On guiding centre orbits of particles in toroidal systems

Passing particles in toroidal geometry are described in a Hamiltonian forma lism including time-dependent electric and magnetic fields. These particles are characterized by a non-vanishing toroidal velocity. The introduction o f the toroidal angle as independent variable instead of the time allows one to derive a map of the poloidal plane onto itself, which is similar to the Poincare map of magnetic field lines. In time-dependent fields the energy of the particles is not conserved leading to two coupled maps, which is cha racteristic for autonomous systems with three degrees of freedom. As a resu lt, Arnold diffusion occurs and Kolmogorov-Arnold-Moser (KAM) surfaces, whi ch in the case of energy conservation separate stochastic regions in phase space, can be bypassed leading to enhanced radial transport of particles. T he mechanism of enhanced transport is resonance streaming along resonance l ines, which constructs the complex Arnold web. The structure of this web de pends on the drift rotational transform of drift orbits and the toroidal tr ansit time of passing particles. Numerical examples of Arnold diffusion of test particles will be given. The theory will be applied to passing particl es in a toroidal plasma and to trapped particles in stellarators and tokama ks. Some numerical examples of Arnold diffusion of circulating particles wi ll be given.