Magnetic structures in the explicitly time-dependent nontwist map

We investigate how the magnetic structures of the plasma change in a large aspect ratio tokamak perturbed by an ergodic magnetic limiter, when a system parameter is non-adiabatically varied in time. We model such a scenario by considering the Ullmann-Caldas nontwist map, where we introduce an explicit time-dependence to the ratio of the limiter and plasma currents. We apply the tools developed recently in the field of chaotic Hamiltonian systems subjected to parameter drift. Namely, we follow trajectory ensembles initially forming Kolmogorov Arnold Moser (KAM) tori and island chains in the autonomous configuration space. With a varying parameter, these ensembles, called snapshot tori, develop time-dependent shapes. An analysis of the time evolution of the average distance of point pairs in such an ensemble reveals that snapshot tori go through a transition to chaos, with a positive Lyapunov exponent. We find empirical power-law relationships between both the Lyapunov exponent and the beginning of the transition to chaos (the so-called critical instant), as a function of the rate of the parameter drift, with the former showing an increasing trend and the latter a decreasing trend. We conclude that, in general, coherent tori and magnetic islands tend to break up and become chaotic as the perturbation increases, similar to the case of subsequent constant perturbations. However, because of the continuous drift, some structures can persist longer and exist even at perturbation values where they would not be observable in the constant perturbation case.