokes components) are calculated using GX simulator.
Results: It is found that flaring twisted coronal loops produce GSMW radiation with a gradient of circular polarisation across the loop. However, these patterns may be visible only for a relatively short period of time owing to fast magnetic reconfiguration after the instability. Their visibility also depends on the orientation and position of the loop on the solar disk. Typically, it would be difficult to see these characteristic polarisation patterns in a twisted loop seen from the top (I.e. close to the centre of the solar disk), but easier in a twisted loop seen from the side (I.e. observed very close to the limb). Title: A relaxation model of coronal heating in multiple interacting flux ropes Authors: Hussain, A. S.; Browning, P. K.; Hood, A. W. Bibcode: 2017A&A...600A...5H Altcode: Context. Heating the solar corona requires dissipation of stored magnetic energy, which may occur in twisted magnetic fields. Recently published numerical simulations show that the ideal kink instability in a twisted magnetic thread may trigger energy release in stable twisted neighbours, and demonstrate an avalanche of heating events.
Aims: We aim to construct a Taylor relaxation model for the energy release from two flux ropes and compare this with the outcomes of the simulations. We then aim to extend the model to large numbers of flux ropes, allowing the possibility of modelling a heating avalanche, and calculation of the energy release for ensembles of twisted threads with varying twist profiles.
Methods: The final state is calculated by assuming a helicity-conserving relaxation to a minimum energy state. Multiple scenarios are examined, which include kink-unstable flux ropes relaxing on their own, as well as stable and unstable flux ropes merging into a single rope as a result of magnetic reconnection. We consider alternative constraints that determine the spatial extent of the final relaxed state.
Results: Good agreement is found between the relaxation model and the magnetohydrodynamic simulations, both for interactions of two twisted threads and for a multi-thread avalanche. The model can predict the energy release for flux ropes of varying degrees of twist, which relax individually or which merge through reconnection into a single flux rope. It is found that the energy output of merging flux ropes is dominated by the energy of the most strongly twisted rope.
Conclusions: The relaxation approach provides a very good estimate of the energy release in an ensemble of twisted threads of which one is kink-unstable. Title: Magnetic reconnection in twisted magnetic fields in solar flares - heating, particle acceleration and observational signatures Authors: Browning, Philippa K. Bibcode: 2017psio.confE..65B Altcode: No abstract at ADS Title: Plasma motions and non-thermal line broadening in flaring twisted coronal loops Authors: Gordovskyy, M.; Kontar, E. P.; Browning, P. K. Bibcode: 2016A&A...589A.104G Altcode: 2015arXiv150806412G Context. Observation of coronal extreme ultra-violet (EUV) spectral lines sensitive to different temperatures offers an opportunity to evaluate the thermal structure and flows in flaring atmospheres. This, in turn, can be used to estimate the partitioning between the thermal and kinetic energies released in flares.
Aims: Our aim is to forward-model large-scale (50-10 000 km) velocity distributions to interpret non-thermal broadening of different spectral EUV lines observed in flares. The developed models allow us to understand the origin of the observed spectral line shifts and broadening, and link these features to particular physical phenomena in flaring atmospheres.
Methods: We use ideal magnetohydrodynamics (MHD) to derive unstable twisted magnetic fluxtube configurations in a gravitationally stratified atmosphere. The evolution of these twisted fluxtubes is followed using resistive MHD with anomalous resistivity depending on the local density and temperature. The model also takes thermal conduction and radiative losses in the continuum into account. The model allows us to evaluate average velocities and velocity dispersions, which would be interpreted as non-thermal velocities in observations, at different temperatures for different parts of the models.
Results: Our models show qualitative and quantitative agreement with observations. Thus, the line-of-sight (LOS) velocity dispersions demonstrate substantial correlation with the temperature, increasing from about 20-30 km s-1 around 1 MK to about 200-400 km s-1 near 10-20 MK. The average LOS velocities also correlate with velocity dispersions, although they demonstrate a very strong scattering compared to the observations. We also note that near footpoints the velocity dispersions across the magnetic field are systematically lower than those along the field. We conclude that the correlation between the flow velocities, velocity dispersions, and temperatures are likely to indicate that the same heating mechanism is responsible for heating the plasma, its turbulisation, and expansion/evaporation. Title: Energy Release in Driven Twisted Coronal Loops Authors: Bareford, M. R.; Gordovskyy, M.; Browning, P. K.; Hood, A. W. Bibcode: 2016SoPh..291..187B Altcode: 2015arXiv150601312B; 2015SoPh..tmp..177B We investigate magnetic reconnection in twisted magnetic fluxtubes, representing coronal loops. The main goal is to establish the influence of the field geometry and various thermodynamic effects on the stability of twisted fluxtubes and on the size and distribution of heated regions. In particular, we aim to investigate to what extent the earlier idealised models, based on the initially cylindrically symmetric fluxtubes, are different from more realistic models, including the large-scale curvature, atmospheric stratification, thermal conduction and other effects. In addition, we compare the roles of Ohmic heating and shock heating in energy conversion during magnetic reconnection in twisted loops. The models with straight fluxtubes show similar distribution of heated plasma during the reconnection: it initially forms a helical shape, which subsequently becomes very fragmented. The heating in these models is rather uniformly distributed along fluxtubes. At the same time, the hot plasma regions in curved loops are asymmetric and concentrated close to the loop tops. Large-scale curvature has a destabilising influence: less twist is needed for instability. Footpoint convergence normally delays the instability slightly, although in some cases, converging fluxtubes can be less stable. Finally, introducing a stratified atmosphere gives rise to decaying wave propagation, which has a destabilising effect. Title: An MHD Avalanche in a Multi-threaded Coronal Loop. Authors: Hood, A. W.; Cargill, P. J.; Browning, P. K.; Tam, K. V. Bibcode: 2016ApJ...817....5H Altcode: 2015arXiv151200628H For the first time, we demonstrate how an MHD avalanche might occur in a multithreaded coronal loop. Considering 23 non-potential magnetic threads within a loop, we use 3D MHD simulations to show that only one thread needs to be unstable in order to start an avalanche even when the others are below marginal stability. This has significant implications for coronal heating in that it provides for energy dissipation with a trigger mechanism. The instability of the unstable thread follows the evolution determined in many earlier investigations. However, once one stable thread is disrupted, it coalesces with a neighboring thread and this process disrupts other nearby threads. Coalescence with these disrupted threads then occurs leading to the disruption of yet more threads as the avalanche develops. Magnetic energy is released in discrete bursts as the surrounding stable threads are disrupted. The volume integrated heating, as a function of time, shows short spikes suggesting that the temporal form of the heating is more like that of nanoflares than of constant heating. Title: Thermal and non-thermal emission from reconnecting twisted coronal loops Authors: Pinto, R. F.; Gordovskyy, M.; Browning, P. K.; Vilmer, N. Bibcode: 2016A&A...585A.159P Altcode: 2015arXiv150601251P Context. Twisted magnetic fields should be ubiquitous in the solar corona, particularly in flare-producing active regions where the magnetic fields are strongly non-potential. The magnetic energy contained in such twisted fields can be released during solar flares and other explosive phenomena. It has recently been shown that reconnection in helical magnetic coronal loops results in plasma heating and particle acceleration distributed within a large volume, including the lower coronal and chromospheric sections of the loops. Hence, the magnetic reconnection and particle acceleration scenario involving magnetic helicity can be a viable alternative to the standard flare model, where particles are accelerated only in a small volume located in the upper corona.
Aims: The key goal of this study is to investigate the links and observational signatures of plasma heating and particle acceleration in kink-unstable twisted coronal loops.
Methods: We used a combination of magnetohydrodynamic (MHD) simulations and test-particle methods. These simulations describe the development of kink instability and magnetic reconnection in twisted coronal loops using resistive compressible MHD and incorporate atmospheric stratification and large-scale loop curvature. The resulting distributions of hot plasma let us estimate thermal X-ray emission intensities. With the electric and magnetic fields we obtained, we calculated electron trajectories using the guiding-centre approximation. These trajectories combined with the MHD plasma density distributions let us deduce synthetic hard X-ray bremsstrahlung intensities.
Results: Our simulations emphasise that the geometry of the emission patterns produced by hot plasma in flaring twisted coronal loops can differ from the actual geometry of the underlying magnetic fields. In particular, the twist angles revealed by the emission threads (soft X-ray thermal emission; SXR) are consistently lower than the field-line twist present at the onset of the kink instability. Hard X-ray (HXR) emission that is due to the interaction of energetic electrons with the stratified background is concentrated at the loop foot-points in these simulations, even though the electrons are accelerated everywhere within the coronal volume of the loop. The maximum of the HXR emission consistently precedes that of SXR emission, with the HXR light curve being approximately proportional to the temporal derivative of the SXR light curve. Title: Reduced drift-kinetics with thermal velocity distribution across magnetic field Authors: Gordovskyy, Mykola; Browning, Philippa Bibcode: 2016arXiv160200341G Altcode: The goal of this study is to develop an approximate self-consistent description of particle motion in strongly magnetised solar corona. We derive a set of reduced drift-kinetic equations based on the assumption that the gyro-velocity distribution is Maxwellian. The equations are tested using simple 1D models. Title: Coronal heating in multiple magnetic threads Authors: Tam, K. V.; Hood, A. W.; Browning, P. K.; Cargill, P. J. Bibcode: 2015A&A...580A.122T Altcode: 2015arXiv150700259T Context. Heating the solar corona to several million degrees requires the conversion of magnetic energy into thermal energy. In this paper, we investigate whether an unstable magnetic thread within a coronal loop can destabilise a neighbouring magnetic thread.
Aims: By running a series of simulations, we aim to understand under what conditions the destabilisation of a single magnetic thread can also trigger a release of energy in a nearby thread.
Methods: The 3D magnetohydrodynamics code, Lare3d, is used to simulate the temporal evolution of coronal magnetic fields during a kink instability and the subsequent relaxation process. We assume that a coronal magnetic loop consists of non-potential magnetic threads that are initially in an equilibrium state.
Results: The non-linear kink instability in one magnetic thread forms a helical current sheet and initiates magnetic reconnection. The current sheet fragments, and magnetic energy is released throughout that thread. We find that, under certain conditions, this event can destabilise a nearby thread, which is a necessary requirement for starting an avalanche of energy release in magnetic threads.
