Trnasport in nontwiast hamiltonian systems

Author(s)

Celso Vieira Abud

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2013-11-19

Examining board members

Ibere Luiz Caldas; Ricardo Egydio de Carvalho; Edson Denis Leonel; Felipe Barbedo Rizzato; Ricardo Luiz Viana

• Advisor: Ibere Luiz Caldas

Abstract

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. (AU)

• FAPESP's process: 10/00740-6 - Transport in Nontwist Hamiltonian systems
• Grantee: Celso Vieira Abud
• Support Opportunities: Scholarships in Brazil - Doctorate