Magnetic field lines in plasmas can be regarded as trajectories of Hamiltonian systems. For the field line tracing two methods can be applied: i) integration of the trajectory and ii) mapping of the trajectory. The latter is a modern technique for the Hamiltonian system. It is more than an order of magnitude, faster than the integration. A properly chosen mapping procedure always conserves the main flux preserving property of the magnetic field, which is important for a correct reprOduction of the long term behavior of field lines in stochastic regions. Simplistic maps form any Hamiltonian problems have been extensively used during the last four decades. This paper is devoted to the study of some mapping models for the study of magnetic configurations in tokamaks which exhibit non-axisymmetric MHD or RMP perturbations. The destruction of a transport barrier is described using the transmissivity between the chaotic zones situated of its both sides. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.