Conclusions: It is possible to initiate an energy release in a nearby, non-potential magnetic thread, because the energy released from one unstable magnetic thread can trigger energy release in nearby threads, provided that the nearby structures are close to marginal stability. Title: Solar and Heliospheric Physics with the Square Kilometre Array Authors: Nakariakov, V.; Bisi, M. M.; Browning, P. K.; Maia, D.; Kontar, E. P.; Oberoi, D.; Gallagher, P. T.; Cairns, I. H.; Ratcliffe, H. Bibcode: 2015aska.confE.169N Altcode: 2015PoS...215E.169N; 2015arXiv150700516N The fields of solar radiophysics and solar system radio physics, or radio heliophysics, will benefit immensely from an instrument with the capabilities projected for SKA. Potential applications include interplanetary scintillation (IPS), radio-burst tracking, and solar spectral radio imaging with a superior sensitivity. These will provide breakthrough new insights and results in topics of fundamental importance, such as the physics of impulsive energy releases, magnetohydrodynamic oscillations and turbulence, the dynamics of post-eruptive processes, energetic particle acceleration, the structure of the solar wind and the development and evolution of solar wind transients at distances up to and beyond the orbit of the Earth. The combination of the high spectral, time and spatial resolution and the unprecedented sensitivity of the SKA will radically advance our understanding of basic physical processes operating in solar and heliospheric plasmas and provide a solid foundation for the forecasting of space weather events. Title: Recent advances in coronal heating Authors: De Moortel, Ineke; Browning, Philippa Bibcode: 2015RSPTA.37340269D Altcode: 2015arXiv151000977D The solar corona, the tenuous outer atmosphere of the Sun, is orders of magnitude hotter than the solar surface. This 'coronal heating problem' requires the identification of a heat source to balance losses due to thermal conduction, radiation and (in some locations) convection. The review papers in this Theo Murphy meeting issue present an overview of recent observational findings, large- and small-scale numerical modelling of physical processes occurring in the solar atmosphere and other aspects which may affect our understanding of the proposed heating mechanisms. At the same time, they also set out the directions and challenges which must be tackled by future research. In this brief introduction, we summarize some of the issues and themes which reoccur throughout this issue. Title: Notes on Magnetohydrodynamics of Magnetic Reconnection in Turbulent Media Authors: Browning, Philippa; Lazarian, Alex Bibcode: 2014mpcp.book..249B Altcode: 2014mcp..book..249B Astrophysical fluids have very large Reynolds numbers and therefore turbulence is their natural state. Magnetic reconnection is an important process in many astrophysical plasmas, which allows restructuring of magnetic fields and conversion of stored magnetic energy into heat and kinetic energy. Turbulence is known to dramatically change different transport processes and therefore it is not unexpected that turbulence can alter the dynamics of magnetic field lines within the reconnection process. We shall review the interaction between turbulence and reconnection at different scales, showing how a state of turbulent reconnection is natural in astrophysical plasmas, with implications for a range of phenomena across astrophysics. We consider the process of magnetic reconnection that is fast in magnetohydrodynamic (MHD) limit and discuss how turbulence—both externally driven and generated in the reconnecting system—can make reconnection independent on the microphysical properties of plasmas. We will also show how relaxation theory can be used to calculate the energy dissipated in turbulent reconnecting fields. As well as heating the plasma, the energy dissipated by turbulent reconnection may cause acceleration of non-thermal particles, which is briefly discussed here. Title: Accelerated particles and their observational signatures from confined solar flares in twisted coronal loops Authors: Browning, Philippa; Kontar, Eduard; Vilmer, Nicole; Gordovskyy, Mykola; Pinto, Rui; Bian, Nicolas Bibcode: 2014cosp...40E.416B Altcode: Twisted magnetic fields provide a reservoir of free magnetic energy, and are ubiquitous in the solar corona. Recent theoretical studies suggest that the onset of the kink instability in twisted coronal loops may generate fragmented current sheets throughout the loop, leading to fast magnetic reconnection which dissipates magnetic energy. This provides a viable model for small self-contained flares. Using a combination of 3D MHD and guiding-centre test-particle simulations, incorporating collisions with the background plasma, we study the kinetics of non-thermal particles accelerated during magnetic reconnection in a flaring twisted coronal loop. It is shown that this model can provide the number of high-energy electrons and acceleration efficiency comparable with those obtained from observations of small flares. We consider various geometries: including idealised cylindrical loop models, as well as, more realistically, curved loops. The effects of gravitational stratification, which has very significant effects on the non-thermal particles through collisions, are included. The calculated loop temperatures and densities, and the energy spectra and pitch-angles of the accelerated particles, are used to forward-model the emission in both Soft X-rays and Hard X-rays, predicting spatial distributions and temporal evolution, as well as radio emission arising from cyclotron/synchrotron radiation. These properties may be compared with observations. Title: Particle acceleration and transport in reconnecting twisted loops in a stratified atmosphere Authors: Gordovskyy, M.; Browning, P. K.; Kontar, E. P.; Bian, N. H. Bibcode: 2014A&A...561A..72G Altcode: 2015arXiv150106418G Context. Twisted coronal loops should be ubiquitous in the solar corona. Twisted magnetic fields contain excess magnetic energy, which can be released during magnetic reconnection, causing solar flares.
Aims: The aim of this work is to investigate magnetic reconnection, and particle acceleration and transport in kink-unstable twisted coronal loops, with a focus on the effects of resistivity, loop geometry and atmospheric stratification. Another aim is to perform forward-modelling of bremsstrahlung emission and determine the structure of hard X-ray sources.
Methods: We use a combination of magnetohydrodynamic (MHD) and test-particle methods. First, the evolution of the kinking coronal loop is considered using resistive MHD model, incorporating atmospheric stratification and loop curvature. Then, the obtained electric and magnetic fields and density distributions are used to calculate electron and proton trajectories using a guiding-centre approximation, taking into account Coulomb collisions.
Results: It is shown that electric fields in twisted coronal loops can effectively accelerate protons and electrons to energies up to 10 MeV. High-energy particles have hard, nearly power-law energy spectra. The volume occupied by high-energy particles demonstrates radial expansion, which results in the expansion of the visible hard X-ray loop and a gradual increase in hard X-ray footpoint area. Synthesised hard X-ray emission reveals strong footpoint sources and the extended coronal source, whose intensity strongly depends on the coronal loop density. Title: Microphysics of Cosmic Plasmas: Hierarchies of Plasma Instabilities from MHD to Kinetic Authors: Brown, M. R.; Browning, P. K.; Dieckmann, M. E.; Furno, I.; Intrator, T. P. Bibcode: 2014mpcp.book..281B Altcode: 2014mcp..book..281B In this article, we discuss the idea of a hierarchy of instabilities that can rapidly couple the disparate scales of a turbulent plasma system. First, at the largest scale of the system, L, current carrying flux ropes can undergo a kink instability. Second, a kink instability in adjacent flux ropes can rapidly bring together bundles of magnetic flux and drive reconnection, introducing a new scale of the current sheet width, ℓ, perhaps several ion inertial lengths (δ i ) across. Finally, intense current sheets driven by reconnection electric fields can destabilize kinetic waves such as ion cyclotron waves as long as the drift speed of the electrons is large compared to the ion thermal speed, v D ≫v i . Instabilities such as these can couple MHD scales to kinetic scales, as small as the proton Larmor radius, ρ i . Title: Simulations of energy release and particle acceleration in forced magnetic reconnection in solar flare current sheets Authors: Browning, Philippa; Gordovskyy, Mykola Bibcode: 2014cosp...40E.415B Altcode: Solar flares are a release of stored magnetic energy through magnetic reconnection. The electric fields associated with reconnection are a strong candidate for explaining the origin of the large numbers of non-thermal electrons and ions which are produces in flares. A useful model for large-scale current sheets in solar flares is forced magnetic reconnection, triggered by a boundary disturbance, in a force-free current sheet. A chain of magnetic islands is generated, where particles may be trapped, as well as remaining open field lines which allow particles to escape to the solar surface or into the heliosphere. We present results both from test particle codes coupled to magnetohydrodynamic simulations, and particle-in-cell codes, and compare the results of the two approaches with regard to the energy spectra and spatial locations of both ions and electrons. Title: The origins of space weather: recent advances in understanding solar flares Authors: Browning, Philippa Bibcode: 2014cosp...40E.414B Altcode: “Space weather” events affecting the terrestrial magnetosphere have their origins in explosive events in the solar atmosphere, notably solar flares. Solar flares may affect the magnetosphere through EUV/X-ray radiation and energetic charged particles (both ions and electrons) , as well as the production of Coronal Mass Ejections (CMEs). A brief overview of our current theoretical and observational understanding of solar flares will be given, focusing on the generation of radiation, particles and CMEs. Recent new models of the acceleration of charged particles by magnetic reconnection in large-scale current sheets solar flares will be described, showing how populations of both trapped and escaping non-thermal particles are generated - the latter propagating into the heliosphere. Test particle and particle-in-cell modelling allow prediction of the time evolution of energy spectra and pitch angles of energetic particles, and their spatial distributions. Smaller, confined flares may occur due to instabilities in twisted magnetic loops. Recent modelling of the heating and particle acceleration in unstable twisted loops will be described, using a coupled magnetohydrodynamic and test particle approach. The time dependence of the radiation in EUV and soft X-rays, due to plasma heating, as well as the Hard X-rays associated with the non-thermal particles are forward-modelled, allowing comparison with data from SDO and RHESSI, and radio instruments. Title: Models of Fine Structure in Coronal Loops Authors: Browning, Philippa; Gordovskyy, Mykola Bibcode: 2014cosp...40E.413B Altcode: Modelling based on the magnetohydrodynamic (MHD) equations shows that fine structure naturally arises in coronal loops. Magnetic reconnection may occur in narrow current structures, leading to efficient dissipation of stored magnetic energy and heating of the coronal plasma. An overview of such models will be presented, and the relevance to recent observations will be considered. One approach proposes that complex motions in the photosphere lead to braiding of the field and the formation of current sheets in the corona. Alternatively, even very simple footpoint motions, in the form of rotations, can lead to kink instabilities which inevitably generate fine structure in the form of current sheets. The results of 3D MHD simulations of unstable twisted loops will be presented, including recent results which consider realistic curved loops in a gravitationally stratified atmosphere, showing how a network of fragmented current sheet arises. Forward-modelling of the observable properties of fine structure in unstable twisted loops will be described, together with the implications for heating of the coronal plasma. The generation of fine structure leads to significant modelling challenges, including a need to include physics beyond MHD, and a brief discussion of some of these issues will be given. Title: Two-fluid simulations of driven reconnection in the mega-ampere spherical tokamak Authors: Stanier, A.; Browning, P.; Gordovskyy, M.; McClements, K. G.; Gryaznevich, M. P.; Lukin, V. S. Bibcode: 2013PhPl...20l2302S Altcode: 2013arXiv1308.2855S In the merging-compression method of plasma start-up, two flux-ropes with parallel toroidal current are formed around in-vessel poloidal field coils, before merging to form a spherical tokamak plasma. This start-up method, used in the Mega-Ampere Spherical Tokamak (MAST), is studied as a high Lundquist number and low plasma-beta magnetic reconnection experiment. In this paper, 2D fluid simulations are presented of this merging process in order to understand the underlying physics, and better interpret the experimental data. These simulations examine the individual and combined effects of tight-aspect ratio geometry and two-fluid physics on the merging. The ideal self-driven flux-rope dynamics are coupled to the diffusion layer physics, resulting in a large range of phenomena. For resistive MHD simulations, the flux-ropes enter the sloshing regime for normalised resistivity η ≲10-5. In Hall-MHD, three regimes are found for the qualitative behaviour of the current sheet, depending on the ratio of the current sheet width to the ion-sound radius. These are a stable collisional regime, an open X-point regime, and an intermediate regime that is highly unstable to tearing-type instabilities. In toroidal axisymmetric geometry, the final state after merging is a MAST-like spherical tokamak with nested flux-surfaces. It is also shown that the evolution of simulated 1D radial density profiles closely resembles the Thomson scattering electron density measurements in MAST. An intuitive explanation for the origin of the measured density structures is proposed, based upon the results of the toroidal Hall-MHD simulations. Title: Notes on Magnetohydrodynamics of Magnetic Reconnection in Turbulent Media Authors: Browning, Philippa; Lazarian, Alex Bibcode: 2013SSRv..178..325B Altcode: 2013SSRv..tmp...92B Astrophysical fluids have very large Reynolds numbers and therefore turbulence is their natural state. Magnetic reconnection is an important process in many astrophysical plasmas, which allows restructuring of magnetic fields and conversion of stored magnetic energy into heat and kinetic energy. Turbulence is known to dramatically change different transport processes and therefore it is not unexpected that turbulence can alter the dynamics of magnetic field lines within the reconnection process. We shall review the interaction between turbulence and reconnection at different scales, showing how a state of turbulent reconnection is natural in astrophysical plasmas, with implications for a range of phenomena across astrophysics. We consider the process of magnetic reconnection that is fast in magnetohydrodynamic (MHD) limit and discuss how turbulence—both externally driven and generated in the reconnecting system—can make reconnection independent on the microphysical properties of plasmas. We will also show how relaxation theory can be used to calculate the energy dissipated in turbulent reconnecting fields. As well as heating the plasma, the energy dissipated by turbulent reconnection may cause acceleration of non-thermal particles, which is briefly discussed here. Title: Microphysics of Cosmic Plasmas: Hierarchies of Plasma Instabilities from MHD to Kinetic Authors: Brown, M. R.; Browning, P. K.; Dieckmann, M. E.; Furno, I.; Intrator, T. P. Bibcode: 2013SSRv..178..357B Altcode: 2013SSRv..tmp...80B In this article, we discuss the idea of a hierarchy of instabilities that can rapidly couple the disparate scales of a turbulent plasma system. First, at the largest scale of the system, L, current carrying flux ropes can undergo a kink instability. Second, a kink instability in adjacent flux ropes can rapidly bring together bundles of magnetic flux and drive reconnection, introducing a new scale of the current sheet width, ℓ, perhaps several ion inertial lengths ( δ i ) across. Finally, intense current sheets driven by reconnection electric fields can destabilize kinetic waves such as ion cyclotron waves as long as the drift speed of the electrons is large compared to the ion thermal speed, v D ≫ v i . Instabilities such as these can couple MHD scales to kinetic scales, as small as the proton Larmor radius, ρ i . Title: Effect of Collisions and Magnetic Convergence on Electron Acceleration and Transport in Reconnecting Twisted Solar Flare Loops Authors: Gordovskyy, M.; Browning, P. K.; Kontar, E. P.; Bian, N. H. Bibcode: 2013SoPh..284..489G Altcode: 2012SoPh..tmp..225G; 2015arXiv150106436G We study a model of particle acceleration coupled with an MHD model of magnetic reconnection in unstable twisted coronal loops. The kink instability leads to the formation of helical currents with strong parallel electric fields resulting in electron acceleration. The motion of electrons in the electric and magnetic fields of the reconnecting loop is investigated using a test-particle approach taking into account collisional scattering. We discuss the effects of Coulomb collisions and magnetic convergence near loop footpoints on the spatial distribution and energy spectra of high-energy electron populations and possible implications on the hard X-ray emission in solar flares. Title: Coronal heating by the partial relaxation of twisted loops Authors: Bareford, M. R.; Hood, A. W.; Browning, P. K. Bibcode: 2013A&A...550A..40B Altcode: 2012arXiv1211.3855B Context. Relaxation theory offers a straightforward method for estimating the energy that is released when continual convective driving causes a magnetic field to become unstable. Thus, an upper limit to the heating caused by ensembles of nanoflaring coronal loops can be calculated and checked against the level of heating required to maintain observed coronal temperatures (T ≳ 106 K).
