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Sawtooth disruptions and limit cycle oscillations. (English) Zbl 1123.37050

Summary: 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.

MSC:

37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
34C60 Qualitative investigation and simulation of ordinary differential equation models
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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