Abstract
We analyze probe data obtained from a toroidal magnetized plasma configuration suitable for studies of low-frequency gradient-driven instabilities. These instabilities give rise to field-aligned convection rolls analogous to Rayleigh-Benard cells in neutral fluids, and may theoretically develop similar routes to chaos. When using mean-field dimension analysis, we observe low dimensionality, but this could originate from either low-dimensional chaos, periodicity or quasi-periodicity. Therefore, we apply recurrence plot analysis as well as estimation of the largest Lyapunov exponent. These analyses provide evidence of low-dimensional chaos, in agreement with theoretical predictions. Our results can be applied to other magnetized plasma configurations, where gradient-driven instabilities dominate the dynamics of the system.
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References
K. Rypdal, S. Ratynskaia, Phys. Rev. Lett. 94, 225002 (2005)
K. Rypdal, O. Garcia, Phys. Plasm. 14, 022101 (2007)
A.Y. Ukhorskiy, M.I. Sitnov, A.S. Sharma, K. Papadopoulos, Ann. Geophys. 21, 1913 (2003)
F. Takens, Dynamical Systems and Turbulence, edited by D. Rand, L.S. Young (Springer, Berlin, 1981), p. 366
H. Abarbanel, Analysis of Observed Chaotic Data (Springer, New York, 1996), p. 28
L. Cao, A. Mees, K. Judd, Physica D 121, 75 (1998)
J.P. Eckmann, S.O. Kamphorst, D. Ruelle, Europhys. Lett. 5, 973 (1987)
N. Marwan, J. Kurths, Phys. Lett. A 302, 299 (2002)
M.C. Romano, M. Thiel, J. Kurths, W. von Bloh, Phys. Lett. A 330, 214 (2004)
N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007)
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Živković, T., Rypdal, K. Evidence of low-dimensional chaos in magnetized plasma turbulence. Eur. Phys. J. Spec. Top. 164, 157–164 (2008). https://doi.org/10.1140/epjst/e2008-00841-5
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Keywords
- Lyapunov Exponent
- European Physical Journal Special Topic
- Normalize Mean Square Error
- Large Lyapunov Exponent
- Recurrence Plot