Aims: We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. All of the initial loop configurations discussed are known to be linearly kink unstable. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. In addition, we show for two cases how the relaxation process unfolds.
Methods: A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of a line-tied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewise-constant current profile, featuring three parameters. Initially, all configurations carry zero-net-current fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicity-conserving relaxation theory.
Results: For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analytically-determined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion.
Conclusions: The results presented here support the use of partial relaxation theory, specifically, when calculating the heating-event distributions produced by ensembles of kink-unstable loops. The energy release increases with relaxation radius; but, once the loop has expanded by more than 50%, further expansion yields little more energy. We conclude that the relaxation methodology may be used for coronal heating studies. Title: Magnetic reconnection and particle acceleration in twisted coronal loops Authors: Gordovskyy, M.; Browning, P. Bibcode: 2012AGUFMSH43B2153G Altcode: We consider models of magnetic reconnection and particle acceleration occurring in twisted coronal loops. In this scenario, a potential field over bipolar magnetic region is twisted by photospheric rotation yielding an unstable nearly force-free magnetic loop with the strong field convergence near foot-points. The kink instability results in drastic increase of the current density, which, in turn, leads to magnetic reconnection. Appearance of strong electric field with very fragmented structure results in particle acceleration. Based on this 3D time-dependent MHD model, proton and electron motion is considered using the relativistic guiding centre motion equations and taking into account Coulomb collisions. We derive spectral and spatial distribution of HXR emission and discuss possible observational implications. Title: Particle Acceleration at Reconnecting 3D Null Points Authors: Stanier, A.; Browning, P.; Gordovskyy, M.; Dalla, S. Bibcode: 2012AGUFMSH51A2208S Altcode: Hard X-ray observations from the RHESSI spacecraft indicate that a significant fraction of solar flare energy release is in non-thermal energetic particles. A plausible acceleration mechanism for these are the strong electric fields associated with reconnection, a process that can be particularly efficient when particles become unmagnetised near to null points. This mechanism has been well studied in 2D, at X-points within reconnecting current sheets; however, 3D reconnection models show significant qualitative differences and it is not known whether these new models are efficient for particle acceleration. We place test particles in analytic model fields (eg. Craig and Fabling 1996) and numerical solutions to the the resistive magnetohydrodynamic (MHD) equations near reconnecting 3D nulls. We compare the behaviour of these test particles with previous results for test particle acceleration in ideal MHD models (Dalla and Browning 2005). We find that the fan model is very efficient due to an increasing "guide field" that stabilises particles against ejection from the current sheet. However, the spine model, which was the most promising in the ideal case, gives weak acceleration as the reconnection electric field is localised to a narrow cylinder about the spine axis. Title: Editorial: How JGR works Authors: Lysak, R. L.; Fujimoto, M.; Browning, P. Bibcode: 2012JGRA..11710001L Altcode: 2012JGRA..11710001. No abstract at ADS Title: Solar particle acceleration at reconnecting 3D null points Authors: Stanier, A.; Browning, P.; Dalla, S. Bibcode: 2012A&A...542A..47S Altcode: 2012arXiv1201.4846S Context. The strong electric fields associated with magnetic reconnection in solar flares are a plausible mechanism to accelerate populations of high energy, non-thermal particles. One such reconnection scenario, in a fully 3D geometry, occurs at a magnetic null point. Here, global plasma motion can give rise to strong currents in the spine axis or fan plane.
Aims: We aim to understand the mechanism of charged particle energy gain in both the external drift region and the diffusion region associated with 3D magnetic reconnection. In doing so we aim to evaluate the efficiency of resistive spine and fan models for particle acceleration, and find possible observables for each.
Methods: We used a full orbit test particle approach to study proton trajectories within electromagnetic fields that are exact solutions to the steady and incompressible magnetohydrodynamic equations. We studied the acceleration physics of single particle trajectories and found energy spectra from many particle simulations. The scaling properties of the accelerated particles with respect to field and plasma parameters was investigated.
Results: For fan reconnection, strong non-uniform electric drift streamlines can accelerate the bulk of the test particles. The highest energy gain is for particles that enter the current sheet, where an increasing "guide field" stabilises particles against ejection. The energy is only limited by the total electric potential energy difference across the fan current sheet. The spine model has both slow external electric drift speed and weak energy gain for particles reaching the current sheet.
Conclusions: The electromagnetic fields of fan reconnection can accelerate protons to the high energies observed in solar flares, gaining up to 0.1 GeV for anomalous values of resistivity. However, the spine model, which gave a harder energy spectrum in the ideal case, is not an efficient accelerator after pressure constraints in the resistive model are included. Title: Magnetic Relaxation and Particle Acceleration in a Flaring Twisted Coronal Loop Authors: Gordovskyy, M.; Browning, P. K. Bibcode: 2012SoPh..277..299G Altcode: In the present work we aim to study particle acceleration in twisted coronal loops. For this purpose, an MHD model of magnetic reconnection in a linearly unstable twisted magnetic fluxtube is considered. Further, the electric and magnetic fields obtained in the MHD simulations are used to calculate proton and electron trajectories in the guiding-centre approximation. It is shown that particle acceleration in such a model is distributed rather uniformly along the coronal loop and the high-energy population remains generally neutral. It also follows from the model that the horizontal cross-section of the volume occupied by high-energy particles near the loop footpoints increases with time, which can be used as an observational proxy. Title: Solar Particle Acceleration Radiation and Kinetics (SPARK). A mission to understand the nature of particle acceleration Authors: Matthews, Sarah A.; Williams, David R.; Klein, Karl-Ludwig; Kontar, Eduard P.; Smith, David M.; Lagg, Andreas; Krucker, Sam; Hurford, Gordon J.; Vilmer, Nicole; MacKinnon, Alexander L.; Zharkova, Valentina V.; Fletcher, Lyndsay; Hannah, Iain G.; Browning, Philippa K.; Innes, Davina E.; Trottet, Gerard; Foullon, Clare; Nakariakov, Valery M.; Green, Lucie M.; Lamoureux, Herve; Forsyth, Colin; Walton, David M.; Mathioudakis, Mihalis; Gandorfer, Achim; Martinez-Pillet, Valentin; Limousin, Olivier; Verwichte, Erwin; Dalla, Silvia; Mann, Gottfried; Aurass, Henri; Neukirch, Thomas Bibcode: 2012ExA....33..237M Altcode: 2011ExA...tmp..124M Energetic particles are critical components of plasma populations found throughout the universe. In many cases particles are accelerated to relativistic energies and represent a substantial fraction of the total energy of the system, thus requiring extremely efficient acceleration processes. The production of accelerated particles also appears coupled to magnetic field evolution in astrophysical plasmas through the turbulent magnetic fields produced by diffusive shock acceleration. Particle acceleration is thus a key component in helping to understand the origin and evolution of magnetic structures in, e.g. galaxies. The proximity of the Sun and the range of high-resolution diagnostics available within the solar atmosphere offers unique opportunities to study the processes involved in particle acceleration through the use of a combination of remote sensing observations of the radiative signatures of accelerated particles, and of their plasma and magnetic environment. The SPARK concept targets the broad range of energy, spatial and temporal scales over which particle acceleration occurs in the solar atmosphere, in order to determine how and where energetic particles are accelerated. SPARK combines highly complementary imaging and spectroscopic observations of radiation from energetic electrons, protons and ions set in their plasma and magnetic context. The payload comprises focusing-optics X-ray imaging covering the range from 1 to 60 keV; indirect HXR imaging and spectroscopy from 5 to 200 keV, γ-ray spectroscopic imaging with high-resolution LaBr3 scintillators, and photometry and source localisation at far-infrared wavelengths. The plasma environment of the regions of acceleration and interaction will be probed using soft X-ray imaging of the corona and vector magnetography of the photosphere and chromosphere. SPARK is designed for solar research. However, in addition it will be able to provide exciting new insights into the origin of particle acceleration in other regimes, including terrestrial gamma-ray flashes (TGF), the origin of γ-ray bursts, and the possible existence of axions. Title: Relaxation and Heating Triggered by Nonlinear Kink Instability: Application to Solar Flares and Coronal Heating Authors: Browning, Philippa K.; Bareford, Michael R.; Gordovskyy, Mykola Bibcode: 2012ASSP...33...69B Altcode: 2012msdp.book...69B Energy release and particle acceleration in kink-unstable twisted coronal loops are discussed. If the magnetic field in a coronal loop is sufficiently strongly twisted, it may become unstable to the ideal kink instability. We present results of 3D MHD simulations which show that in the nonlinear phase of the instability, current sheets form in which magnetic reconnection rapidly dissipates magnetic energy. In the later phase, the current sheet fragments. The energy release is well-modelled by a helicity conserving relaxation to a minimum energy state. We exploit this in order to calculate a distribution of energy-release events, and show how this is relevant to the solar coronal heating problem. Using test particle approach coupled with 3D MHD simulations, we also show how the electric fields associated with the fragmented currents sheet can efficiently accelerate charged particles. This has implications for the origin of high-energy particles in solar flares. Title: Acceleration of charged particles in solar flares by magnetic reconnection in twisted coronal loops Authors: Browning, P.; Gordovskyy, M. Bibcode: 2011AGUFMSH51E..04B Altcode: A coronal loop twisted by photospheric footpoint motions may become unstable to the ideal kink mode. Numerical simulations show that, in the nonlinear phase of this instability, current sheets develop, leading to magnetic reconnection and energy dissipation - this is manifest as a confined flare. The electric fields associated with these fragmented current sheets are an efficient accelerator of charged particles. Test particle simulations, coupled to 3D MHD simulations, are used to determine the time-evolution of particle populations, and show that the loop quickly fills with high-energy ions and electrons. Firstly, we consider the evolution of loops whose initial magnetic field configuration is kink-unstable, consisting of a one-dimensional twisted flux tube. Then, we model loops with initially purely-axial field, which become twisted as a result of slow footpoint motions and thus become unstable; this model also includes the effects of flux tube expansion from the footpoints to the loop apex. Results are also presented showing the effects of collisions in the denser chromospheric plasma near the loop footpoints. Thus, transport is considered along with acceleration. Properties such as energy spectra and pitch-angle distributions are calculated, as well as spatial and temporal variations of particle properties, which may be compared with data. Title: The Flare-Energy Distributions Generated by Kink-Unstable Ensembles of Zero-Net-Current Coronal Loops Authors: Bareford, M. R.; Browning, P. K.; Van der Linden, R. A. M. Bibcode: 2011SoPh..273...93B Altcode: 2011SoPh..tmp..338B; 2011arXiv1103.5378B It has been proposed that the million-degree temperature of the corona is due to the combined effect of barely detectable energy releases, called nanoflares, that occur throughout the solar atmosphere. Unfortunately, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release; thus we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory; i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold. Title: Recent Advances in Understanding Particle Acceleration Processes in Solar Flares Authors: Zharkova, V. V.; Arzner, K.; Benz, A. O.; Browning, P.; Dauphin, C.; Emslie, A. G.; Fletcher, L.; Kontar, E. P.; Mann, G.; Onofri, M.; Petrosian, V.; Turkmani, R.; Vilmer, N.; Vlahos, L. Bibcode: 2011SSRv..159..357Z Altcode: 2011SSRv..tmp..156Z; 2011SSRv..tmp..249Z; 2011SSRv..tmp..232Z; 2011arXiv1110.2359Z; 2011SSRv..tmp..278Z We review basic theoretical concepts in particle acceleration, with particular emphasis on processes likely to occur in regions of magnetic reconnection. Several new developments are discussed, including detailed studies of reconnection in three-dimensional magnetic field configurations (e.g., current sheets, collapsing traps, separatrix regions) and stochastic