Mapping the Sawtooth: Brouwer's fixed point theorem in a tokamak fusion reactor
Thursday, June 27, 2019 - 11:30am - 12:30pm
The sawtooth oscillation is an instability inside of a tokamak fusion reactor where the core temperature slowly rises followed by a sudden drop. A tokamak confines plasma with a magnetic field created inside a toroidal domain. The magnetic field defines a mapping from a cross-section of this domain to itself through following magnetic field lines once around the torus. Such a mapping by Brouwer's theorem contains at least one fixed point. The sawtooth crash involves changes in the magnetic topology when additional fixed points appear and the original fixed point disappears. In this lecture I describe how the magnetic topology and properties of the field line map directly relate to processes occurring inside fusion reactors, and demonstrate how the sawtooth process takes place by numerically finding and tracing the location of fixed points during a numerical simulation of a tokamak discharge.