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 existenc
e of magnetic structures is reviewed. If neighbouring chains of island
s overlap, a region of stochastic field is formed. In a stochastic fie
ld, a field line fills up a region of space and thus makes significant
radial excursions. Particles following a stochastic field line may ex
perience rapid radial transport. The problem of computing transport in
a stochastic field has to stages: what is the behaviour of field line
s in a stochastic region? and what is the implication for particle tra
nsport? The much used formula due to Rechester & Rosenbluth for collis
ionless transport in a fully ergodic field is treated. It is shown tha
t the conditions for the validity of this formula are normally not met
in a tokamak.