Transport properties in nontwist area-preserving maps

Szezech Jr., J. D.; Caldas, I. L.; Lopes, S. R.; Viana, R. L.; Morrison, P. J.

doi:10.1063/1.3247349

Title: Transport properties in nontwist area-preserving maps

Abstract

Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds.

Authors:

Szezech Jr., J. D. ^[1]; Caldas, I. L. ^[1]; Lopes, S. R. ^[2]; Viana, R. L. ^[2]; Morrison, P. J. ^[3]

Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)
Departamento de Fisica, Universidade Federal do Parana, Curitiba (Brazil)
Univ. of Texas at Austin (United States)

Publication Date:: Fri Oct 23 00:00:00 EDT 2009

Research Org.:: Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1076438

Grant/Contract Number:: FG03-96ER54346

Resource Type:: Accepted Manuscript

Journal Name:: Chaos: An Interdisciplinary Journal of Nonlinear Science

Additional Journal Information:: Journal Volume: 19; Journal Issue: 4; Journal ID: ISSN 1054-1500

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Manifolds; Diffusion; Toroidal plasma confinement; Magnetic fields

Citation Formats


                    Szezech Jr., J. D., Caldas, I. L., Lopes, S. R., Viana, R. L., and Morrison, P. J. Transport properties in nontwist area-preserving maps.  United States: N. p., 2009. 
Web.  doi:10.1063/1.3247349.

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                    Szezech Jr., J. D., Caldas, I. L., Lopes, S. R., Viana, R. L., & Morrison, P. J. Transport properties in nontwist area-preserving maps.  United States.  https://doi.org/10.1063/1.3247349

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                    Szezech Jr., J. D., Caldas, I. L., Lopes, S. R., Viana, R. L., and Morrison, P. J. Fri .  
"Transport properties in nontwist area-preserving maps".  United States.  https://doi.org/10.1063/1.3247349.  https://www.osti.gov/servlets/purl/1076438.

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@article{osti_1076438,

  title        = {Transport properties in nontwist area-preserving maps},

  author       = {Szezech Jr., J. D. and Caldas, I. L. and Lopes, S. R. and Viana, R. L. and Morrison, P. J.},

  abstractNote = {Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds.},

  doi          = {10.1063/1.3247349},

  journal      = {Chaos: An Interdisciplinary Journal of Nonlinear Science},

  number       = 4,

  volume       = 19,

  place        = {United States},

  year         = {Fri Oct 23 00:00:00 EDT 2009},

  month        = {Fri Oct 23 00:00:00 EDT 2009}

}

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Works referencing / citing this record:

Recurrence-based analysis of barrier breakup in the standard nontwist map
journal, August 2018

Santos, Moises S.; Mugnaine, Michele; Szezech, José D.
Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 28, Issue 8
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Influence of the radial electric field on the shearless transport barriers in tokamaks
journal, February 2019

Marcus, F. A.; Roberto, M.; Caldas, I. L.
Physics of Plasmas, Vol. 26, Issue 2
DOI: 10.1063/1.5071437

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Title: Transport properties in nontwist area-preserving maps

Abstract

Citation Formats

Monotone twist mappings and the calculus of variations journal, September 1986

A universal instability of many-dimensional oscillator systems journal, May 1979

Chaotic transport by Rossby waves in shear flow journal, April 1993

Area preserving nontwist maps: periodic orbits and transition to chaos journal, March 1996

Renormalization and transition to chaos in area preserving nontwist maps journal, February 1997

Stability of Multihelical Tearing Modes in Shaped Tokamaks journal, August 1982

Hamiltonian Maps for Heliac Magnetic Islands journal, January 1995

Hamiltonian approach to the existence of magnetic surfaces journal, September 1985

Magnetic field lines, Hamiltonian dynamics, and nontwist systems journal, June 2000

Turbulent Fluctuations in TFTR Configurations with Reversed Magnetic Shear journal, October 1996

Drift wave test particle transport in reversed shear profile journal, November 1998

The structure of chaotic magnetic field lines in a tokamak with external nonsymmetric magnetic perturbations journal, January 2001

Threshold to global diffusion in a nonmonotonic map with quadratic nonlinearity journal, July 1999

Chaotic transport in zonal flows in analogous geophysical and plasma systems journal, May 2000

Chaotic transport in reversed shear tokamaks journal, January 2008

Reduction of chaotic particle transport driven by drift waves in sheared flows journal, November 2008