acceleration in a turbulent environment. Fluid, test-particle, and particle-in-cell approaches are used and results compared. While these studies show considerable promise in accounting for the various observational manifestations of solar flares, they are limited by a number of factors, mostly relating to available computational power. Not the least of these issues is the need to explicitly incorporate the electrodynamic feedback of the accelerated particles themselves on the environment in which they are accelerated. A brief prognosis for future advancement is offered. Title: Particle Acceleration by Magnetic Reconnection in a Twisted Coronal Loop Authors: Gordovskyy, Mykola; Browning, Philippa K. Bibcode: 2011ApJ...729..101G Altcode: Photospheric motions may lead to twisted coronal magnetic fields which contain free energy that can be released by reconnection. Browning & Van der Linden suggested that such a relaxation event may be triggered by the onset of ideal kink instability. In the present work, we study the evolution of a twisted magnetic flux tube with zero net axial current following Hood et al. Based on the obtained magnetic and electric fields, proton and electron trajectories are calculated using the test-particle approach. We discuss resulting particle distributions and possible observational implications, for example, for small solar flares. Title: Acceleration of charged particles by reconnection by small solar flares in twisted loops Authors: Browning, P.; Gordovskyy, M. Bibcode: 2010AGUFMSH33B1845B Altcode: Solar flares produce large numbers of high energy ions and electrons. The primary energy release in solar flares is almost certainly magnetic reconnection, and the electric fields associated with reconnection are a strong candidate as a mechanism for particle acceleration. Test particle studies are a very useful tool to understanding this process, and particle acceleration in idealized steady 2D geometries has been widely studied with this approach. We extend this to consider both time-dependent and 3D fields, coupling a test particle approach with 3D MHD simulations of reconnecting fields. Time-dependent fields are used, so that the time evolution of the energy spectra and other properties can be explored. Results are presented for particle acceleration in fields arising in reconnecting current sheets which arise in the nonlinear phase of kink instability of a twisted coronal loop (Hood et al; Astron Astrophys. 506, 913 , 2009). This models small solar flares occurring in single loops. We compare behaviour in the early phase, which has a single monolithic helical current sheet, with the later phase, in which the current sheet structure is turbulent and fragmented, which allows particles to undergo multiple accelerations. In the turbulent phase, particles are accelerated throughout the loop volume, which mitigates some of the problems associated with the highly localised acceleration region postulated in the "standard flare model". We present results for the energy spectra, spatial distribution and pitch angles of the accelerated particles, and explore how these depend on the properties of the twisted coronal loop. Title: A nanoflare distribution generated by repeated relaxations triggered by kink instability Authors: Bareford, M. R.; Browning, P. K.; van der Linden, R. A. M. Bibcode: 2010A&A...521A..70B Altcode: 2010arXiv1005.5249B Context. It is thought likely that vast numbers of nanoflares are responsible for the corona having a temperature of millions of degrees. Current observational technologies lack the resolving power to confirm the nanoflare hypothesis. An alternative approach is to construct a magnetohydrodynamic coronal loop model that has the ability to predict nanoflare energy distributions.
Aims: This paper presents the initial results generated by a coronal loop model that flares whenever it becomes unstable to an ideal MHD kink mode. A feature of the model is that it predicts heating events with a range of sizes, depending on where the instability threshold for linear kink modes is encountered. The aims are to calculate the distribution of event energies and to investigate whether kink instability can be predicted from a single parameter.
Methods: The loop is represented as a straight line-tied cylinder. The twisting caused by random photospheric motions is captured by two parameters, representing the ratio of current density to field strength for specific regions of the loop. Instability onset is mapped as a closed boundary in the 2D parameter space. Dissipation of the loop's magnetic energy begins during the nonlinear stage of the instability, which develops as a consequence of current sheet reconnection. After flaring, the loop evolves to the state of lowest energy where, in accordance with relaxation theory, the ratio of current to field is constant throughout the loop and helicity is conserved.
Results: There exists substantial variation in the radial magnetic twist profiles for the loop states along the instability threshold. These results suggest that instability cannot be predicted by any simple twist-derived property reaching a critical value. The model is applied such that the loop undergoes repeated episodes of instability followed by energy-releasing relaxation. Hence, an energy distribution of the nanoflares produced is collated. This paper also presents the calculated relaxation states and energy releases for all instability threshold points.
Conclusions: The final energy distribution features two nanoflare populations that follow different power laws. The power law index for the higher energy population is more than sufficient for coronal heating.

Appendices are only available in electronic form at http://www.aanda.org Title: Scaling of particle acceleration in 3D reconnection at null points Authors: Browning, P. K.; Dalla, S.; Peters, D.; Smith, J. Bibcode: 2010A&A...520A.105B Altcode: Context. The strong electric fields associated with magnetic reconnection are likely to be responsible for the presence of high energy protons and electrons observed in solar flares. There is much evidence for 3D reconnection in the solar corona, and we discuss particle acceleration at 3D reconnection sites. The simplest configuration for 3D reconnection is at a 3D null point, where reconnection can take place in spine and fan modes.
Aims: The aim is to understand the properties of accelerated particles generated by 3D magnetic reconnection, using a test particle approach, and thus contribute to understanding the origin of high energy protons and electrons in solar flares. We analyse the properties of electrons in the magnetic configuration we previously used to study protons. In addition, we discuss the dependence of the particle properties on the parameters of the reconnection, such as strengths of electric and magnetic fields.
Methods: A theoretical framework is presented which can be used to interpret particle acceleration at 3D null points, and which shows how strong acceleration can arise. We also use a test particle approach to calculate particle trajectories in simple model 3D reconnecting nulls. A modified guiding-centre approach is used for electrons, whilst the full equation of motion is solved for protons.
Results: Most particle acceleration takes place when particles closely approach the spine or fan, and we have derived scalings for the sizes of the localised regions in which strong acceleration occurs. The energy spectra of protons and electrons are compared, and it is shown that the spatial distribution of accelerated electrons differs from protons. A significant number of trapped, high-energy particles can be generated, which may be observed as coronal HXR sources. The effectiveness of acceleration increases with the electric-field magnitude, and decreases with magnetic-field magnitude.
Conclusions: Both protons and electrons can be effectively accelerated at 3D reconnecting null points. The particle properties depend on the geometry and field parameters, so that, in principle, the field configuration may be inferred from observed properties of particles. Title: Particle acceleration in a transient magnetic reconnection event Authors: Gordovskyy, M.; Browning, P. K.; Vekstein, G. E. Bibcode: 2010A&A...519A..21G Altcode: Context. In the present paper, we investigate particle acceleration by direct electric field in solar flares.
Aims: Proton and electron kinetics are considered based on MHD simulations of magnetic reconnection, with the aim of determining the properties of accelerated particles in a time-dependent reconnecting event model.
Methods: At first, we considered several two-dimensional numerical models of forced reconnection in the initially force-free Harris current sheet. The electric and magnetic fields from these models were then used to study proton and electron motion with the guiding centre, test particle approach.
Results: It is shown that protons and electrons can be accelerated to very high energies up to tens of MeV in the present model. The energy spectra for both particle species are combinations of exponential and rather hard power-law shapes. Also, protons and electrons are ejected from the CS in different directions. Title: Particle Acceleration in Fragmenting Periodic Reconnecting Current Sheets in Solar Flares Authors: Gordovskyy, M.; Browning, P. K.; Vekstein, G. E. Bibcode: 2010ApJ...720.1603G Altcode: Proton and electron acceleration in a fragmenting periodic current sheet (CS) is investigated, based on the forced magnetic reconnection scenario. The aim is to understand the role of CS fragmentation in high-energy beam generation in solar flares. We combine magnetohydrodynamics and test-particle models to consider particle trajectories consistent with a time-dependent reconnection model. It is shown that accelerated particles in such a model form two distinct populations. Protons and electrons moving in open magnetic field have energy spectra that are a combination of the initial Maxwellian distribution and a power-law high-energy (E>20 keV) part. The second population contains particles moving in a closed magnetic field around O-points. These particles move predominantly along the guiding field and their energies fall within quite a narrow range between ~1 MeV and ~10 MeV. It is also found that particles moving in an open magnetic field have a considerably wider pitch-angle distribution. Title: Magnetic reconnection in the solar atmosphere: from proposal to paradigm Authors: Cargill, Peter; Parnell, Clare; Browning, Philippa; de Moortel, Ineke; Hood, Alan Bibcode: 2010A&G....51c..31C Altcode: MEETING REPORT On 13 November 2009, the RAS hosted a discussion meeting to commemorate the formal retirement of Prof. Eric Priest. Here Peter Cargill, Clare Parnell, Philippa Browning, Ineke de Moortel and Alan Hood examine how magnetic reconnection has evolved over the past 50 years from an important but controversial proposal, to a general paradigm. Title: Microflare Activity Driven by Forced Magnetic Reconnection Authors: Jess, D. B.; Mathioudakis, M.; Browning, P. K.; Crockett, P. J.; Keenan, F. P. Bibcode: 2010ApJ...712L.111J Altcode: 2010arXiv1002.3792J High cadence, multiwavelength, optical observations of a solar active region, obtained with the Swedish Solar Telescope, are presented. Two magnetic bright points are seen to separate in opposite directions at a constant velocity of 2.8 km s-1. After a separation distance of ≈4400 km is reached, multiple Ellerman bombs are observed in both Hα and Ca-K images. As a result of the Ellerman bombs, periodic velocity perturbations in the vicinity of the magnetic neutral line, derived from simultaneous Michelson Doppler Imager data, are generated with amplitude ±6 km s-1 and wavelength ≈1000 km. The velocity oscillations are followed by an impulsive brightening visible in Hα and Ca-K, with a peak intensity enhancement of 63%. We interpret these velocity perturbations as the magnetic field deformation necessary to trigger forced reconnection. A time delay of ≈3 minutes between the Hα-wing and Ca-K observations indicates that the observed magnetic reconnection occurs at a height of ~200 km above the solar surface. These observations are consistent with theoretical predictions and provide the first observational evidence of microflare activity driven by forced magnetic reconnection. Title: Particle acceleration by magnetic reconnection in unstable twisted coronal loop Authors: Gordovskyy, Mykola; Browning, Philippa; Vekstein, Grigory Bibcode: 2010cosp...38.2994G Altcode: 2010cosp.meet.2994G Photospheric motions may result in twisting of a coronal loop magnetic field. Such a field configuration contains free energy that may be released by reconnection with the magnetic field relaxing to the linear force-free configuration. Browning & Van der Linden (2003) suggested that such a relaxation event may be triggered by onset of ideal kink instability. In the present work we study the evolution of a twisted magnetic fluxtube with zero net ax-ial current following Browning et al. (2008). Further, proton and electron trajectories are investigated using the test-particle approach consistently with the time-dependent reconnec-tion model. We discuss temporal evolution of proton and electron energy spectra and possible observational implications. Title: Coronal heating by magnetic reconnection in loops with zero net current Authors: Hood, A. W.; Browning, P. K.; van der Linden, R. A. M. Bibcode: 2009A&A...506..913H Altcode: Context: The paper is concerned with heating of the solar corona by nanoflares: a superposition of small transient events in which stored magnetic energy is dissipated by magnetic reconnection. It is proposed that heating occurs in the nonlinear phase of an ideal kink instability, where magnetic reconnection leads to relaxation to a state of minimum magnetic energy.
