Anomalous transport due to magnetic turbulence

Transport in a toroidal system with broken flux surfaces is considered. Flux surfaces with rational field line winding number can degenerate and form magnetic islands. The experimental evidence for the existence of magnetic structures is reviewed. If neighbouring chains of islands overlap, a region of stochastic field is formed. In a stochastic field, a field line fills up a region of space and thus makes significant radial excursions. Particles following a stochastic field line may experience rapid radial transport. The problem of computing transport in a stochastic field has to stages: what is the behaviour of field lines in a stochastic region? and what is the implication for particle transport? The much used formula due to Rechester & Rosenbluth for collisionless transport in a fully ergodic field is treated. It is shown that the conditions for the validity of this formula are normally not met in a tokamak