Bora, Madhurjya P.; Sarmah, Dipak Sawtooth disruptions and limit cycle oscillations. (English) Zbl 1123.37050 Commun. Nonlinear Sci. Numer. Simul. 13, No. 2, 296-313 (2008). 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. Cited in 1 Document 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 Keywords:Tokamak; sawtooth oscillation; limit cycle; nonlinear dynamics; dynamical model PDFBibTeX XMLCite \textit{M. P. Bora} and \textit{D. Sarmah}, Commun. Nonlinear Sci. Numer. Simul. 13, No. 2, 296--313 (2008; Zbl 1123.37050) Full Text: DOI arXiv References: [1] von Goeler, S.; Stodiek, W.; Sauthoff, N., Studies of internal disruptions and \(m=1\) oscillations in tokamak discharges with soft-X-ray tecniques, Phys Rev Lett, 33, 1201-1203 (1974) [2] Strogatz, S. 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