Traces of stable and unstable manifolds in heat flux patterns journal, April 2007

Experimental and numerical studies of separatrix splitting and magnetic footprints in DIII-D journal, June 2007

On reconnection phenomena in the standard nontwist map journal, January 2004

Meanders and reconnection–collision sequences in the standard nontwist map journal, June 2005

Greene's residue criterion journal, January 1992

KAM Theory and a Partial Justification of Greene's Criterion for Nontwist Maps journal, January 2000

Invariant curves of analytic perturbed nontwist area preserving maps journal, January 1998

Generic twistless bifurcations journal, December 1999

A symplectic mapping for the ergodic magnetic limiter and its dynamical analysis journal, October 2000

Hierarchical structures in the phase space and fractional kinetics: I. Classical systems journal, March 2000

Fractional diffusion in plasma turbulence journal, August 2004

Finite-time Lyapunov spectrum for chaotic orbits of non-integrable Hamiltonian systems journal, February 2005

Manifold reconnection in chaotic regimes journal, December 1998

Modeling of stochastic magnetic flux loss from the edge of a poloidally diverted tokamak journal, December 2002

Repellers, semi-attractors, and long-lived chaotic transients journal, August 1985

Fractal and wada exit Basin Boundaries in Tokamaks journal, November 2007

Transport in Hamiltonian systems journal, August 1984

Recurrence-based analysis of barrier breakup in the standard nontwist map journal, August 2018

Influence of the radial electric field on the shearless transport barriers in tokamaks journal, February 2019

Monotone twist mappings and the calculus of variations
journal, September 1986

A universal instability of many-dimensional oscillator systems
journal, May 1979

Chaotic transport by Rossby waves in shear flow
journal, April 1993

Area preserving nontwist maps: periodic orbits and transition to chaos
journal, March 1996

Renormalization and transition to chaos in area preserving nontwist maps
journal, February 1997

Stability of Multihelical Tearing Modes in Shaped Tokamaks
journal, August 1982

Hamiltonian Maps for Heliac Magnetic Islands
journal, January 1995

Hamiltonian approach to the existence of magnetic surfaces
journal, September 1985

Magnetic field lines, Hamiltonian dynamics, and nontwist systems
journal, June 2000

Turbulent Fluctuations in TFTR Configurations with Reversed Magnetic Shear
journal, October 1996

Drift wave test particle transport in reversed shear profile
journal, November 1998

The structure of chaotic magnetic field lines in a tokamak with external nonsymmetric magnetic perturbations
journal, January 2001

Threshold to global diffusion in a nonmonotonic map with quadratic nonlinearity
journal, July 1999

Chaotic transport in zonal flows in analogous geophysical and plasma systems
journal, May 2000

Chaotic transport in reversed shear tokamaks
journal, January 2008

Reduction of chaotic particle transport driven by drift waves in sheared flows
journal, November 2008

Traces of stable and unstable manifolds in heat flux patterns
journal, April 2007

Experimental and numerical studies of separatrix splitting and magnetic footprints in DIII-D
journal, June 2007

On reconnection phenomena in the standard nontwist map
journal, January 2004

Meanders and reconnection–collision sequences in the standard nontwist map
journal, June 2005

Greene's residue criterion
journal, January 1992

KAM Theory and a Partial Justification of Greene's Criterion for Nontwist Maps
journal, January 2000

Invariant curves of analytic perturbed nontwist area preserving maps
journal, January 1998

Generic twistless bifurcations
journal, December 1999

A symplectic mapping for the ergodic magnetic limiter and its dynamical analysis
journal, October 2000

Hierarchical structures in the phase space and fractional kinetics: I. Classical systems
journal, March 2000

Fractional diffusion in plasma turbulence
journal, August 2004

Finite-time Lyapunov spectrum for chaotic orbits of non-integrable Hamiltonian systems
journal, February 2005

Manifold reconnection in chaotic regimes
journal, December 1998

Modeling of stochastic magnetic flux loss from the edge of a poloidally diverted tokamak
journal, December 2002

Repellers, semi-attractors, and long-lived chaotic transients
journal, August 1985

Fractal and wada exit Basin Boundaries in Tokamaks
journal, November 2007

Transport in Hamiltonian systems
journal, August 1984

Recurrence-based analysis of barrier breakup in the standard nontwist map
journal, August 2018

Influence of the radial electric field on the shearless transport barriers in tokamaks
journal, February 2019