HAMILTONIAN NONTWIST MAP FOR MAGNETIC-FIELD LINES WITH LOCALLY REVERSED SHEAR IN TOROIDAL GEOMETRY

A simple Hamiltonian map is constructed, fulfilling the minimum requir ements 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 no t apply. It is shown that in the revtokamap, for finite stochasticity parameter, a critical surface appears, separating an external, globall y stochastic region from a robust nonstochastic core region. This phen omenon of ''semiglobal chaos'' is analogous to the well-known appearan ce of an internal transport barrier in reversed shear tokamak experime nts. An analysis of the fixed points reveals a variety of bifurcation and reconnection phenomena, which appear to be generic for nontwist ma ps with an impenetrable polar axis.