Shearless Invariants in Non twist Symplectic Maps
Ibere Caldas  1@  , Celso Abud  2@  , Moises Santos  3@  , Michele Mugnaine  4@  , Jose Danilo Szezech  3@  , Antonio Batista  3@  , Murilo Batista  5@  , Ricardo Viana  4@  , Francisco Marcus  1@  , Marisa Roberto  6@  , Yves Elskens  7@  
1 : University of Sao Paulo  (USP)  -  Website
Instituto de Fisica, USP Rua do Matao Nr.1371 CEP 05508090 Cidade Universitaria, Sao Paulo Brasil -  Brazil
2 : Federal University of Goias  (UFG)  -  Website
Av. Dr. Lamartine Pinto de Avelar 1120, St. Universitário, 75704-020, Catalão - Goiás - Brasil -  Brazil
3 : Universidade Estadual de Ponta Grossa - State University of Ponta Grossa  (UEPG)  -  Website
R. Cel. Bitencourt, 689 - Centro, Ponta Grossa - PR, 84010-290 -  Brazil
4 : Federal University of Parana  (UFP)  -  Website
Departamento de Física Universidade Federal do Paraná Caixa Postal 19044 81531-980, Curitiba, Paraná Brazil -  Brazil
5 : Institute for Complex Systems and Mathematical Biology [Aberdeen]  (ICSMB)  -  Website
University of Aberdeen, Meston Building, Old Aberdeen, Aberdeen AB24 3UE -  United Kingdom
6 : Instituto Tecnologica da Aeronautica  (ITA)  -  Website
Instituto Tecnológico de Aeronáutica Praça Marechal Eduardo Gomes, 50 - Vila das Acacias, São José dos Campos - SP, 12228-900 -  Brazil
7 : Aix Marseille Université  (AMU)  -  Website
Aix-Marseille Université - AMU
Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France -  France

Nontwist Hamiltonian systems have shearless invariant curves that act like transport barriers in phase space [1, 2]. We use Slater's theorem to develop a qualitative and quantitative numerical approach to determine the breakup of these shearless invariant curves in the phase space of area-preserving maps [3]. We also determine the breakup critical parameters, of the shearless curves, with a procedure based on the determinism analysis performed on the recurrence plot of orbits near the critical transition [4]. As numerical examples we present the onset of such transport barriers in tokamaks and their dependence on the control parameters, namely, the fluctuating electric field and the equilibrium electric field shear [5]. 

 

References

1- P. J. Morrison, Physics of Plasmas 7, 2279 [2000].

2- D. Del-Castillo-Negrete, Physics of Plasmas 7, 1702 [2000].

3- C. V. Abud, I. L. Caldas. Physica D 308, 34 (2015).

4- M. S. Santos, M. Mugnaine, J. D. Szezech Jr, A. M. Batista, I. L. Caldas, M. S. Baptista, R. L. Viana. Chaos 28, 085717 (2019).

5- F. A.Marcus, M. Roberto, I. L. Caldas, K. C. Rosalem, Y. Elskens. Physics of Plasmas 26, 022302 (2019).


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