SelfConsistent Chaotic Transport in a HighDimensional MeanField Hamiltonian Map Model
Abstract
We studied the selfconsistent chaotic transport in a Hamiltonian meanfield model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Selfconsistency is incorporated through a meanfield that couples all the degreesoffreedom. The model is formulated as a large set of N coupled standardlike areapreserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherent structures. Furthermore, numerical simulations show that selfconsistency leads to the formation of a coherent macroparticle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a nonautonomous map that allows a detailed study of the onset of global transport. A turnstiletype transport mechanism that allows transport across instantaneous KAM invariant circles in nonautonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that,more »
 Authors:

 Applied Mathematics and Systems Research Inst., Mexico D.F. (Mexico)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24)
 OSTI Identifier:
 1341549
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Qualitative Theory of Dynamical Systems
 Additional Journal Information:
 Journal Volume: 14; Journal Issue: 2; Journal ID: ISSN 15755460
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Selfconsistent transport; Normal forms; Sequential periodic orbits; Singlewave model; PLASMAS
Citation Formats
MartínezdelRío, D., delCastilloNegrete, D., Olvera, A., and Calleja, R. SelfConsistent Chaotic Transport in a HighDimensional MeanField Hamiltonian Map Model. United States: N. p., 2015.
Web. doi:10.1007/s1234601501686.
MartínezdelRío, D., delCastilloNegrete, D., Olvera, A., & Calleja, R. SelfConsistent Chaotic Transport in a HighDimensional MeanField Hamiltonian Map Model. United States. doi:https://doi.org/10.1007/s1234601501686
MartínezdelRío, D., delCastilloNegrete, D., Olvera, A., and Calleja, R. Fri .
"SelfConsistent Chaotic Transport in a HighDimensional MeanField Hamiltonian Map Model". United States. doi:https://doi.org/10.1007/s1234601501686. https://www.osti.gov/servlets/purl/1341549.
@article{osti_1341549,
title = {SelfConsistent Chaotic Transport in a HighDimensional MeanField Hamiltonian Map Model},
author = {MartínezdelRío, D. and delCastilloNegrete, D. and Olvera, A. and Calleja, R.},
abstractNote = {We studied the selfconsistent chaotic transport in a Hamiltonian meanfield model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Selfconsistency is incorporated through a meanfield that couples all the degreesoffreedom. The model is formulated as a large set of N coupled standardlike areapreserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherent structures. Furthermore, numerical simulations show that selfconsistency leads to the formation of a coherent macroparticle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a nonautonomous map that allows a detailed study of the onset of global transport. A turnstiletype transport mechanism that allows transport across instantaneous KAM invariant circles in nonautonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, highdimensional sequential periodic orbits can be generated starting from lowdimensional periodic orbits. We show that sequential periodic orbits in the selfconsistent map can be continued from trivial (uncoupled) periodic orbits of standardlike maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.},
doi = {10.1007/s1234601501686},
journal = {Qualitative Theory of Dynamical Systems},
number = 2,
volume = 14,
place = {United States},
year = {2015},
month = {10}
}
Web of Science
Works referenced in this record:
Diffusive transport and selfconsistent dynamics in coupled maps
journal, February 2003
 Boffetta, Guido; delCastilloNegrete, Diego; López, Cristóbal
 Physical Review E, Vol. 67, Issue 2
Fast numerical computation of quasiperiodic equilibrium states in 1D statistical mechanics, including twist maps
journal, April 2009
 Calleja, Renato; de la Llave, Rafael
 Nonlinearity, Vol. 22, Issue 6
Dynamics and transport in meanfield coupled, many degreesoffreedom, areapreserving nontwist maps
journal, March 2012
 Carbajal, L.; delCastilloNegrete, D.; Martinell, J. J.
 Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 22, Issue 1
Weakly nonlinear dynamics of electrostatic perturbations in marginally stable plasmas
journal, November 1998
 delCastilloNegrete, D.
 Physics of Plasmas, Vol. 5, Issue 11
Selfconsistent chaotic transport in fluids and plasmas
journal, March 2000
 delCastilloNegrete, Diego
 Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 10, Issue 1
KAM Theory and a Partial Justification of Greene's Criterion for Nontwist Maps
journal, January 2000
 Delshams, Amadeu; de la Llave, Rafael
 SIAM Journal on Mathematical Analysis, Vol. 31, Issue 6
A method for determining a stochastic transition
journal, June 1979
 Greene, John M.
 Journal of Mathematical Physics, Vol. 20, Issue 6
Periodic orbits for reversible, symplectic mappings
journal, April 1989
 Kook, Hyungtae; Meiss, James D.
 Physica D: Nonlinear Phenomena, Vol. 35, Issue 12
Symplectic maps, variational principles, and transport
journal, July 1992
 Meiss, J. D.
 Reviews of Modern Physics, Vol. 64, Issue 3
Nonlinear Interaction of a Small Cold Beam and a Plasma
journal, January 1971
 O'Neil, T. M.
 Physics of Fluids, Vol. 14, Issue 6
Estimation of the Amplitude of Resonance in the General Standard Map
journal, January 2001
 Olvera, Arturo
 Experimental Mathematics, Vol. 10, Issue 3
Works referencing / citing this record:
Hyperchaos in constrained Hamiltonian system and its control
journal, July 2018
 Li, Junhong; Wu, Huibin; Mei, Fengxiang
 Nonlinear Dynamics, Vol. 94, Issue 3
Hyperchaos in constrained Hamiltonian system and its control
journal, July 2018
 Li, Junhong; Wu, Huibin; Mei, Fengxiang
 Nonlinear Dynamics, Vol. 94, Issue 3