Forced reconnection in 3D fields

We present a theory of the 3D magnetic reconnection that occurs when an Alfvén-wave packet is introduced to separating field lines. The separation causes magnetic-flux tubes to narrow and thus the perpendicular (to the local field) wavenumber of the packet to increase, allowing magnetic diffusion to be accessed. Under resistive magnetohydrodynamics (MHD), we show that field lines that separate linearly with distance (linear magnetic shear) reconnect on a timescale proportional to S^3/5, where S is the Lundquist number. This the same as in the 2D tearing-mode theory of Furth, Killeen & Rosenbluth (1963). If the field-line separation is instead exponential with distance, we show that MHD reconnection is suppressed: its timescale becomes proportional to S log S. In the case that the driven Alfvén waves are kinetic (i.e., their perpendicular wavelength is smaller than the ion Larmor radius), we show that resistive reconnection is faster than in the MHD case, with timescale proportional to S^1/3. We discuss the application of our theory to reconnection at a separatrix in a magnetic-confinement-fusion device.