On guiding centre orbits of particles in toroidal systems

Abstract

Passing particles in toroidal geometry are described in a Hamiltonianformalism including time-dependent electric and magnetic fields. Theseparticles are characterized by a non-vanishing toroidal velocity. Theintroduction of the toroidal angle as independent variable instead of thetime allows one to derive a map of the poloidal plane onto itself, which issimilar to the Poincaré map of magnetic field lines. In time-dependentfields the energy of the particles is not conserved leading to two coupledmaps, which is characteristic for autonomous systems with three degrees offreedom. As a result, Arnold diffusion occurs and Kolmogorov-Arnold-Moser (KAM) surfaces, which inthe case of energy conservation separate stochastic regions in phase space,can be bypassed leading to enhanced radial transport of particles. Themechanism of enhanced transport is resonance streaming along resonancelines, which constructs the complex Arnold web. The structure of this webdepends on the drift rotational transform of drift orbits and the toroidaltransit time of passing particles. Numerical examples of Arnold diffusionof test particles will be given. The theory will be applied to passingparticles in a toroidal plasma and to trapped particles in stellarators andtokamaks. Some numerical examples of Arnold diffusion of circulatingparticles will be given.