P. K. Browning

Recent Advances in Understanding Particle Acceleration Processes in Solar Flares

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.

Heating the corona by nanoflares: simulations of energy release triggered by a kink instability

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.

Coronal heating by magnetic reconnection in loops with zero net current

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.

Particle acceleration at a three dimensional reconnection site in the solar corona

We study test panicle 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 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.

MECHANISMS OF SOLAR CORONAL HEATING

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.

PARTICLE ACCELERATION IN FRAGMENTING PERIODIC RECONNECTING CURRENT SHEETS IN SOLAR FLARES

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.

Particle acceleration by magnetic reconnection in a twisted coronal loop

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.

Recent advances in coronal heating

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.

Particle acceleration and transport in reconnecting twisted loops in a stratified atmosphere

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.

Particle acceleration in a transient magnetic reconnection event

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.