The structure of chaotic magnetic field lines in a tokamak with external nonsymmetric magnetic perturbations

We consider the effects of external nonsymmetric magnetostatic perturbation s caused by resonant helical windings and a chaotic magnetic limiter on the plasma confined in a tokamak. The main purpose of both types of perturbati on is to create a region in which field lines are chaotic in the Lagrangian sense: two initially nearby field lines diverge exponentially through many turns around the tokamak. The equilibrium field is obtained from the equat ions of magneto-hydrodynamic equilibrium written down in a polar toroidal c oordinate system. The magnetic fields generated by the resonant helical win dings and the chaotic magnetic limiter are obtained through an. analytical solution of Laplace equation. The magnetic field line equations are integra ted to give a Hamiltonian mapping of field lines that we use to characteriz e the structure of chaotic field lines. In the case of resonant windings, w e obtained the map by both numerical integration and a Hamiltonian formulat ion. For a chaotic limiter, we analytically derived a symplectic map by usi ng a Hamiltonian formulation.