Torsional magnetic reconnection derived from resistive magnetohydrodynamics equations

The onset of magnetic reconnection results from the diffusion of the magnetic field through a resistive plasma due to the imbalance between plasma pressure and magnetic pressure (plasma β parameter). In following a generalized procedure to solve for a two-dimensional (2D) Sweet–Parker diffusion region, we have extended this analysis to the three-dimensional (3D) case of torsional magnetic reconnection (TMR). One key advancement of the 3D case over the 2D case includes imposing a geometrically localized plasma resistivity profile to explore how magnetic field diffusion arises at t=0 without deriving an analytical electric field or reconnection rate. Analytical solutions to the resistive magnetohydrodynamics (MHD) equations are given for both the torsional fan reconnection and torsional spine reconnection cases. Numerical solutions identify localized regions of magnetic field dissipation, enhanced pressure gradients, and helical motions, which together suggest the transition from a low-to-high plasma β and magnetic reconnection. Comparisons of these diffusion region locations to relative helicity dissipation are demonstrated, thus highlighting the importance of tracking helicity during TMR. These analytical procedures can be used to study the onset and evolution of any 3D reconnection mode without having to undertake complex time-dependent resistive MHD modeling architectures.