Escape dynamics in a Hamiltonian map for double-null diverted tokamaks

We introduce a simple symmetric Hamiltonian map that models the magnetic field lines of a double-null diverted tokamak and compare its behavior with the corresponding symmetric single-null map. The phase-space structure of both models is characterized using the finite-time Lyapunov exponent and the escape time of magnetic field line trajectories. For increasing perturbation strength, the area of the chaotic layer grows in both systems, but their escape fractions exhibit distinct oscillatory behaviors. To understand the origin of these oscillations, we analyze the mean transient measure and trace the invariant manifolds of hyperbolic fixed points. The results reveal that variations in the escape fraction arise from changes in the formation of escape channels and from the presence of stickiness near secondary island chains.