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Doctoral Thesis
DOI
https://doi.org/10.11606/T.43.2013.tde-06102014-154803
Document
Author
Full name
Celso Vieira Abud
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Caldas, Ibere Luiz (President)
Carvalho, Ricardo Egydio de
Leonel, Edson Denis
Rizzato, Felipe Barbedo
Viana, Ricardo Luiz
Title in Portuguese
Transporte em sistemas hamiltonianos não-twist
Keywords in Portuguese
Caos
Fenômenos de transporte
Sistemas hamiltonianos
Tokamaks
Abstract in Portuguese
O tema desta tese é a propriedade não-twist em sistemas Hamiltonianos. Sistemas com essa propriedade violam a condição twist ao longo de uma curva sem shear e, consequentemente, sua topologia não é descrita pelos cenários típicos previstos pelos teoremas KAM (Kolmogorov - Arnold - Moser) e Poincar´e - Birkhoff. A curva sem shear é identificada pelo valor de máximo ou mínimo no perfil espacial do número de rotação do sistema. Além disso, próximo `a curva sem shear podemos observar algumas bifurcações atípicas como: colisões de ´orbitas periódicas e reconexão de separatrizes. As características dos sistemas não-twist são bem particulares, mas n´os demonstramos que seus cenários podem ser encontrados, localmente, em sistemas Hamiltonianos genéricos, devido ao nascimento de uma curva sem shear no interior de ilhas regulares. Inicialmente, nossas investigações numéricas constataram que esse fenômeno pode surgir não somente para a concomitante bifurcação de período 3 do ponto elíptico, mas também para outras bifurcações, tais como período 4 e período 5. Posteriormente, consideramos um modelo que descreve o comportamento das linhas de campos magnéticos em tokamaks com limitadores ergódigos. Nesse caso, o modelo utilizado é um mapa simplético parametrizado a partir das características físicas de um tokamak de grande razão de aspecto. Para esse sistema, estudamos os efeitos no transporte causados pelas bifurcações oriundas da presença da curva sem shear secundária e, também, pelas modificações do perfil rotacional das linhas de campo.
Title in English
Trnasport in nontwiast hamiltonian systems
Keywords in English
Chaos
Hamiltoniam systems
Tokamaks
Transport phenomena
Abstract in English
The topic of this Thesis is the nontwist property in Hamiltonian systems. Systems with such property violate the twist condition along the shearless curve and, therefore, its topology is not described for typical scenarios provided by KAM (Kolmogorov - Arnold - Moser ) and Poincar´e Birkhoff theorems. The shearless curve is identified by the maximum or minimum values of the spatial rotation number profile of the system. Moreover, close to the shearless curve we observe some atypical bifurcations as periodic orbits collisions and separatrix reconnection. The features of nontwist systems are very particular, but we have shown that its scenarios can be found locally in generic Hamiltonian systems, due to the onset of a secondary shearless curve within regular islands. Initially, our numerical investigations have found that this phenomenon may arise not only for the concomitant period 3 bifurcation of the elliptic point, but also for others bifurcations such as period 4 and period 5. Subsequently, we considered a model that describes magnetic field lines in tokamaks with ergodic limiters. In this case, the model is a symplectic map parameterized from the physical characteristics of a large aspect ratio tokamaks. For this system, we studied the effects on the transport caused by the presence of secondary shearless torus and also by changing the field lines rotational profile.
 
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Tese_Celso_Abud.pdf (8.30 Mbytes)
Publishing Date
2014-10-07
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • Caldas, I L, et al. Shearless transport barriers in magnetically confined plasmas [doi:10.1088/0741-3335/54/12/124035]. Plasma Physics and Controlled Fusion [online], 2012, vol. 54, p. 124035.
  • VIEIRA ABUD, C., and CALDAS, I. L. Secondary nontwist phenomena in area-preserving maps [doi:10.1063/1.4750040]. Chaos (Woodbury, N.Y.) [online], 2012, vol. 22, p. 033142.
  • ABUD, C V, and Caldas, I L. Biffurcation effects on the plasma edge of tokamaks with ergodic limiter. In 40th EPS Conference on Plasma Physics, Espoo (Finlândia), 2013. Proceedings of 40th EPS Conference on Plasma Physics.Madri : European Physical Society, 2013. Available from: http://eps2013.aalto.fi.
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