Aims: The aim is to investigate the nonlinear aspects of magnetic relaxation on a current loop with zero net axial current. The dynamical processes leading to the establishment of a relaxed state are explored. The efficiency of loop heating is investigated.
Methods: A 3D magnetohydrodynamic numerical code is used to simulate the evolution of coronal loops which are initially in ideally unstable equilibrium. The initial states have zero net current. The results are interpreted by comparison both with linear stability analysis and with helicity-conserving relaxation theory.
Results: The disturbance due to the unstable mode is strongly radially confined when the loop carries zero net current. Strong current sheets are still formed in the nonlinear phase with dissipation of magnetic energy by fast reconnection. The nonlinear development consists first of reconnection in a large scale current sheet, which forms near the quasi-resonant surface of the equilibrium field. Subsequently, the current sheet extends and then fragments, leading to multiple reconnections and effective relaxation to a constant α field.
Conclusions: Magnetic reconnection is triggered in the nonlinear phase of kink instability in loops with zero net current. Initially, reconnection occurs in a single current sheet, which then fragments into multiple reconnection sites, allowing almost full relaxation to the minimum energy state. The loop is heated to high temperatures throughout its volume. Title: Particle Acceleration in a Model of a Turbulent Reconnecting Plasma: A Fractional Diffusion Approach Authors: Bian, N. H.; Browning, P. K. Bibcode: 2008ApJ...687L.111B Altcode: High-energy charged particles are produced during solar flares. These may be accelerated by the strong electric fields associated with the magnetic reconnection process which is the source of energy release in flares. A simple model of random acceleration of charged particles due to fragmented electric fields is considered for the case of a turbulent reconnecting plasma in which the fluctuating electric field is highly localized and its magnitude distributed according to power laws. The statistical properties of the acceleration process are expressed in terms of a fractional diffusion equation in velocity space, whose solution displays a power-law tail related only to the statistics of the electric field. Title: Particle trajectories and acceleration during 3D fan reconnection Authors: Dalla, S.; Browning, P. K. Bibcode: 2008A&A...491..289D Altcode: 2008arXiv0811.1144D Context: The primary energy release in solar flares is almost certainly due to magnetic reconnection, making this a strong candidate as a mechanism for particle acceleration. While particle acceleration in 2D geometries has been widely studied, investigations in 3D are a recent development. Two main classes of reconnection regimes at a 3D magnetic null point have been identified: fan and spine reconnection
Aims: Here we investigate particle trajectories and acceleration during reconnection at a 3D null point, using a test particle numerical code, and compare the efficiency of the fan and spine regimes in generating an energetic particle population.
Methods: We calculated the time evolution of the energy spectra. We discuss the geometry of particle escape from the two configurations and characterise the trapped and escaped populations.
Results: We find that fan reconnection is less efficent than spine reconnection in providing seed particles to the region of strong electric field where acceleration is possible. The establishment of a steady-state spectrum requires approximately double the time in fan reconnection. The steady-state energy spectrum at intermediate energies (protons 1 keV to 0.1 MeV) is comparable in the fan and spine regimes. While in spine reconnection particle escape takes place in two symmetric jets along the spine, in fan reconnection no jets are produced and particles escape in the fan plane, in a ribbon-like structure. Title: Heating the corona by nanoflares: simulations of energy release triggered by a kink instability Authors: Browning, P. K.; Gerrard, C.; Hood, A. W.; Kevis, R.; van der Linden, R. A. M. Bibcode: 2008A&A...485..837B Altcode: Context: The heating of solar coronal plasma to millions of degrees is likely to be due to the superposition of many small energy-releasing events, known as nanoflares. Nanoflares dissipate magnetic energy through magnetic reconnection.
Aims: A model has been recently proposed in which nanoflare-like heating naturally arises, with a sequence of dissipation events of various magnitudes. It is proposed that heating is triggered by the onset of ideal instability, with energy release occurring in the nonlinear phase due to fast magnetic reconnection. The aim is to use numerical simulations to investigate this heating process.
Methods: Three-dimensional magnetohydrodynamic numerical simulations of energy release are presented for a cylindrical coronal loop model. Initial equilibrium magnetic-field profiles are chosen to be linearly unstable, with a two-layer parameterisation of the current profile. The results are compared with calculations of linear instability, with line-tying, which are extended to account for a potential field layer surrounding the loop. The energy release is also compared with predictions that the field relaxes to a state of minimum magnetic energy with conserved magnetic helicity (a constant α force-free field).
Results: The loop initially develops a helical kink, whose structure and growth rate are generally in accordance with linear stability theory, and subsequently a current sheet forms. During this phase, there is a burst of kinetic energy while the magnetic energy decays. A new relaxed equilibrium is established that corresponds quite closely to a constant α field. The fraction of stored magnetic energy released depends strongly on the initial current profile, which agrees with the predictions of relaxation theory.
Conclusions: Energy dissipation events in a coronal loop are triggered by the onset of ideal kink instability. Magnetic energy is dissipated, leading to large or small heating events according to the initial current profile. Title: The way forward for coronal heating Authors: De Moortel, Ineke; Browning, Philippa; Bradshaw, Stephen J.; Pintér, Balázs; Kontar, Eduard P. Bibcode: 2008A&G....49c..21D Altcode: Ineke De Moortel, Philippa K Browning, Stephen J Bradshaw, Balázs Pintér and Eduard P Kontar consider approaches to the longstanding and enigmatic problem of coronal heating, as presented at the RAS discussion meeting on 11 January 2008. Title: Coronal heating by nanoflares: a model based on Taylor relaxation following kink instability Authors: van der Linden, Ronald; Browning, Philippa; Hood, Alan Bibcode: 2008cosp...37.3285V Altcode: 2008cosp.meet.3285V In this work we present progress on a recently proposed model in which coronal heating is generated by nanoflares, with a sequence of dissipation events of various magnitudes according to the initial current profile. In this model it was proposed that heating is triggered by the onset of ideal instability, with energy release occurring in the nonlinear phase due to fast magnetic reconnection. As a proof of principle, the model was applied to a simplified representation of coronal loops consisting of two regions of constant-alpha force-free magnetic fields joined together at an interface. By adding an evolutionary scenario, the field evolves until it reaches the stability threshold, after which a kink instability sets in with resistive dissipation of the magnetic energy. The distribution of nanoflares energies can be obtained in a straightforward way by using the Taylor relaxation principle, whereby the field evolves to the lowest energy state under the constraint of conservation of helicity (a constant-alpha field). This heating process has also been verified for a number of cases using numerical simulations. These studies showed that the loop initially develops a helical kink, whose structure and growth rate are generally in accordance with linear stability theory, and subsequently a current sheet forms, which leads to a burst of kinetic energy whilst magnetic energy decays. A new relaxed equilibrium is established which corresponds quite closely to a constant-alpha field. The fraction of stored magnetic energy released depends strongly on the initial current profile, and this is in agreement with the predictions of relaxation theory. It is discussed how observational data of loop structure and footpoint motions could be used to apply this model so as to generate a nanoflare distribution. Title: Jets of energetic particles generated by magnetic reconnection at a three-dimensional magnetic null Authors: Dalla, Silvia; Browning, Philippa K. Bibcode: 2007HiA....14...98D Altcode: Magnetic reconnection is a candidate mechanism for particle acceleration in a variety of astrophysical contexts. It is now widely accepted that reconnection plays a key role in solar flares, and reconstructions of coronal magnetic fields indicate that three-dimensional (3D) magnetic null points can be present during flares. We investigate particle acceleration during spine reconnection at a 3D magnetic null point, using a test particle numerical code. We observe efficient particle acceleration and find that two energetic populations are produced: a trapped population of particles that remain in the vicinity of the null, and an escaping population, which leave the configuration in two symmetric jets along field lines near the spine. While the parameters used in our simulation aim to represent solar coronal plasma conditions of relevance for acceleration in flares, the fact that the 3D spine reconnection configuration naturally results in energetic particle jets may be of importance in other astrophysical situations. We also compare the results obtained for the spine reconnection regime with those for the other possible mode of 3D reconnection, fan reconnection. We find that in the latter case energetic particle jets are not produced, though acceleration is observed. Title: Proton acceleration by 3D magnetic reconnection in solar flares Authors: Browning, P. K.; Dalla, S. Bibcode: 2007AGUSMSH22A..03B Altcode: High energy charged particles are an important feature of solar activity such as flares, and indeed non thermal particles play a significant role in flare energy balance. Magnetic reconnection is the primary energy release mechanism in flares, and the strong DC electric fields associated with this reconnection may well be the origin of the high energy charged particles. Whilst particle acceleration has been widely studied for 2D configurations, little is known about 3D configurations. We investigate particle acceleration using a test particle approach, in the simplest 3D reconnection configuration, a 3D magnetic null point. Two modes of reconnection are possible: with a strong current filament along the "spine" field line connecting to the null, or with a sheet current at the "fan" plane of field lines emerging from the null. Using simple model fields, incorporating intiially only thee ideal reconnection region outside the current sheet (or filament), particle trajectories are investigated and the energy spectra and spatial distribution of accelerated particles are determined. We consider and compare fan and spine reconnection, and determine how the properties of the accelerated particles depend on the parameters of the reonnecting field. We also present preliminary results using more realistic, self consistent model fields. Title: Particle acceleration at 3D magnetic reconnection sites . Authors: Browning, P.; Dalla, S. Bibcode: 2007MmSAI..78..255B Altcode: It is proposed that the direct electric fields associated with magnetic reconnection may be responsible for accelerating high energy charged particles which are observed in solar flares. We investigate charged particle acceleration using a test particle approach, with electromagnetic fields arising from a simple model of magnetic reconnection at a 3D magnetic null point for both spine and fan modes of reconnection. Title: Jets of Energetic Particles Generated by Magnetic Reconnection at a Three-Dimensional Magnetic Null Authors: Dalla, S.; Browning, P. K. Bibcode: 2006IAUJD...1E..14D Altcode: Magnetic reconnection is a candidate mechanism for particle acceleration in a variety of astrophysical contexts. It is now widely accepted that reconnection plays a key role in solar flares, and reconstructions of coronal magnetic fields indicate that three-dimensional (3D) magnetic null points can be present during flares. We investigate particle acceleration during spine reconnection at a 3D magnetic null point, using a test particle numerical code. We observe efficient particle acceleration and find that two energetic populations are produced: a trapped population of particles that remain in the vicinity of the null, and an escaping population, which leave the configuration in two symmetric jets along field lines near the spine. While the parameters used in our simulation aim to represent solar coronal plasma conditions of relevance for acceleration in flares, the fact that the 3D spine reconnection configuration naturally results in energetic particle jets may be of importance in other astrophysical situations. We also compare the results obtained for the spine reconnection regime with those for the other possible mode of 3D reconnection, fan reconnection. We find that in the latter case energetic particle jets are not produced, though acceleration is observed. Title: