Forced magnetic reconnection and the persistence of current sheets in static and rotating plasmas due to a sinusoidal boundary perturbation

The problem of forced reconnection in static and rotating plasmas due to a sinusoidal boundary perturbation is revisited. The primary focus of this paper is on inner region dynamics, including the effects of resistivity as well as viscosity. It is shown that for high-Lundquist-number plasmas, the use of the "constant-ψ" approximation in the linear and nonlinear regimes of forced reconnection is not justified. The linear and nonlinear dynamics in the inner region are characterized by the persistence of current sheets. Explicit analytical solutions for the time dependence of the reconnected flux and current sheet density are given, and tested by numerical simulations. These results differ qualitatively from earlier analytical results on forced reconnection in static plasmas [T. S. Hahm and R. M. Kulsrud, Phys. Fluids 28, 2412 (1985)] (except in a very restricted range of parameters) as well as rotating plasmas [R. Fitzpatrick and T. C. Hender, Phys. Fluids B 3, 644 (1991)]. Some qualitative implications for laboratory and space plasmas are discussed.