A numerical study of forced magnetic reconnection in the viscous Taylor problem

Two-dimensional, nonlinear magnetohydrodynamical simulations are used to investigate the so-called Taylor problem, in which a small amplitude boundary perturbation is suddenly applied to a tearing stable, slab plasma equilibrium—the perturbation being such as to drive magnetic reconnection within the plasma. This type of reconnection, which is not due to an intrinsic plasma instability, is generally known as ‘‘forced reconnection.’’ For numerical reasons, the investigation is restricted to the large magnetic Prandtl number limit. The simulation results are highly consistent with the analysis of Hahm and Kulsrud @Phys. Fluids 28, 2412 ~1985!# ~modified by strong plasma viscosity!. At high perturbation amplitudes, the system exhibits a phase of Sweet–Parker reconnection, as predicted by Wang and Bhattacharjee @Phys. Fluids B 4, 1795 ~1992!#. An expression for the threshold perturbation amplitude required to trigger Sweet–Parker reconnection is derived, and successfully benchmarked against numerical simulations. This expression suggests that a Sweet–Parker phase is only likely to occur during forced reconnection in tokamaks when the plasma is extremely hot and perturbation amplitude relatively large. © 2003 American Institute of Physics. @DOI: 10.1063/1.1574516#