Nonlinear dynamics of them=1 instability and fast sawtooth collapse in high-temperature plasmas

A theory is given for the nonlinear dynamical evolution of the m=1 instability, governed by a generalized Ohm's law that includes the Hall term. An island equation is derived for the entire nonlinear evolution which includes an almost explosive growth phase followed by a rapid decay phase. The predictions of the theory are compared with recent numerical results and experiments.