Tokamap: A model of a partially stochastic toroidal magnetic field

Abstract

We have shown that a simple Hamiltonian map can be constructed, fulfilling the minimum requirements for a representation of a magnetic field in toroidal geometry. This tokamap describes a structure that is very robust in the central region, the stochasticity starting (for increasing K) in the edge region: the map could therefore prove useful as a model of a tokamak with an ergodic divertor. The central region has some quite interesting topological features, which can change dramatically (including a bifurcation) as the value of the safety factor on axis is varied. Typical configurations known from tokamak physics are qualitatively reproduced by the map.

Many more properties of the tokamap have been or will be studied in forth-coming works. These include questions such as the influence of the shape of the winding number, the dependence on of various physical properties, similarity and scaling properties. Last but not least, we intend to put charged particles in this magnetic field and study the transport properties in a partially chaotic tokamak configuration. This problem, which is very poorly understood, is of crucial importance for fusion physics.