Transport Barriers in Symplectic Maps
Abstract
Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be obtained from simple dynamical systems like two-dimensional area-preserving (symplectic) maps, where powerful mathematical results like KAM theory are available. In this work we review recent works on transport barriers in area-preserving maps, focusing on systems which do not obey the so-called twist property. For such systems KAM theory no longer holds everywhere and novel dynamical features show up as nonresistive reconnection, shearless curves and shearless bifurcations. After presenting some general features using a standard nontwist mapping, we consider magnetic field line maps for magnetically confined plasmas in tokamaks.
- Authors:
-
[1];
- Universidade Federal do Parana, Parana (Brazil). Departamento de Fisica
- Univ. of Sao Paulo (Brazil). Instituto de Fısica. Departamento de Fısica Aplicada
- Universidade Estadual de Ponta Grossa, Ponta Grossa, Parana (Brazil). Departamento de Matematica e Estatıstica
- Universidade Estadual de Ponta Grossa, Ponta Grossa, Parana (Brazil). Departamento de Matematica e Estatıstica
- Universidade Federal de Goias, Goias (Brazil)
- Universidade de Brasılia, Brasılia (Brazil). Instituto de Fısica
- Univ. of Texas, Austin, TX (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE; FAPESP
- OSTI Identifier:
- 1850237
- Grant/Contract Number:
- FG05-80ET53088; 2018/03211-6
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Brazilian Journal of Physics
- Additional Journal Information:
- Journal Volume: 51; Journal Issue: 3; Journal ID: ISSN 0103-9733
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics
Citation Formats
Viana, R. L., Caldas, I. L., Szezech, J. D., Batista, A. M., Abud, C. V., Schelin, A. B., Mugnaine, M., Santos, M. S., Leal, B. B., Bartoloni, B., Mathias, A. C., Gomes, J. V., and Morrison, P. J. Transport Barriers in Symplectic Maps. United States: N. p., 2021.
Web. doi:10.1007/s13538-021-00894-8.
Viana, R. L., Caldas, I. L., Szezech, J. D., Batista, A. M., Abud, C. V., Schelin, A. B., Mugnaine, M., Santos, M. S., Leal, B. B., Bartoloni, B., Mathias, A. C., Gomes, J. V., & Morrison, P. J. Transport Barriers in Symplectic Maps. United States. https://doi.org/10.1007/s13538-021-00894-8
Viana, R. L., Caldas, I. L., Szezech, J. D., Batista, A. M., Abud, C. V., Schelin, A. B., Mugnaine, M., Santos, M. S., Leal, B. B., Bartoloni, B., Mathias, A. C., Gomes, J. V., and Morrison, P. J. Wed .
"Transport Barriers in Symplectic Maps". United States. https://doi.org/10.1007/s13538-021-00894-8. https://www.osti.gov/servlets/purl/1850237.
@article{osti_1850237,
title = {Transport Barriers in Symplectic Maps},
author = {Viana, R. L. and Caldas, I. L. and Szezech, J. D. and Batista, A. M. and Abud, C. V. and Schelin, A. B. and Mugnaine, M. and Santos, M. S. and Leal, B. B. and Bartoloni, B. and Mathias, A. C. and Gomes, J. V. and Morrison, P. J.},
abstractNote = {Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be obtained from simple dynamical systems like two-dimensional area-preserving (symplectic) maps, where powerful mathematical results like KAM theory are available. In this work we review recent works on transport barriers in area-preserving maps, focusing on systems which do not obey the so-called twist property. For such systems KAM theory no longer holds everywhere and novel dynamical features show up as nonresistive reconnection, shearless curves and shearless bifurcations. After presenting some general features using a standard nontwist mapping, we consider magnetic field line maps for magnetically confined plasmas in tokamaks.},
doi = {10.1007/s13538-021-00894-8},
journal = {Brazilian Journal of Physics},
number = 3,
volume = 51,
place = {United States},
year = {Wed Apr 07 00:00:00 EDT 2021},
month = {Wed Apr 07 00:00:00 EDT 2021}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Secondary nontwist phenomena in area-preserving maps
journal, September 2012
- Vieira Abud, C.; Caldas, I. L.
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 22, Issue 3
Current Clamp at Zero Level in JT-60U Current Hole Plasmas
journal, August 2005
- Fujita, T.; Suzuki, T.; Oikawa, T.
- Physical Review Letters, Vol. 95, Issue 7
Fluctuations and anomalous transport in tokamaks
journal, December 1990
- Wootton, A. J.; Carreras, B. A.; Matsumoto, H.
- Physics of Fluids B: Plasma Physics, Vol. 2, Issue 12
Hamiltonian nontwist map for magnetic field lines with locally reversed shear in toroidal geometry
journal, September 1998
- Balescu, R.
- Physical Review E, Vol. 58, Issue 3
Thirty years of turnstiles and transport
journal, September 2015
- Meiss, J. D.
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 25, Issue 9
Dimerized island chains in tokamaks
journal, January 1995
- Oda, Gisele A.; Caldas, IberêL.
- Chaos, Solitons & Fractals, Vol. 5, Issue 1
Transport properties in nontwist area-preserving maps
journal, December 2009
- Szezech, J. D.; Caldas, I. L.; Lopes, S. R.
