FRACTAL AND WADA EXIT BASIN BOUNDARIES IN TOKAMAKS

JEFFERSON S. E. PORTELA, IBERÊ L. CALDAS, RICARDO L. VIANA, MIGUEL A. F. SANJUÁN
2007 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
The creation of an outer layer of chaotic magnetic field lines in a tokamak is useful to control plasma-wall interactions. Chaotic field lines (in the Lagrangian sense) in this region eventually hit the tokamak wall and are considered lost. Due to the underlying dynamical structure of this chaotic region, namely a chaotic saddle formed by intersections of invariant stable and unstable manifolds, the exit patterns are far from being uniform, rather presenting an involved fractal structure. If
more » ... ee or more exit basins are considered, the respective basins exhibit the even stronger Wada property, for which a boundary point is arbitrarily close to points belonging to all exit basins. We describe such a structure for a tokamak with an ergodic limiter by means of an analytical Poincaré field line mapping. scenario [Chirikov, 1979] . We stress that chaotic motion is to be intended here in its Lagrangian sense: two magnetic field lines, which may be very close to one another at some point, diverge exponentially as they wind around the toroidal direction, with a rate given by the corresponding (positive) maximal Lyapunov exponent [Ott, 1993] . Moreover, identifying the flux surfaces as KAM tori of the corresponding Hamiltonian system, the existence of a chaotic region implies the breaking of flux surfaces. Hence, the chaotic magnetic field lines are volume-filling over a presumably limited extent of the tokamak torus [Meiss, 1992] . One can design the perturbing fields so as to create a wide chaotic region (in terms of the
doi:10.1142/s021812740701986x fatcat:r7ragzegsfdqzhepxs2uxmxpfe