Jets of Energetic Particles Generated by Magnetic Reconnection at a Three-dimensional Magnetic Null Authors: Dalla, S.; Browning, P. K. Bibcode: 2006ApJ...640L..99D Altcode: We investigate particle acceleration during magnetic reconnection at a three-dimensional magnetic null point, in the spine reconnection regime, using a test particle numerical code. We observe efficient particle acceleration and find that two energetic populations are produced: a trapped population of particles that remain in the vicinity of the null and an escaping population, which leave the configuration in two symmetric jets along field lines near the spine. While the parameters used in our simulation aim to represent solar coronal plasma conditions of relevance for acceleration in flares, the fact that the reconnection configuration we studied naturally results in energetic particle jets may be of importance in other astrophysical contexts. Title: Particle Acceleration at Three-Dimensional Reconnection Sites in Solar Flares Authors: Browning, P. K.; Dalla, S. Bibcode: 2005ESASP.600E..40B Altcode: 2005dysu.confE..40B; 2005ESPM...11...40B No abstract at ADS Title: a Model of Nanoflare Energies Based on Relaxation Theory Authors: Browning, P. K.; van der Linden, R.; Gerrard, C.; Kevis, R.; Hood, A. Bibcode: 2005ESASP.600E..82B Altcode: 2005dysu.confE..82B; 2005ESPM...11...82B No abstract at ADS Title: On Solar Coronal Heating by Forced Magnetic Reconnection Authors: Jain, R.; Browning, P.; Kusano, K. Bibcode: 2005ESASP.596E..23J Altcode: 2005ccmf.confE..23J No abstract at ADS Title: Solar and Fusion Plasmas Authors: Browning, Philippa Bibcode: 2005AIPC..795Q.198B Altcode: The poster describes work I have published with co-authors in theoretical and experimental studies of plasmas: both in the laboratory, with relevance to magnetically confined fusion, and naturally occurring, in the Sun's atmosphere (the corona). In the case of fusion plasmas, recent work on recombining plasmas in a linear plasma device, the ULS, is described, which develops understanding of the processes by which detachment is obtained in a tokamak divertor. Results of experimental studies of recombining plasmas are presented, interpreted through 1D plasma models and collisional-radiative models. In the case of the solar corona, we discuss coronal heating by magnetic reconnection. The question of how the solar corona is heated to temperatures of millions of degrees is a major outstanding problem in astrophysics. Some recent results of numerical simulation of forced magnetic reconnection are presented, focusing on the energy release, and we describe how relaxation theory can be used to calculate heating by multiple reconnection events. The presence of high-energy charged particles is an important diagnostic of magnetic reconnection, and models of particle acceleration by reconnecting fields are also presented. Title: Particle acceleration at a three-dimensional reconnection site in the solar corona Authors: dalla, S.; Browning, P. K. Bibcode: 2005A&A...436.1103D Altcode: We study test particle trajectories in the vicinity of a three-dimensional (3D) magnetic null point during spine reconnection. Particles are injected into the steady-state non-uniform magnetic and electric fields derived by Priest & Titov (1996), and the equations of motion numerically integrated. We use input parameters typical of the solar corona, for which reconnection has been suggested as the fundamental mechanism responsible for particle acceleration in flare events. We show that substantial acceleration is possible in the 3Dspine reconnection configuration, in the strong electric field regime. The energy gain is strongly dependent on the location of injection into the simulation box, as was the case in 2DX-point configurations. In our 3Dgeometry, we first vary the location of injection within a plane through the spine, and derive an analytical value for the injection angle for which maximum energy gain is achieved. Secondly we vary the azimuthal location of particle injection and show that as one moves away from the plane with maximum electric field magnitude, higher final energies can be achieved, though this requires substantially longer times. Title: Particle acceleration at a 3D reconnection site Authors: dalla, S.; Browning, P. K. Bibcode: 2005AGUSMSM23B..06D Altcode: We study test particle trajectories in the vicinity of a three-dimensional (3D) magnetic null point during spine reconnection. Particles are injected into the steady-state non-uniform magnetic and electric fields derived by Priest and Titov (1996), and the equations of motion numerically integrated. We use input parameters typical of the solar corona, for which reconnection has been suggested as the fundamental mechanism responsible for particle acceleration in flare events. We show that substantial acceleration is possible in the 3D spine reconnection configuration, in the strong electric field regime. The energy gain is strongly dependent on the location of injection into the simulation box, as was the case in 2D X-point configurations. In our 3D geometry, we first vary the location of injection within a plane through the spine, and derive an analytical value for the injection angle for which maximum energy gain is achieved. Secondly we vary the azimuthal location of particle injection and show that as one moves away from the plane with maximum electric field magnitude, higher final energies can be achieved, though this requires substantially longer times. We also discuss application of our trajectory code to the study of particle acceleration during reconnection in the Earth's magnetotail. Title: Solar coronal heating by forced magnetic reconnection: Multiple reconnection events Authors: Jain, Rekha; Browning, Philippa; Kusano, K. Bibcode: 2005PhPl...12a2904J Altcode: Magnetic reconnection is a strong candidate for a coronal heating mechanism, and heating by forced magnetic reconnection is investigated here. Two dimensional, nonlinear magnetohydrodynamic simulations are used to investigate forced magnetic reconnection in a compressible plasma. The reconnection occurs when a sheared force-free field is perturbed by a slow disturbance (pulse) at the boundary which is representative of the solar corona where the reconnection is induced by the photospheric motions. The case of driving by successive pulses, which generate a series of heating events which may interact with each other, is considered. This is in order to model the heating of the corona by a series of nanoflare events. For small perturbations, the simulation results are consistent with the previous analytic theory based on linear approach where a current sheet is formed initially at the resonant surface followed by reconnection and then release of magnetic energy. For large amplitude perturbations, or close to the threshold for tearing instability, the system exhibits strong nonlinear aspects. Following the second driving pulse, the current sheet expands along the separatrix before relaxing to a reconnective equilibrium and releasing even more magnetic energy for the same amplitude perturbation. Title: Coronal Heating by Forced Magnetic Reconnection with Multi-Pulse Driving Authors: Browning, P. K.; Jain, R. Bibcode: 2004ESASP.575..474B Altcode: 2004soho...15..474B No abstract at ADS Title: Particle Acceleration at a 3d Reconnection Site Authors: dalla, S.; Browning, P. K. Bibcode: 2004ESASP.575..222D Altcode: 2004soho...15..222D No abstract at ADS Title: Coronal Heating by Nanoflares: a Reconnection Model Authors: Browning, P. K.; van der Linden, R.; Gerrard, C.; Kevis, R.; Hood, A. Bibcode: 2004ESASP.575..210B Altcode: 2004soho...15..210B No abstract at ADS Title: Solar coronal heating by relaxation events Authors: Browning, P. K.; Van der Linden, R. A. M. Bibcode: 2003A&A...400..355B Altcode: A coronal heating model is proposed which predicts heating by a series of discrete events of various energies, analogous to the observed range of events from large scale flares through various transient brightening phenomena down to the often discussed ``nanoflares''. We suggest that an energy release event occurs when a field becomes linearly unstable to ideal MHD modes, with dissipation during the nonlinear phase of such an instability due to reconnection in fine-scale structures such as current sheets. The energy release during this complex dynamic period can be evaluated by assuming the field relaxes to a minimum energy state subject to the constraint of helicity conservation. A model problem is studied: a cylindrical coronal loop, with a current profile generated by slow twisting of the photospheric footpoints parameterised by two values of alpha (the ratio of current density to field strength). Different initial alpha profiles, corresponding to different footpoint twisting profiles, lead to energy release events of a wide range of magnitudes, but our model predicts an observationally realistic minimum size for these events. Title: A solar coronal heating model: multi-energy relaxation events Authors: Browning, P. K.; van der Linden, R. A. M. Bibcode: 2002ESASP.508..263B Altcode: 2002soho...11..263B A coronal heating model is proposed which predicts heating by a series of events of various energies, analogous to flares and the often discussed "nanoflares". We suggest that an energy release event occurs when a field becomes unstable to ideal MHD modes, with dissipation during the nonlinear phase of such an instability due to fine-scale structures such as current sheets. The energy release during this complex dynamic period can be evaluated by assuming the field relaxes to a minimum energy state subject to the constraint of helicity conservation. A model problem is studied: a cylindrical coronal loop, with a current profile generated by slow twisting of the photospheric footpoints parametrised by two values of α (the ratio of current density to field strength). Different initial α profiles, corresponding to different footpoint twisting profiles, lead to energy release events of a wide range of magnitudes. Title: Particle acceleration at an X-type reconnection site with a parallel magnetic field Authors: Browning, P. K.; Vekstein, G. E. Bibcode: 2001JGR...10618677B Altcode: The acceleration of charged particles at a two-dimensional magnetic reconnection site is investigated. The magnetic field has an X-type neutral point, while reconnection is driven by a uniform transverse electric field; the effect of including a uniform magnetic field component parallel to the driving electric field and transverse to the plane of the X point is studied. We focus on the adiabatic motion of strongly magnetized particles, a valid assumption everywhere for sufficiently strong parallel magnetic fields but one which excludes a region around the neutral point for weaker fields. The regime of interest is fast driven reconnection, in which the electric drift is strong. The trajectories of particles and their dependence on the magnitude of the parallel magnetic field component are investigated. Particles can be accelerated along the magnetic field lines both because of the coupling of the perpendicular electric drift with the parallel motion, which occurs in an inhomogeneous magnetic field, and the direct acceleration by the electric field. The energy spectra of particles leaving the reconnection site are also calculated. Title: A Cosmic Ray Signature of Equatorial Coronal Holes Authors: Bromage, B. J. I.; Browning, P. K.; Clegg, J. R. Bibcode: 2001SSRv...97...13B Altcode: The evolution of open field regions on the Sun over the last cycle is illustrated by observations of coronal holes in SOHO EIT images. The development of a large equatorial coronal hole near solar minimum is discussed, indicating the processes which led to the appearance of open field regions at low latitude. The observed cosmic ray signature is presented and interpreted in terms of the passage of the Earth through the streamer belt, which at this time had become distorted by the coronal hole and associated active region. The times when such equatorial coronal holes might be expected to directly influence cosmic ray counts in this way are seen to be limited to the approach to solar minimum, around minimum and the approach to maximum. Title: Particle Acceleration in Collisionless Magnetic Reconnection Authors: Browning, P. K.; Vekstein, G. E. Bibcode: 2001IAUS..203..555B Altcode: Magnetic reconnection is a process of fundamental importance in the solar atmosphere, particularly in flares and in coronal heating. The acceleration of charged particles is a key diagnostic of reconnection, and we investigate this process in the framework of collisionless reconnection, relevant to hot tenuous plasmas where the length scale of the reconnection region is less than the particle mean free paths. We consider a steady reconnection scenario, with a two dimensional X-point magnetic field geometry, and an inductive electric field generating an inflow of particles. The aim is to investigate the effect of adding a uniform field component transverse to the plane of the X-point field. Test particles trajectories are studied, and the energy spectra of the accelerated particles leaving the reconnection site are determined. The interesting parameter regime is when there is both significant direct acceleration, due to the component of the magnetic field parallel to the driving electric field, and parallel acceleration generated through the interaction of the electric drift motion with the inhomogeneous magnetic field. Title: The linear force-free field in a spherical