Reversed magnetic shear configurations in tokamaks reduce substantially particle diffusivity and improve plasma confinement due to the formation of a transport barrier, as a result of magnetic field line reconnection and bifurcation. The latter are caused by the resonant perturbation of an ergodic limiter on a tokamak with reversed magnetic shear, which creates a region with chaotic field lines in the vicinity of the dimerized island chains. An analytically derived nontwist map for field lines is used to describe the formation of a transport barrier, manifested in the decrease of field line diffusion rate. This barrier appears due to the chaotic field line trapping near the reconnection layer that survives the bifurcation.
Fractal structures appear in many situations related to the dynamics of conservative as well as dissipative dynamical systems, being a manifestation of chaotic behaviour. In open area-preserving discrete dynamical systems we can find fractal structures in the form of fractal boundaries, associated to escape basins, and even possessing the more general property of Wada. Such systems appear in certain applications in plasma physics, like the magnetic field line behaviour in tokamaks with ergodic limiters. The main purpose of this paper is to show how such fractal structures have observable consequences in terms of the transport properties in the plasma edge of tokamaks, some of which have been experimentally verified. We emphasize the role of the fractal structures in the understanding of mesoscale phenomena in plasmas, such as electromagnetic turbulence.
Escape patterns of chaotic magnetic field lines in a tokamak with reversed magnetic shear and an ergodic limiter PHYSICS OF PLASMAS, v.15, n.9, 2008 http://producao.usp.br/handle/BDPI/15972 The existence of a reversed magnetic shear in tokamaks improves the plasma confinement through the formation of internal transport barriers that reduce radial particle and heat transport. However, the transport poloidal profile is much influenced by the presence of chaotic magnetic field lines at the plasma edge caused by external perturbations. Contrary to many expectations, it has been observed that such a chaotic region does not uniformize heat and particle deposition on the inner tokamak wall. The deposition is characterized instead by structured patterns called magnetic footprints, here investigated for a nonmonotonic analytical plasma equilibrium perturbed by an ergodic limiter. The magnetic footprints appear due to the underlying mathematical skeleton of chaotic magnetic field lines determined by the manifold tangles. For the investigated edge safety factor ranges, these effects on the wall are associated with the field line stickiness and escape channels due to internal island chains near the flux surfaces. Comparisons between magnetic footprints and escape basins from different equilibrium and ergodic limiter characteristic parameters show that highly concentrated magnetic footprints can be avoided by properly choosing these parameters.
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