Dynamics of Magnetic Relaxation inside a Cylindrical Flux Conserver

Abstract

Rapid localized magnetic reconnection events within a magnetohydrodynamic (MHD) unstable plasma produce rapid dissipation of magnetic energy while leaving system’s global magnetic helicity almost unaffected. This is the basis of a robust principle called magnetic relaxation. When the plasma is bounded by flux conserving walls, magnetic relaxation induces the spontaneous formation of large scale coherent magnetic structures (plasma self-organization). In this work, the dynamics of magnetic relaxation inside a simply connected volume (a cylinder) is studied by solving the visco-resistive MHD system of equations in three spatial dimensions. The discretization of the governing equations is performed with the finite-volume method and a high resolution total-variation-diminishing (TVD) solver is employed to treat non linearities. The formation and sustainment of a toroidal configuration, known as spheromak, inside the simply connected domain is demonstrated. A set of boundary conditions that correctly models the injection of magnetic energy and helicity, required to balance resistive dissipation, is described. Different initial conditions are tested and their impact on the final quasi-steady state is discussed. In particular, we show that it is possible to sustain the so called “flipped” spheromak. The MHD activity in both cases (normal and flipped) is studied.