C. L. Gerrard

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.

The triggering of MHD instabilities through photospheric footpoint motions

The results of 3D numerical simulations modelling the twisting of a coronal loop due to photospheric vortex motions are presented. The simulations are carried out using an initial purely axial field and an initial equilibrium configuration with twist, . The non-linear and resistive evolutions of the instability are followed. The magnetic field is twisted by the boundary motions into a loop which initially has boundary layers near the photospheric boundaries as has been suggested by previous work. The boundary motions increase the twist in the loop until it becomes unstable. For both cases the boundary twisting triggers the kink instability. In both cases a helical current structure wraps itself around the kinked central current. This current scales linearly with grid resolution indicating current sheet formation. For the cases studied 35-40% of the free magnetic energy is released. This is sufficient to explain the energy released in a compact loop flare.

Numerical simulations of kink instability in line-tied coronal loops

The results from numerical simulations carried out using a new shock-capturing, Lagrangian-remap, 3D MHD code, Lare3d are presented. We study the evolution of them = 1 kink mode instability in a photospherically line-tied coronal loop that has no net axial current. During the non-linear evolution of the kink instability, large current concentrations develop in the neighbourhood of the innite length mode rational surface. We investigate whether this strong current saturates at a nite value or whether scaling indicates current sheet formation. In particular, we consider the eect of the shear, dened by r 0 = where = LB=rBz is the eldline twist of the loop, on the current concentration. We also include a non-uniform resistivity in the simulations and observe the amount of free magnetic energy released by magnetic reconnection.

Non-linear kink instabilities in line-tied coronal loops

Photospheric line-tying has a stabilizing effect that allows magnetic energy to build up in coronal loops until critical conditions are reached and the loop becomes unstable to the m=1 kink instability [1]. Recent research has concentrated on the non-linear evolution of instabilities in line-tied coronal loops. There are suggestions [2–5] that current sheets form during the non-linear evolution of the kink instability. We present 3D MHD simulations of the non-linear evolution of MHD instabilities in line-tied coronal loops. These simulations are carried out on a multi-processor cluster at St Andrews using a new 3D MHD Lagrangian remap code (Lare3d) which we shall discuss briefly. Results are presented for loops with different shear profiles to test the conditions for current sheet formation. We begin by presenting the test case of the Gold-Hoyle field, and compare our results with previous results [1,6]. New results for equilibria with no net axial current are presented and the formation of current sheets...