Search

Funding: Carnegie Trust for the Universities of Scotland; Science and Technology Facilities Council (grants ST/N000609/1 and ST/P000428/1). 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. Publisher PDF

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. 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. 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., 16 pages, 13 figures

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., Comment: Accepted as a mini-review in Advances in Space Research

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.

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.

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 .

We acknowledge the financial support of STFC through the Consolidated grants to the University of St Andrews and the University of Manchester. 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. Publisher PDF

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.

It has been proposed that the million degree temperature of the corona is due to the combined effect of barely-detectable energy releases, so called nanoflares, that occur throughout the solar atmosphere. Alas, 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 and so 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.

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 similar to 1 MeV and similar to 10 MeV. It is also found that particles moving in an open magnetic field have a considerably wider pitch-angle distribution.

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 a 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 a 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.

In the present study we investigate magnetic reconnection in twisted magnetic fluxtubes with different initial configurations. In all considered cases, energy release is triggered by the ideal kink instability, which is itself the result of applying footpoint rotation to an initially potential field. The main goal of this work is to establish the influence of the field topology and various thermodynamic effects on the energy release process. Specifically, we investigate convergence of the magnetic field at the loop footpoints, atmospheric stratification, as well as thermal conduction. In all cases, the application of vortical driving at the footpoints of an initally potential field leads to an internal kink instability. With the exception of the curved loop with high footpoint convergence, the global geometry of the loop change little during the simulation. Footpoint convergence, curvature and atmospheric structure clearly influences the rapidity with which a loop achieves instability as well as the size of the subsequent energy release. Footpoint convergence has a stabilising influence and thus the loop requires more energy for instability, which means that the subsequent relaxation has a larger heating effect. Large-scale curvature has the opposite result: less energy is needed for instability and so the amount of energy released from the field is reduced. Introducing a stratified atmosphere gives rise to decaying wave phenomena during the driving phase, and also results in a loop that is less stable., Submitted to Solar Physics

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.

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. 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. 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. 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.

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 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, but our model predicts an observationally realistic minimum size for these events.

Models of the ideal magnetohydrodynamic (MHD) stability of spheromaks and spherical tokamaks are presented, including the effects of current on the open flux which plays a key role in helicity-injected current drive. The stability of spheromak equilibria with both open and closed flux and realistic current profiles representative of helicity-injected state is investigated, where a kink instability in the open flux is shown to dominate a tilt mode in the closed flux as the open flux current density is increased. A previous one-dimensional model is extended to more realistic two-dimensional equilibria which properly incorporate a region of closed magnetic flux as well as open flux penetrating the boundaries at electrodes. A new stability code SCOTS has been developed and benchmarked which can determine the growth rates of ideal MHD modes in this geometry. The coordinate system for this code has been developed such that it extends smoothly across the separatrix between closed and open flux, thus not imposing...

Two-dimensional numerical simulations are used to investigate nonlinear aspects of forced magnetic reconnection in a zero β highly conducting plasma. This is representative of the solar corona, where reconnection may be induced by external perturbations, e.g., at the photospheric boundary of the corona. The aim is to investigate the energy dissipation by the reconnection, which may provide a mechanism for heating the coronal plasma. The field is taken to be initially a sheared force-free equilibrium in a slab, and the effects of applying a slow deformation to the boundaries are investigated. Previous analytical studies assuming small departures from the initial equilibrium have found that a current sheet forms during an initial ideal phase of evolution, which subsequently relaxes to a reconnected equilibrium, releasing some magnetic energy. The linear theory predicts that the energy release has a singularity when the field is marginally stable to the tearing mode. The nonlinear evolution of the field is c...

Context: Relaxation theory offers a straightforward method for estimating the energy that is released when a magnetic field becomes unstable, as a result of continual convective driving. Aims: We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. 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. 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. 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. Postprint

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.

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 .

Observation of coronal EUV spectral lines sensitive to different temperatures offers an opportunity to evaluate the thermal structure and flows in flaring atmospheres. This can be used to estimate the partitioning between the thermal and kinetic energies. Our aim is to model large-scale (50-10000km) velocity distributions in order to interpret non-thermal broadening of different spectral EUV lines. The developed models allow us to understand the origin of the observed spectral line shifts and broadening, and link these features to particular physical effects in flaring atmospheres. We use ideal MHD to derive twisted magnetic fluxtube configurations in a stratified atmosphere. The evolution of these fluxtubes is followed using resistive MHD, with anomalous resistivity depending on the local density and temperature. The model also takes into account the thermal conduction and radiative losses. 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. Our models show qualitative and quantitative agreement with observations. The line-of-sight (LOS) velocity dispersions demonstrate substantial correlation with the temperature, increasing from about 20-30 km/s around 1 MK to about 200-400 km/s near 10-20 MK. The average LOS velocities also correlate with velocity dispersions, although they demonstrate a very strong scattering, compared to observations. We also note that near foot-points 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., Comment: Accepted to Astronomy & Astrophysics

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.

We present measurements of the magnetohydrodynamic ``dynamo'' due to correlated fluctuations of velocity and magnetic field in the SPHEX spheromak. We show that there are both single-mode and turbulent dynamo processes present, although the single-mode process is in this case an ``antidynamo'' opposing the externally applied electric field. The size of the turbulent dynamo at the magnetic axis is close to that required to drive the toroidal current there.

A major problem in astrophysical plasma physics is to explain how the outer atmosphere, the corona, of the Sun is heated to temperatures of millions of degrees Kelvin. It is accepted that the heating mechanism is magnetic, with the energy source being turbulent motions below the solar surface. Two classes of theory are proposed, according to the timescale of the driving motions in relation to the Alfven timescale of the coronal plasma. Fast motions generate MHD waves which propagate up into the corona carrying energy and can heat the corona if the waves are damped. Slow motions move the footpoints of the coronal field, generating field-aligned currents which may dissipate to provide heat. In each case, the main difficulty is in finding an adequate means of dissipation in the highly-conducting coronal plasma. Some proposed heating mechanisms are outlined, which present a number of interesting plasma physics problems closely related to those arising for fusion plasma; in particular, Alfven wave propagation and absorption in a nonuniform medium, and anomalous heating by reconnection, turbulence and relaxation.

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...

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 eta < 1E-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., 12 pages, 12 figures. The following article has been submitted to Physics of Plasmas. After it is published, it will be found at pop.aip.org

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.

Two-dimensional, nonlinear magnetohydrodynamic simulations in a compressible plasma to investigate magnetic energy release during the process of forced magnetic reconnection are carried out. This is in order to study the heating of the Sun's corona where it is believed that reconnection is induced by the photospheric motions. A sheared force-free field is perturbed by a transitory slow disturbance (pulse) at the boundary. This disturbance triggers the formation of a current sheet that subsequently releases stored magnetic energy through magnetic reconnection. Previously, it has been shown that for small boundary perturbations, the simulation results are consistent with the previous analytic theory based on a linear approach. For larger amplitude perturbations, or close to the threshold for tearing instability, the evolution shows nonlinear behavior. Solar coronal heating may arise due to a series of reconnection events, and a primary aim of this work is to study the interaction of such heating events. Thu...

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.

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.