Chaotic escape of impurities and sticky orbits in toroidal plasmas.

We investigate chaotic impurity transport in toroidal fusion plasmas (tokamaks) from the point of view of passive advection of charged particles due to E×B drift motion. We use realistic tokamak profiles for electric and magnetic fields as well as toroidal rotation effects, and consider also the effects of electrostatic fluctuations due to drift instabilities on particle motion. A time-dependent one degree-of-freedom Hamiltonian system is obtained and numerically investigated through a symplectic map in a Poincaré surface of section. We show that the chaotic transport in the outer plasma region is influenced by fractal structures that are described in topological and metric point of views. Moreover, the existence of a hierarchical structure of islands-around-islands, where the particles experience the stickiness effect, is demonstrated using a recurrence-based approach.

Fractal structures in the parameter space of nontwist area-preserving maps.

Fractal structures are very common in the phase space of nonlinear dynamical systems, both dissipative and conservative, and can be related to the final state uncertainty with respect to small perturbations on initial conditions. Fractal structures may also appear in the parameter space, since parameter values are always known up to some uncertainty. This problem, however, has received less attention, and only for dissipative systems. In this work we investigate fractal structures in the parameter space of two conservative dynamical systems: the standard nontwist map and the quartic nontwist map. For both maps there is a shearless invariant curve in the phase space that acts as a transport barrier separating chaotic orbits. Depending on the values of the system parameters this barrier can break up. In the corresponding parameter space the set of parameter values leading to barrier breakup is separated from the set not leading to breakup by a curve whose properties are investigated in this work, using tools as the uncertainty exponent and basin entropies. We conclude that this frontier in parameter space is a complicated curve exhibiting both smooth and fractal properties, that are characterized using the uncertainty dimension and basin and basin boundary entropies.

Dynamical characterization of transport barriers in nontwist Hamiltonian systems.

The turnstile provides us a useful tool to describe the flux in twist Hamiltonian systems. Thus, its determination allows us to find the areas where the trajectories flux through barriers. We show that the mechanism of the turnstile can increase the flux in nontwist Hamiltonian systems. A model which captures the essence of these systems is the standard nontwist map, introduced by del Castillo-Negrete and Morrison. For selected parameters of this map, we show that chaotic trajectories entering in resonances zones can be explained by turnstiles formed by a set of homoclinic points. We argue that for nontwist systems, if the heteroclinic points are sufficiently close, they can connect twin-islands chains. This provides us a scenario where the trajectories can cross the resonance zones and increase the flux. For these cases the escape basin boundaries are nontrivial, which demands the use of an appropriate characterization. We applied the uncertainty exponent and the entropies of the escape basin boundary in order to quantify the degree of unpredictability of the asymptotic trajectories.