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Doctoral Thesis
DOI
10.11606/T.43.2008.tde-19052008-124857
Document
Author
Full name
Jefferson Stafusa Elias Portela
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2008
Supervisor
Committee
Caldas, Ibere Luiz (President)
Pakter, Renato
Rizzato, Felipe Barbedo
Roberto, Marisa
Vannucci, Alvaro
Title in Portuguese
Descrição dos campos magnéticos em tokamaks por mapas hamiltonianos
Keywords in Portuguese
Caos
Física de plasma
Transporte
Abstract in Portuguese
Estudamos a estrutura das linhas de campo magnético de tokamaks, descrita pela dinâmica de mapas hamiltonianos. Utilizando mapas bidimensionais simples, investigamos a interação das linhas de campo com obstáculos no interior da câmara do tokamak, suas propriedades gerais de transporte e a influência de perfis da transformada rotacional não monotónicos. Obstáculos posicionados no interior do vaso correspondem a saídas no espaço de fases do mapa e, sendo a parede da câmara também uma saída, obtemos que as fronteiras das bacias de saída são assintoticamente fractais, apresentando também a propriedade de Wada. Assim, as linhas de campo magnético que atingem um dado obstáculo não se distribuem necessariamente próximas deste, o que pode ter implicações, e. g., para sistemas de medida. Mapas dotados de perfis não monofônicos da transformada rotacional, ditos não twist, modelam tokamaks no regime de reversed shear e apresentam uma barreira invariante resistente, que reflete o melhor confinamento observado em tokamaks neste regime. Verificamos que, mesmo após a quebra da barreira invariante, permanece uma barreira efetiva, através da qual o transporte é difusivo e cerca de duas ordens de grandeza mais lento que o transporte poloidal na região.
Title in English
Chaotic transport in plasmas
Keywords in English
Caos
Física de plasma
Transporte
Abstract in English
We consider the magnetic field line structure of tokamaks, described by the dynamics of Hamiltonian maps. Using simple bidimensional maps, we study the field line interaction with obstacles inside the tokamak chamber, their general transport properties, and the influence of non-monotonic rotational transform profiles. The obstacles positioned inside the vessel correspond to exits in the map phase space and, being the tokamak wall itself an exit, we find that the boundaries of the exit basins are asymptotically fractal, presenting also the Wada property. Thus, the magnetic field lines that reach a given obstacle are not necessarily wandering closeby this exit, what may have implications, e. g., for measuring systems. Maps endowed with a non-monotonic rotational transform, called nontwist maps, model tokamaks in the reversed shear regime. The maps present a strong invariant barrier in phase space which mirrors the enhanced confinement observed for tokamaks in such regime. We find that even after the breaking of the invariant barrier an effective barrier remains, through which the transport is diffusive and about two orders of magnitude slower than the poloidal transport in the same region.
 
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teseJSEP_Final.pdf (24.45 Mbytes)
Publishing Date
2008-06-11
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • PORTELA, J S e, et al. Diffusive Transport Through a Nontwist barrier in tokamaks [doi:10.1142/S0218127407017926]. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering [online], 2007, vol. 17, p. 1589-1598.
  • PORTELA, J S e, et al. Fractal and Wada Exit Basin Boundaries in Tokamaks [doi:10.1142/S021812740701986X]. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering [online], 2007, vol. 17, p. 4067-4079.
  • SILVA, E.c., et al. Escape Pattern and Transport Barrier due to Ergodic Magnetic Limiters in tokamaks with Reversed Magnetic Shear [doi:10.1088/0029-5515/46/4/S11]. Nuclear Fusion [online], 2006, vol. 46, p. S192-S198.
All rights of the thesis/dissertation are from the authors
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