Macroscopic transport in mixed phase space Hamiltonian systems and the role of a distinct time-scale for the power-law decay

Motivated by the losses of runaway electrons during disruptive events in present and future tokamaks like the ITER, we investigate the transport in mixed phase space Hamiltonian systems. We are interested in the regime where the sticky regions, remaining after the disintegration of invariant transport barriers, form layers in the phase space separated by partial barriers to transport. The example we use is the standard map. We show that the survival probability from the internal region can be thought of as the resultant of a radial passage from layer to layer. We show that both exponential and power-law decays are present at the same time, but with independent effective time-scales.