Mapping the sawtooth

The sawtooth oscillation involves a topological change of the magnetic field lines in the core of a tokamak discharge. We simulate a steady state sawtoothing discharge using the M3DC ¹-code. During the sawtooth the topological structure of the magnetic field is analyzed by tracking the fixed points of the field line map: the mapping induced by the field lines going once around the tokamak. We numerically locate the fixed points of the field line map (of which the magnetic axis is one) and use them construct a Poincaré section that resolves the core region and the (1, 1) island. By following the evolution of the magnetic field through the motion and bifurcation of the fixed points of the field line map we get an intuitive picture of the processes that take place during a Kadomtsev style sawtooth crash. (paper)