Investigation of topology-driven magnetic reconnection with CWENO finite volume numerics

Abstract

Magnetic reconnection is a process in a plasma that changes the magnetic field topology due to finite electrical resistivity in the field’s plasma environment. A possible trigger for the onset of reconnection is a high entanglement of the field lines which can exponentially amplify the influence of small resistive effects. This type of topology-driven reconnection is investigated by direct numerical simulations based on finite-volume numerics, in which the plasma is described by the ideal magnetohydrodynamic (MHD) equations. Numerical dissipation is utilized as a proxy of viscous and resistive non-idealities. A simple numerical configuration is used to study the relation of potential reconnection events and field line entanglement. The application of an external velocity field induces magnetic field line movement through the frozen-in condition. It is used to drive the field lines of an initially homogeneous magnetic field with constant mean value pointing in the z-direction to a high degree of entanglement. The footpoints of the field lines are fixed at the boundaries in the z-direction, such that reconnection events can be observed by changes in the footpoint mapping from one z-boundary to the other. Damping layers at these boundaries are included in order to damp any perturbations caused by Alfvén waves propagating along the field lines. The boundary conditions orthogonal to the z-direction of the box-shaped simulation volume are periodic. In this configuration the system initially relaxes into a stationary state, in which the forces acting on the plasma balance each other and the field lines settle into a twisted state. This state of force-balance is spontaneously disrupted and a fast transition from the stationary state to a chaotic state is observed, which is accompanied by a sudden increase in both kinetic and magnetic energy. The influence of the grid resolution, the forcing amplitude and the damping coefficient is investigated and discussed.The chaotic phase is further investigated and shown to be characterized by locally enhanced current densities, large separations of neighboring field lines and a change in the mapping of footpoints of particular field line bundles. The correlation of two key diagnostics is used to investigate the proposed connection between high entanglement and reconnection: the exponentiation number, which quantifies the separation of field lines and which is a measure of the degree of entanglement, and the foot point velocity, which is an indicator for potential reconnection events. It is shown that these two quantities are indeed temporally correlated, supporting the proposed theory. Furthermore, individual field lines undergo distinct reconnection events which happen on sub-Alfvénic timescales and which are correlated with high footpoint velocities. The abruptness of the events suggests that it is reconnection rather than resistive diffusion that causes the motion of the field lines.