The Role of Stochasticity in Sawtooth Oscillation

"Stochastization of field lines, resulting from the interaction of the fundamental m/n=1/1 helical mode with other periodicities, plays an important role in sawtooth oscillations. The time scale for the stochastic temperature diffusion is shown to be sufficiently fast to account for the fast sawtooth crash. The enhanced electron and ion viscosity, arising from the stochastic field lines, are calculated. The enhanced electron viscosity always leads to an initial increase in the growth rate of the mode, the ""magnetic trigger"". The enhanced ion viscosity can ultimately lead to mode stabilization before a complete temperature redistribution or flux reconnection has occurred. A dynamical model is introduced to calculate the path of the sawtooth oscillation through a parameter space of shear and amplitude of the helical perturbation, including a stochastic trigger to an enhanced growth rate, stabilization by ion viscosity, and a prescription for flux reconnection at the end of the growth phase. Our model predicts that four types of the sawtooth oscillations are possible even for a plasma with monotonic q(r) profile. There are two types of rearrangement of the magnetic configuration: a partial-magnetic reconnection, in which the safety factor on axis q(0) value oscillates around 0.7 with delta q(0) simeq 0.05; and a full magnetic reconnection, for which q(0) oscillates between l and about 0.8 . In a partial reconnection the temperature flattening is rapid and can be either limited to an annulus near the q=1 rational surface , which then gradually propagates to the axis, or the temperature on axis T_e(0) can rapidly decay, when the stochastic region invades the geometrical axis. With a full magnetic reconnection, T_e(0) collapses rapidly when stochasticity is present or slowly without stochasticity. The main features of the model are compared with experimental observations. In particular, they may explain the sudden growth of the helical perturbation, the ""magnetic trigger"", the fast time scale of the temperature collapse, a partial temperature collapse, and the persistence of an m/n=1/1 island throughout the sawtooth cycle.