Abstract
Stickiness refers to the destructed orbits in phase space that remain in a particular region around intact surfaces for a long time before entering the chaotic sea. In fusion plasmas, stickiness regions trap magnetic field lines for many toroidal turns and have considerable effect on plasma transport. We locate stickiness regions in the chaotic phase space of resonant magnetic perturbations in tokamak using three dynamical quantities which are field lines diffusion coefficient, maximal Lyapunov exponent and the growing rate of an infinitesimal line segment. We compare the values of these quantities in regular, stickiness and chaotic regions to find a criterion for distinguishing stickiness from chaotic and regular areas in phase space.
Similar content being viewed by others
References
S S Abdullaev Magnetic Stochasticity in Magnetically Confined Fusion Plasmas, (Switzerland: Springer Series on Atomic, Optical, and Plasma Physics) 78 (2014)
A H Boozer Phys. Fluids 26 1288 (1983).
P J Morrison Phys. Plasmas 7 2279 (2000).
R Balescu, M Vlad and F Spineanu Phys. Rev. E 58 951 (1998).
T J Martin and J B Taylor Plasma Phys. Control. Fusion 26 321 (1984).
S S Abdullaev Nucl. Fusion 44 S12 S27 (2004).
G Contopoulos III Non Periodic Orbits Astron. J. 76 147 (1971).
G Contopoulos and M Harsoula Int. J. Bifurcation Chaos 20 2005 (2010).
J D Meiss Rev. Mod. Phys. 64 795 (1992).
D del-Castillo-Negrete Phys. Plasmas 7 1702 (2000).
J D Szezech et al Chaos 19 043108 (2009).
M Roberto, E C Silva, I L Caldas and R L Viana Plasmas 11 214 (2004).
C G L Martins and M Roberto, I L Caldas IEEE Trans. Plasma Sci. 42 2764 (2014).
G Contopoulos, M Harsoula, N Voglis and R Dvorak J. Phys. A: Math. Gen. 32 5213 (1999).
Y Zou, M Thiel, M C Romano and J Kurths Chaos 17 043101 (2007).
C V Abud and R E Carvalho Phys. Rev. E 88 042922 (2013).
J D Szezech Jr, S R Lopes, and R L Viana Phys. Lett. A 335 394 (2005).
J D Szezech, et al Phys. Lett. A 377 452 (2013)
T Kroetz, et al Phys. Plasmas 15 092310 (2008)
M S Santos, et al Chaos 29 043125 (2019)
S S Abdullaev Construction of Mappings for Hamiltonian Systems and Their Applications (Berlin: Springer Verlag) (2006)
J Wesson Tokamaks (Oxford, U K: Oxford University Press) (1982)
J P Friedberg Ideal Magnetohydrodynamics (New York: Plenum) (1987)
A J Lichtenberg and M A Regular Chaotic Dynamics. (New York: Springer Verlag) (1992)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Sohrabi, A.R., Jazayeri, S.M. Unveiling stickiness regions of magnetic field lines in tokamaks. Indian J Phys 96, 2185–2190 (2022). https://doi.org/10.1007/s12648-021-02174-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12648-021-02174-2