Tokamap: A Hamiltonian twist map for magnetic field lines in a toroidal geometry

A Hamiltonian twist map (tokamap) is constructed as a representation of the stroboscopic plot of magnetic field lines in a toroidal confinement device as used in fusion physics. This “tokamap” is compatible with minimal toroidal geometry requirements (in particular, the polar axis cannot be crossed upon iteration). It depends on two parameters: the stochasticity parameter $K$ and the winding number on axis, $w.\mathrm{}$ With increasing 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 they determine the appearance of the phase portraits near the axis. It is shown that the topology undergoes several bifurcations as $K$ and/or $w$ are varied. The various phase portraits reproduce the qualitative features known in tokamak physics. The time series exhibit a typical behavior describable by a continuous time random walk, as found in previous works on the standard map.