Electron-inertia effects on driven magnetic field reconnection

Electron-inertia effects on the magnetic field reconnection induced by perturbing the boundaries of a slab of plasma with a magnetic neutral surface inside are considered. Energetics of the tearing mode dynamics with electron inertia which controls the linearized collisionless magnetohydrodynamics (MHD) are considered with a view to clarify the role of the plasma pressure in this process. Cases with the boundaries perturbed at rates slow or fast compared with the hydromagnetic evolution rate are considered separately. When the boundaries are perturbed at a rate slow compared with the hydromagnetic evolution rate and fast compared with the resistive diffusion rate, the plasma response for early times is according to ideal MHD. A current sheet formation takes place at the magnetic neutral surface for large times in the ideal MHD stage and plasma becomes motionless. The subsequent evolution of the current sheet is found to be divided into two distinct stages: (i) the electron-inertia stage for small times (when the current sheet is very narrow); (ii) the resistive-diffusion stage for large times. The current sheet mainly undergoes exponential damping in the electron-inertia regime while the bulk of the diffusion happens in the resistivity regime. For large times of the resistive-diffusion stage when plasma flow is present, the current sheet completely disappears and the magnetic field reconnection takes place. When the boundaries are perturbed at a rate fast compared even with the hydromagnetic evolution rate, there is no time for the development of a current sheet and the magnetic field reconnection has been found not to take place

Three-dimensional solutions of the magnetohydrostatic equations : rigidly rotating magnetized coronae in spherical geometry

Context. Magnetohydrostatic (MHS) equilibria are often used to model astrophysical plasmas, for example, planetary magnetospheres or coronae of magnetized stars. However, finding realistic three-dimensional solutions to the MHS equations is difficult, with only a few known analytical solutions and even finding numerical solution is far from easy. Aims. We extend the results of a previous paper on three-dimensional solutions of the MHS equations around rigidly rotating massive cylinders to the much more realistic case of rigidly rotating massive spheres. An obvious application is to model the closed field line regions of the coronae of rapidly rotating stars. Methods. We used a number of simplifying assumptions to reduce the MHS equations to a single elliptic partial differential equation for a pseudo-potential U, from which all physical quantities, such as the magnetic field, the plasma pressure, and the density, can be derived by differentiation. The most important assumptions made are stationarity in the co-rotating frame of reference, a particular form for the current density, and neglect of outflows. Results. In this paper we demonstrate that standard methods can be used to find numerical solutions to the fundamental equation of the theory. We present three simple different cases of magnetic field boundary conditions on the surface of the central sphere, corresponding to an aligned dipole field, a non-aligned dipole field, and a displaced dipole field. Our results show that it should be possible in the future to use this method without dramatically increasing the demands on computational resources to improve upon potential field models of rotating magnetospheres and coronae.PostprintPeer reviewe

Three-dimensional solutions of the magnetohydrostatic equations : rigidly rotating magnetized coronae in cylindrical geometry

Context. Solutions of the magnetohydrostatic (MHS) equations are very important for modelling astrophysical plasmas, such as the coronae of magnetized stars. Realistic models should be three-dimensional, i.e., should not have any spatial symmetries, but finding three-dimensional solutions of the MHS equations is a formidable task. Aims. We present a general theoretical framework for calculating three-dimensional MHS solutions outside massive rigidly rotating central bodies, together with example solutions. A possible future application is to model the closed field region of the coronae of fast-rotating stars. Methods. As a first step, we present in this paper the theory and solutions for the case of a massive rigidly rotating magnetized cylinder, but the theory can easily be extended to other geometries, We assume that the solutions are stationary in the co-rotating frame of reference. To simplify the MHS equations, we use a special form for the current density, which leads to a single linear partial differential equation for a pseudo-potential U. The magnetic field can be derived from U by differentiation. The plasma density, pressure, and temperature are also part of the solution. Results. We derive the fundamental equation for the pseudo-potential both in coordinate independent form and in cylindrical coordinates. We present numerical example solutions for the case of cylindrical coordinates.PostprintPeer reviewe