Forced 3D reconnection in an exponentially separating magnetic field

We present a solvable scenario for 3D reconnection in a sheared magnetic field. We consider a localized external force that is applied slowly to a flux tube and then maintained, generating an Alfv\'{e}nic perturbation that spreads along the field lines. Separation of the sheared field lines reduces the scale of the perturbation across the field, enhancing magnetic diffusion. For a fusion-motivated equilibrium with exponential field-line separation, we find a reconnection timescale proportional to $S/\ln S$ under magnetohydrodynamics (MHD) and to $S^{1/3}$ for semicollisional electron-only reconnection, where $S$ is the Lundquist number of the perturbed flux tube. We generalize these results to arbitrary magnetic geometries, showing that the semicollisional case is geometry independent. Interestingly, we find that slower field-line separation yields an increased reconnection rate in MHD.