shell using a new method to determine the coefficients of the eigenfunction expansion Authors: Clegg, J. R.; Browning, P. K.; Laurence, P.; Bromage, B. J. I.; Stredulinsky, E. Bibcode: 2000A&A...361..743C Altcode: The linear force-free field of a plasma in between spherical shells is found allowing for inhomogeneous boundary conditions. A three-dimensional solution is found by analysis and used as a benchmark to test a solution in terms of an expansion of eigenfunctions where the coefficients are determined by a new method. Alternative methods are also applied in the context of the spherical shell example and used to illustrate some mathematical constraints that can affect their validity. The solution is used to model the solar coronal field in the presence of a large low-latitude coronal hole; SOHO-MDI data provide the inner boundary conditions. Title: Energy dissipation and helicity in coronal loops of variable cross-section Authors: Lothian, R. M.; Browning, P. K. Bibcode: 2000SoPh..194..205L Altcode: A model is developed to describe a coronal loop, which may originate from a photospheric source of smaller size than the coronal radius of the loop. The energy and relative helicity of the loop are evaluated, as are two alternative estimates of the energy available for coronal heating. Both of these estimates are strongly dependent on the size of the photospheric footprint of the loop. A coronal heating rate is then deduced, based on a nanoflare-type scenario, where slowly accumulated energy is rapidly released as heat. An explicit calculation is carried out for one particular choice of loop length and coronal radius, with dissipation timescale and photospheric radius as parameters. Two main conclusions are reached. Firstly, the proposed mechanism can make a significant contribution to coronal heating. Secondly, the mechanism is more effective for a more concentrated photospheric flux source. Title: Structure of a Large low-Latitude Coronal Hole Authors: Bromage, B. J. J.; Alexander, D.; Breen, A.; Clegg, J. R.; Del Zanna, G.; DeForest, C.; Dobrzycka, D.; Gopalswamy, N.; Thompson, B.; Browning, P. K. Bibcode: 2000SoPh..193..181B Altcode: Coronal holes on the Sun are the source of high-speed solar wind streams that produce magnetic disturbances at the Earth. A series of multi-wavelength, multi-instrument observations obtained during the 1996 `Whole Sun Month' campaign examined a large coronal hole in greater detail than ever before. It appeared on the Sun in August, and extended from the north pole to a large active region in the southern hemisphere. Its physical and magnetic structure and subsequent evolution are described. Title: Asymmetries Across a Coronal Hole Extension Authors: Clegg, J. R.; Browning, P. K.; del Zanna, G.; Bromage, B. J. I. Bibcode: 1999ESASP.448.1159C Altcode: 1999ESPM....9.1159C; 1999mfsp.conf.1159C No abstract at ADS Title: Modeling the coronal magnetic field, with a new method for obtaining boundary conditions on the farside of the Sun Authors: Clegg, J. R.; Bromage, B. J. I.; Browning, P. K. Bibcode: 1999JGR...104.9831C Altcode: A novel technique is presented that aids the reconstruction of solar coronal magnetic fields by augmenting the visible solar surface boundary conditions with an estimate of the simultaneous conditions on the far side of the Sun. In converting from line-of-sight measurements, two alternative assumptions are considered: (1) ignore the plasma beta differences between corona and photosphere and so find a radial field component that is consistent with an overlying potential (or force free) field corona; and (2) characterize the change in beta by a boundary layer, matching the coronal field to the photosphere where the field, seen in projection, is taken to be wholly radial. The radial magnetic field (or radial field component) over the unseen hemisphere of the Sun is deduced from information held within a time series of the Solar and Heliospheric Observatory Michelson Doppler imager photospheric magnetograms centered on the time of interest and combined with a full disc of visible data for that time. Comparison is made with the more usual synoptic map boundary conditions to test the time sensitivity of the problem. Several methods of extrapolation to the far side are assessed using data centered on an observation at the end of August 1996, when a large equatorial coronal hole was present on one side of the Sun. The corresponding magnetic field equilibrium in the corona is found, assuming a simple potential approximation, which employs an outer ``source surface'' in addition to the derived inner boundary condition. Together with the inherent assumption that the evolution of the global field is slow, the validity of the technique is confirmed by the self-consistency of the results. Title: The Solar Magnetic Field as a Coronal Hole Extension Forms: Effects of Magnetic Helicity and Boundary Conditions Authors: Clegg, J. R.; Bromage, B. J. I.; Browning, P. K. Bibcode: 1999SSRv...87..145C Altcode: An analytical solution is presented for linear force fields within a spherical shell, representing the solar corona. Allowing for a global magnetic helicity, we find magnetic fields over the entire corona with realistic inner boundary conditions obtained from transformation and extrapolation of photospheric magnetograms and considering alternative outer boundary conditions. Such fields are found for the well known coronal hole extension event of August 1996. Title: Force Free Models of Relaxed and Partially Relaxed Coronal Magnetic Fields Authors: Browning, P. K.; Lothian, R. M.; Clegg, J. R. Bibcode: 1998ASPC..155...95B Altcode: 1998sasp.conf...95B No abstract at ADS Title: Magnetic Reconnection and Dynamos in Laboratory Plasmas Authors: Browning, P. K. Bibcode: 1998ASSL..229...73B Altcode: 1998opaf.conf...73B No abstract at ADS Title: Acceleration of Particles in Collisionles Magnetic Reconnection Authors: Browning, P. K.; Vekstein, G. Bibcode: 1998ASSL..229..313B Altcode: 1998opaf.conf..313B No abstract at ADS Title: Field-Aligned Particle Acceleration in Collisionless Magnetic Reconnection Authors: Vekstein, G. E.; Browning, P. K. Bibcode: 1996ASPC..111..308V Altcode: 1997ASPC..111..308V Specific field-aligned acceleration of charged particles originates from the coupling between the electric drift and longitudinal motion in a non-uniform magnetic field. As a result, initially slow particles entering the reconnection site of an X-type magnetic geometry can leave the latter as substantially accelerated jets directed along the magnetic separatrices. Title: Coronal Magnetic Field Equilibrium with Discrete Flux Sources Authors: Lothian, R. M.; Browning, P. K. Bibcode: 1995SoPh..161..289L Altcode: A model of the equilibrium structure of the coronal magnetic field is developed, taking account of the fact that field lines are rooted in the photosphere, where field is concentrated into isolated flux tubes. The field is force-free, described by ∇ ×B =αB, withα constant; this field has special physical significance, being the state of mininum energy after small-scale reconnections, and is also mathematically convenient in that the principle of superposition can be used to construct complex geometries. First a model of a single loop is presented, with a flux source and sink pair at the photosphere; both point flux tubes and finite radius flux tubes are considered. Then more complex topologies with multiple sources and sinks are investigated. It is shown that significant topology changes arise for different values ofα, indicating the possibility that there can be energy changes through magnetic reconnection if the field evolves ideally and then relaxes to a linear state. Title: Book Review: Physics of the plasma universe / Springer-Verlag, 1992 Authors: Browning, P. K. Bibcode: 1993Ap&SS.206..318B Altcode: 1993Ap&SS.206..318P No abstract at ADS Title: Small-scale activity and coronal heating. Authors: Browning, P. K. Bibcode: 1992AnGeo..10..324B Altcode: 1992AnG....10..324B It is generally accepted that the corona is heated magnetically, with the energy source being photospheric motions. The author considers only slow footpoint motions: these cause the coronal field to evolve quasi-statically, building up free magnetic energy which can dissipate as heat. The dissipation requires small-scale processes such as reconnection in thin current sheets. Three theories are considered. (1) The question of current sheet formation is discussed, (2) an approach to quantifying heating rates, using driven relaxation theory, is described, and (3) recent developments invoking turbulent cascades are outlined. Title: Reconnection, current sheets and relaxation. Authors: Browning, P. K. Bibcode: 1992mrpa.work...29B Altcode: A tutorial introduction to the basic concepts of reconnection, covering both "spontaneous" and "driven" modes is given. Then the question of the formation of current sheets - the potential locations for reconnection - is discussed. The dynamics of a field with reconnection occurring in many sites are considered, and it is shown that the global magnetic helicity is an appropriate invariant; the significance of this quantity is explained, and the reasons for its conservation are discussed. Title: Energy relations in reconnection. Authors: Browning, P. K. Bibcode: 1992mrpa.work..177B Altcode: Spheromak, a laboratory experiment in which reconnection is integral to setting-up the magnetic field configuration, is described, and the application of relaxation theory to this device is outlined. Both the Spheromak and the solar corona have external energy input as well as relaxation, and the properties of such driven systems are discussed. Title: Mechanisms of solar coronal heating Authors: Browning, P. K. Bibcode: 1991PPCF...33..539B Altcode: No abstract at ADS Title: The creation of the magnetic environment for prominence formation in a coronal arcade Authors: Amari, T.; Démoulin, P.; Browning, P.; Hood, A.; Priest, E. Bibcode: 1991A&A...241..604A Altcode: The possibility of prominence formation in sheared coronal arcades is investigated. The creation of a dip at the summit of field lines is a likely requirement before a prominence can form; then dense plasma can be supported against gravity by the Lorentz force. It is proved that, in fact, no shear profile can create a dip in a two-dimensional force-free arcade if the photospheric field is bipolar. However, numerical investigations show that shearing an arcade can induce very flat field lines. It is investigated, in order of magnitude, how this flattening of the field can increase the free fall time of a dense plasma. Also, the interaction between shear and twist is analyzed; the critical twist needed to have a dip is a decreasing function of shear. Title: Relaxed states in a spheromak with inhomogeneous boundary fields Authors: Dixon, A. M.; Browning, P. K.; Bevir, M. K.; Gimblett, C. G.; Priest, E. R. Bibcode: 1990JPlPh..43..357D Altcode: In this paper we consider force-free equilibrium solutions of the MHD equations in a spherical geometry for the case in which magnetic flux crosses the boundary of the containing vessel. The main motivation is to model more faithfully actual spheromak experiments in the laboratory, for which boundaries are unlikely to be magnetic surfaces. We show how a general inhomogeneous boundary field may be constructed from individual components. In particular, we consider the cases of a boundary field of dipolar form and one of quadrupolar form. We then go on to discuss solutions for fields embedded in point or ring electrodes using the ‘general solution’, some of which can be used to model experiments such as the PS-1- or CTX-type spheromaks. Title: Twisted flux ropes in the solar corona Authors: Browning, P. K. Bibcode: 1990GMS....58..219B Altcode: Loop structures, which are essentially magnetic flux tubes, often with twist, are common in the solar corona. This paper considers the magnetic equilibrium of twisted coronal loops. Ignoring curvature, as a loop is twisted at the photospheric footpoints, longitudinal structure develops with the center of the loop tending to expand radially. Results of a 2D numerical code show that nearly all of the expansion occurs in narrow boundary layers near the photosphere, and most of the loop is approximately a straight cylinder. Title: A generalization of the Woltjer minimum-energy principle Authors: Dixon, A. M.; Berger, M. A.; Priest, E. R.; Browning, P. K. Bibcode: 1989A&A...225..156D Altcode: The theorem of Woltjer (1958) for the minimization of the magnetic energy of a magnetic structure is extended to include the case of a free boundary subjected to external magnetic or plasma pressure forces. The case where the boundary is not a magnetic surface is also treated. Applications to a finite cylindrical flux tube and a spheromak are given to illustrate the theory. It is also shown how the theory may be applied to the construction of stationary Euler flows. Title: The shape of twisted, line-tied coronal loops Authors: Browning, P. K.; Hood, A. W. Bibcode: 1989SoPh..124..271B Altcode: The magnetostatic equilibrium of a coronal loop in response to slow twisting of the photospheric footpoints is investigated. A numerical code is used to solve the full non-linear 2-D axisymmetric problem, extending earlier linearised models which assume weak twist and large aspect ratio. It is found that often the core of the loop tends to contract into a region of strong longitudinal field while the outer part expands. It is shown that, away from the photospheric footpoints, the equilibrium is very well approximated