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 a typical 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.