Hamiltonian nontwist map for magnetic field lines with locally reversed shear in toroidal geometry

A simple Hamiltonian map is constructed, fulfilling the minimum requirements for the representation of a tokamak magnetic field in reversed shear configuration. This "revtokamap" is atypical nontwist map, for which many theorems of "traditional" dynamical systems theory do not apply. It is shown that in the revtokamap, for finite stochasticity parameter, a critical surface appears, separating an external, globally stochastic region from a robust nonstochastic core region. This phenomenon of ''semiglobal chaos'' is analogous to the well-known appearance of an internal transport barrier in reversed shear tokamak experiments. An analysis of the fixed points reveals a variety of bifurcation and reconnection phenomena, which appear to be generic for nontwist maps with an impenetrable polar axis.