Sawtooth disruptions and limit cycle oscillations

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A minimal (low-dimensional) dynamical model of the sawtooth oscillations is presented. It is assumed that the sawtooth is triggered by a thermal instability which causes the plasma temperature in the central part of the plasma to drop suddenly, leading to the sawtooth crash. It is shown that this model possesses an isolated limit cycle which exhibits relaxation oscillation, in the appropriate parameter regime, which is the typical characteristics of sawtooth oscillations. It is further shown that the invariant manifold of the model is actually the slow manifold of the relaxation oscillation.