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 19, Issue 4
Onset of shearless magnetic surfaces in tokamaks
journal, May 2014
- Vieira Abud, C.; Caldas, I. L.
- Nuclear Fusion, Vol. 54, Issue 6
An analytical study of transport, mixing and chaos in an unsteady vortical flow
journal, May 1990
- Rom-Kedar, V.; Leonard, A.; Wiggins, S.
- Journal of Fluid Mechanics, Vol. 214, Issue -1
Filamentation and Subsequent Decay of Laser Light in Plasmas
journal, April 1975
- Langdon, A. Bruce; Lasinski, Barbara F.
- Physical Review Letters, Vol. 34, Issue 15
Generic twistless bifurcations
journal, December 1999
- Dullin, H. R.; Meiss, J. D.; Sterling, D.
- Nonlinearity, Vol. 13, Issue 1
The use of internal transport barriers in tokamak plasmas
journal, November 2004
- Challis, C. D.
- Plasma Physics and Controlled Fusion, Vol. 46, Issue 12B
Chaotic transport in zonal flows in analogous geophysical and plasma systems
journal, May 2000
- del-Castillo-Negrete, Diego
- Physics of Plasmas, Vol. 7, Issue 5
Dynamical characterization of transport barriers in nontwist Hamiltonian systems
journal, January 2018
- Mugnaine, M.; Mathias, A. C.; Santos, M. S.
- Physical Review E, Vol. 97, Issue 1
Chaotic magnetic field lines in a Tokamak with resonant helical windings
journal, April 2000
- Viana, R. L.
- Chaos, Solitons & Fractals, Vol. 11, Issue 5
Ratchet current in nontwist Hamiltonian systems
journal, September 2020
- Mugnaine, Michele; Batista, Antonio M.; Caldas, Iberê L.
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 30, Issue 9
Fractal structures in the parameter space of nontwist area-preserving maps
journal, November 2019
- Mathias, A. C.; Mugnaine, M.; Santos, M. S.
- Physical Review E, Vol. 100, Issue 5
Transport in Hamiltonian systems
journal, August 1984
- Mackay, R. S.; Meiss, J. D.; Percival, I. C.
- Physica D: Nonlinear Phenomena, Vol. 13, Issue 1-2
Tokamap: A Hamiltonian twist map for magnetic field lines in a toroidal geometry
journal, July 1998
- Balescu, R.; Vlad, M.; Spineanu, F.
- Physical Review E, Vol. 58, Issue 1
Magnetic field lines, Hamiltonian dynamics, and nontwist systems
journal, June 2000
- Morrison, P. J.
- Physics of Plasmas, Vol. 7, Issue 6
Escape patterns of chaotic magnetic field lines in a tokamak with reversed magnetic shear and an ergodic limiter
journal, September 2008
- Kroetz, T.; Roberto, M.; da Silva, E. C.
- Physics of Plasmas, Vol. 15, Issue 9
Drift wave test particle transport in reversed shear profile
journal, November 1998
- Horton, Wendell; Park, Hyoung-Bin; Kwon, Jae-Min
- Physics of Plasmas, Vol. 5, Issue 11
Tokamak magnetic field lines described by simple maps: Dedicated to Professor Celso Grebogi on the occasion of his 60th birthday
journal, December 2008
- Portela, J. S. E.; Caldas, I. L.; Viana, R. L.
- The European Physical Journal Special Topics, Vol. 165, Issue 1
Internal transport barriers in tokamak plasmas*
journal, November 2002
- Wolf, R. C.
- Plasma Physics and Controlled Fusion, Vol. 45, Issue 1
Current Penetration and Plasma Disruption
journal, March 1976
- Stix, Thomas H.
- Physical Review Letters, Vol. 36, Issue 10
Chaotic transport by Rossby waves in shear flow
journal, April 1993
- del‐Castillo‐Negrete, Diego; Morrison, P. J.
- Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 4
Shearless bifurcation on symplectic maps of magnetic field lines in tokamaks with reversed current
journal, July 2016
- Bartoloni, B.; Schelin, A. B.; Caldas, I. L.
- Physics Letters A, Vol. 380, Issue 31-32
A symplectic mapping for the ergodic magnetic limiter and its dynamical analysis
journal, October 2000
- Ullmann, K.; Caldas, I. L.
- Chaos, Solitons & Fractals, Vol. 11, Issue 13
Diffusive Transport Through a Nontwist Barrier in Tokamaks
journal, May 2007
- Portela, J. S. E.; Caldas, I. L.; Viana, R. L.
- International Journal of Bifurcation and Chaos, Vol. 17, Issue 05
Electrostatic turbulence intermittence driven by biasing in Texas Helimak
journal, December 2014
- Toufen, D. L.; Pereira, F. A. C.; Guimarães-Filho, Z. O.
- Physics of Plasmas, Vol. 21, Issue 12
Area preserving nontwist maps: periodic orbits and transition to chaos
journal, March 1996
- del-Castillo-Negrete, D.; Greene, J. M.; Morrison, P. J.
- Physica D: Nonlinear Phenomena, Vol. 91, Issue 1-2