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Current sheets play a crucial role in determining the physics of magnetic reconnection in solar flares. We investigate the structure of a reconnecting visco-resistive (VR) current sheet in two dimensional steady incompressible MHD. We review a number of solutions that demonstrate that several distinct potential length scalings may emerge for VR reconnection. We find a criterion for the presence of a VR length scale in magnetic flux pile-up solutions and we utilise a series expansion technique in order to describe the inner solution of a VR current sheet. We posit that a VR length scale is the fundamental length scale of a VR current sheet and its absence is purely a feature of a limited class of particular solutions for the inflow velocity profile.

We investigate the dynamics and energetics of magnetic reconnection in a general linear magnetohydrodynamic (MHD) model. Our investigation is threefold: First, we formulate a generalized 2.5D linearized MHD system in the presence of viscous, pressure, collisionless, and axial magnetic effects. Second, we find, in accordance with previous studies, that viscous effects, while reducing the rate of reconnection, boost the rate of total energy release. Moreover, viscous dissipation, as opposed to resistive dissipation, is unlikely to be impeded by pressure forces. Third, we compare two different equilibrium axial magnetic field profiles. One profile emulates a quasiseparatrix layer and the other profile emulates a 3D null point. In 2.5D, these profiles actually correspond to a hyperbolic field threaded by an axial field and a null line, respectively. We show evidence that fast reconnection is only attainable in the presence of a null.

An exact self-similar solution is used to investigate current sheet formation at a magnetic neutral line in incompressible Hall magnetohydrodynamics. The collapse to a current sheet is modelled as a finite-time singularity in the solution for electric current density at the neutral line. We establish that a finite-time collapse to the current sheet can occur in Hall magnetohydrodynamics, and we find a criterion for the finite-time singularity in terms of the initial conditions. We derive an asymptotic solution for the singularity formation and a formula for the singularity formation time. The analytical results are illustrated by numerical solutions, and we also investigate an alternative similarity reduction. Finally, we generalise our solution to incorporate resistive, viscous and electron inertia terms.