Exponential nonlinear growth of a resistive m=1 island

An analytical model is given for the exponential growth of a m=1 resistive island in the late nonlinear stage of its dynamics, observed in a recent numerical simulation [A. Aydemir, Phys. Rev. Lett. 78, 4406 (1997)]. This late nonlinear exponential growth phase follows the linear exponential growth phase and an early nonlinear algebraic growth phase. It is shown that the transition from the early nonlinear phase of algebraic growth in time to exponential growth occurs due to change in the geometric structure of the current sheet. Analytical predictions are in reasonable accord with simulation results.