TOKAMAP - A HAMILTONIAN TWIST MAP FOR MAGNETIC-FIELD LINES IN A TOROIDAL GEOMETRY

A Hamiltonian twist map (tokamap) is constructed as a representation o f the stroboscopic plot of magnetic field lines in a toroidal confinem ent device as used in fusion physics. This ''tokamap'' is compatible w ith minimal toroidal geometry requirements (in particular, the polar a xis cannot be crossed upon iteration). It depends on two parameters: t he stochasticity parameter K and the winding number on axis, w. With i ncreasing values of K, chaotic regions appear mostly near the edge of the torus, while the zone near the magnetic axis remains very robust. The number and nature of the fixed points are studied in detail, as th ey determine the appearance of the phase portraits near the axis. It i s shown that the topology undergoes several bifurcations as K and/or w are varied. The various phase portraits reproduce the qualitative fea tures known in tokamak physics. The time series exhibit a typical beha vior describable by a continuous time random walk, as found in previou s works on the standard map.