SelfConsistent Chaotic Transport in a HighDimensional MeanField Hamiltonian Map Model
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:

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 Applied Mathematics and Systems Research Inst., Mexico D.F. (Mexico)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 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
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24)
 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
 OSTI Identifier:
 1341549
MartínezdelRío, D., delCastilloNegrete, D., Olvera, A., and Calleja, R.. SelfConsistent Chaotic Transport in a HighDimensional MeanField Hamiltonian Map Model. United States: N. p.,
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:10.1007/s1234601501686.
MartínezdelRío, D., delCastilloNegrete, D., Olvera, A., and Calleja, R.. 2015.
"SelfConsistent Chaotic Transport in a HighDimensional MeanField Hamiltonian Map Model". United States.
doi: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}
}