by a straight 1-D cylindrical model. This idea is used to develop a simple method for prescribing the footpoint angular displacement and calculating the equilibrium. Title: Magnetohydrodynamics in solar coronal and laboratory plasmas: A comparative study Authors: Browning, P. K. Bibcode: 1988PhR...169..329B Altcode: In this review we discuss the application of MHD theory to plasma in two contexts: the solar atmosphere and magnetically confined fusion experiments. The MHD equations are set up, and their relevance to the two systems discussed. It is shown that in both cases the resistivity is small, and the magnetic field is strong, so that similar physical behaviour should be expected. Three areas of research with relevance to both systems are described, the basic theory and some recent developments being outlined. These are magnetostatic equilibrium, linear stability theory and wave propagation, and relaxation of magnetic fields and helicity conservation. Title: Helicity injection and relaxation in a solar-coronal magnetic loop with a free surface Authors: Browning, P. K. Bibcode: 1988JPlPh..40..263B Altcode: A solar-coronal magnetic loop is rooted in the photosphere, where motions shuffle the footpoints of the field, generating currents in the corona. The dissipation of these currents provides a possible mechanism for heating the solar corona. A theory is described based on a generalization of Taylor's hypothesis, predicting that as the loop is twisted up, it relaxes towards a minimum-energy state V × B = μB. The footpoint motions inject helicity as well as energy, and the evolution is determined through a helicity-injection equation. The loop is modelled as a straight magnetic-flux tube, with twisting motions at the ends, confined by a constant external pressure at the curved surface, which is a free boundary. The problem of the loop evolution in response to given footpoint motions is solved, and an interesting example of multiple equilibria arises. The heating rate is calculated for an almost-potential loop. The model may also be regarded as representing a laboratory experiment: in particular, a simple idealization of a spheromak, with the footpoint motions replaced by an applied voltage. Title: Magnetic relaxation in solar and laboratory plasmas Authors: Browning, P. K. Bibcode: 1988PPCF...30....1B Altcode: No abstract at ADS Title: Coronal heating by relaxation in a sunspot magnetic field Authors: Dixon, A. M.; Browning, P. K.; Priest, E. R. Bibcode: 1988GApFD..40..293D Altcode: The heating by resistive turbulence of solar coronal magnetic fields is evaluated by means of the Taylor-Heyvaerts hypothesis, which enables one to calculate the evolution of the magnetic helicity and magnetic field in the corona in response to prescribed motions of the photospheric footpoints. The relationship between the photospheric velocity field and the helicity generation rate is considered for a coronal arcade and the energy release is proved to be positive definite in general. Also, the evolution and dissipation is determined for the axisymmetric magnetic field above a single sunspot which is being twisted up from below. Title: Coronal Evolution and Heating by Magnetic Reconnection in Closely Packed Flux Tubes Authors: Browning, P. K. Bibcode: 1987sman.work..173B Altcode: It is now widely accepted that the solar corona is heated to temperatures of more than 106K by a magnetic mechanism, with energy supplied by motions of the photospheric footpoints of the coronal magnetic field. One approach to heating by reconnection has been developed by Parker (1972, 1982, 1983). While Parker suggests that the field will reconnect and release heat, the ultimate state of the field and the amount of energy released are yet to be determined. The author's aim is to develop an alternative approach to answer these questions, using some recent developments in coronal heating theory which is outlined here. Title: The Shape of Buoyant Coronal Loops in a Magnetic Field and the Eruption of Coronal Transients and Prominences Authors: Browning, P. K.; Priest, E. R. Bibcode: 1986SoPh..106..335B Altcode: The equilibrium and non-equilibrium properties of a coronal loop embedded in a stratified isothermal atmosphere are investigated. The shape of the loop is determined by a balance between magnetic tension, buoyancy, and external pressure gradients. The footpoints of the loop are anchored in the photosphere; if they are moved too far apart, no equilibrium is possible and the loop erupts upwards. This critical separation is independent of the pressure differential between the loop and the external medium if the loop has enhanced magnetic field, but varies if instead the loop pressure is increased. The maximum width is proportional to the larger of the gravitational scale-height and the length-scale of the ambient field. In some circumstances, it is shown that multiple solutions exist for the tube path. These results may be relevant to the eruption of prominences during the preflare phase of two-ribbon flares and to the onset of coronal loop transients. Such eruptions may occur if the footpoint separation, internal pressure or internal magnetic field are too great. Title: Coronal heating in closely-packed flux tubes: a Taylor-Heyvaerts relaxation theory. Authors: Browning, P. K.; Sakurai, T.; Priest, E. R. Bibcode: 1986A&A...158..217B Altcode: The aim of this paper is to take a more quantitative and detailed look at dissipation in an array of closely-packed flux tubes. An initially potential coronal loop is investigated, whose footpoints are twisted up by cellular photospheric motions, forming a network of twisted flux tubes. The motions are assumed to be slow compared with the reconnection time-scale, so that the stressed field reconnects and dissipates some of its energy as heat. The generalised Taylor's hypothesis is used to investigate the effects of reconnection on the flux tubes and to determine the efficiency of the dissipation. A basic mathematical model is set up and the procedure for calculating the evolution is outlined. The authors investigate the response of the field to the footpoint motions and evaluate the heating produced. The results are discussed, applications to the coronal heating problem are considered, and the predictions are compared with the known heating requirements of the corona. Title: Heating of coronal arcades by magnetic tearing turbulence, using the Taylor-Heyvaerts hypothesis Authors: Browning, P. K.; Priest, E. R. Bibcode: 1986A&A...159..129B Altcode: The heating of the solar corona by direct currents, which are dissipated by magnetic reconnection, is studied. The coronal field responds to slow photospheric motions by evolving through a series of equilibria, which may be unstable to resistive modes. According to a generalization of Taylor's hypothesis (Heyvaerts and Priest, 1984), the field reconnects and relaxes to a linear force-free state (satisfying Delta X B = alpha B), where the parameter alpha is uniform. During the relaxation process, the field reconnects and dissipates some magnetic energy as heat. The value of alpha at each time and the energy released during relaxation may be determined from the evolution of magnetic helicity. Two theorems concerning this method are proved: First, the invariance of the method with respect to gauge transformations of the vector potential is discussed, and it is shown that the helicity evolution equation in any gauge predicts the same evolution of the field. Second, it is shown that the energy release always vanishes in the limit of infinitely fast reconnection. It is found that similar footpoint motions heat an arcade more efficiently if it is already strongly sheared, such as in a rapidly evolving active region. The general conclusion is that tearing turbulence is a viable heating mechanism for the solar corona. Title: Coronal heating in closely packed flux tubes: a Taylor-Heyvaerts relaxation theory. Authors: Browning, P. K.; Sakurai, T.; Priest, E. R. Bibcode: 1985MPARp.181.....B Altcode: No abstract at ADS Title: Heating of coronal loops by tearing turbulence. Authors: Browning, P. K. Bibcode: 1984ESASP.220..129B Altcode: 1984ESPM....4..129B The heating of a coronal loop by reconnection, in response to slow photospheric motions is discussed. It is shown that the method is invariant to the choice of gauge. General evolution equations of a coronal loop, modelled as a straight cylinder, are then derived. For solid body motions, it is shown that α is constant in time, and the heating is calculated. Title: The Magnetic Non-Equilibrium of Buoyant Flux Tubes in the Solar Corona Authors: Browning, P. K.; Priest, E. R. Bibcode: 1984SoPh...92..173B Altcode: The equilibrium shape of a slender flux tube in the stratified solar atmosphere is studied. The path is determined by a balance between the downwards magnetic tension, which depends on the curvature of the loop, and the upwards buoyancy force. Previous results for untwisted slender tubes are extended to include twisted tubes embedded in an external magnetic field. Title: Global magnetohydrostatic fields in stellar atmosphere Authors: Browning, P. K.; Priest, E. R. Bibcode: 1984GApFD..28..141B Altcode: The equilibrium properties of the magnetic field of an axisymmetric star are studied. A family of analytical solutions to the magnetohydrostatic equations is found, which are used to model the slow evolution of the field through a series of equilibria. Firstly, a model is set up for a force-free dipole-like field, which has a toroidal field component; it is found that, as such a field is twisted up, a critical point is reached, at which the field topology changes. If the twist is increased beyond this point, there is no physically reasonable equilibrium. Next, an untwisted magnetostatic dipole-like field is studied, with an increasing pressure differential between pole and equator. A critical point again occurs when the pressure differential becomes too large. Finally a force-free quadrupole-like field is modelled, which is being twisted up, for example by differential rotation; this has similar properties to the dipole-like field. In each case, it is suggested that, when the critical point is reached, the field will no longer evolve smoothly, but will change catastrophically to a new stable, releasing energy. Such an event could represent the onset of a stellar flare or some other dynamic stellar process. Title: Kelvin-Helmholtz instability of a phased-mixed Alfven wave Authors: Browning, P. K.; Priest, E. R. Bibcode: 1984A&A...131..283B Altcode: The development of the Kelvin-Helmholtz instability at the velocity antinodes of a standing Alfven wave is studied. The problem is investigated at large times, when the velocity profile has a sinusoidal form, and at the onset of instability. At large times it is found that the growth rates of the sinusoidal profile are much smaller, and that the most unstable wavelengths are about 12 times the phase-mixed velocity inhomogeneity length scale, whereas for the square wave, short waves are the most unstable. In a temporally local stability analysis, a critical time is found after which the instability grows significantly within one Alfven wave period. This critical time is related to the dimensionless wave frequency Omega1 = (k-parallel)(a)/M, where k-parallel is the Alfven wavenumber and M is the magnetic Mach number. The growth rate of the instability is determined as a function of time for several values of Omega1, and the critical time is found at which the growth rate is equal to the wave frequency. It is shown that the instability develops within very few wave periods, thus it is expected that a shear Alfven wave would rapidly be disrupted by Kelvin-Helmholtz instability. Title: Inhomogeneous magnetic fields in the solar atmosphere Authors: Browning, Philippa K. Bibcode: 1984PhDT.......210B Altcode: No abstract at ADS Title: The structure of twisted magnetic flux tubes Authors: Browning, P. K.; Priest, E. R. Bibcode: 1983ApJ...266..848B Altcode: The basic physics of untwisted flux tubes confined by an external plasma pressure has been developed by Parker (1979). However, observations indicate that in many situations on the sun flux tubes are twisted. There is, for instance, evidence for helical structures in erupting prominences. It is, therefore, important to extend the results already found for untwisted tubes to include the effects of twist. The present investigation is concerned with the structure of a thick twisted flux tube in an inhomogeneous atmosphere. Previous work on untwisted flux tubes and straight cylindrical twisted tubes is generalized, in order to describe the properties of twisted flux tubes confined by a varying external pressure. The governing equations are nonlinear, and, if the confining pressure is specified, they define a free surface problem. This problem is solved analytically in certain limiting cases, for which the complete structure of the field is found. Two exact solutions for force-free fields are studied in detail. Title: The structure of untwisted magnetic flux tubes Authors: Browning, P. K.; Priest, E. R. Bibcode: 1982GApFD..21..237B Altcode: The equilibrium structure of an axisymmetric magnetic flux tube confined by an external pressure pe(Z) that varies along the length of the tube is studie. In the past, most work has concentrated on slender flux tubes, where the effects of transverse structure and radial fields are neglected. Here the aim is to explore the properties of thick tubes, in order to see to what extent the slender tube theory is valid. The main results are: