Explicit calculations of homoclinic tangles in tokamaks

Explicit numerical calculations of homoclinic tangles are presented for a physically realistic model of a resonantly perturbed magnetic field in a tokamak. The structure of these tangles is consistent with that expected from the general theory of near-integrable Hamiltonian systems commonly studied with simple algebraic twist map models. In addition, understanding the structure of homoclinic tangles corresponding to the primary separatrix of a poloidally diverted tokamak allows one to make predictions of the locations and structure of magnetic footprints and heat buildup on the tokamak wall. These separatrix tangles undergo an interesting bifurcation sequence as the current through a set of error field correction coils is increased. Since this model of the magnetic field is very realistic, these features are expected to be experimentally verifiable.