Quasi-linear theory of forced magnetic reconnection for the transition from the linear to the Rutherford regime

Using the in-viscid two-field reduced MHD model, a new analytical theory is developed to unify Hahm-Kulsrud-Taylor (HKT) linear solution and Rutherford quasi-linear regime. Adopting approach, we obtain closed system of equations for plasma response in static slab geometry. An integral form obtained forced magnetic reconnection, uniformly valid throughout entire regimes from HKT solution. In particular, effect can be described by single coefficient $K_s\propto S^{8/5} \psi_c^2$, where $S=\frac{\tau_R}{\tau_A}$ $\psi_c$ are Lunquist number amplitude external perturbation, respectively. The recovered when index $K_s\rightarrow 0$. On other hand, plays key role island growth $K_s\sim1$. Our has also been compared with simulations agreement.