Probability of Trapping-State Transitions in a Toroidal Device

The probabilities of trapping‐state transitions of single‐particle drift orbits are obtained from a theorem due to Kruskal that is an extension of the usual adiabatic theory. Because such transitions determine the total orbit, they are important to diffusion studies. To apply Kruskal's theorem, we use drift invariants obtained for a large‐aspect‐ratio stellarator (with $\text{l\hspace{0.17em}=\hspace{0.17em}1}$ and $\text{l\hspace{0.17em}=\hspace{0.17em}3}$ helical windings) by means of the stellarator expansion are used. In this model, toroidal and helical field modulations are comparable and the total rotational transform is finite. These three effects interact with the particle drift and, with transitions, determine the orbits in the large. When a small horizontal magnetic field is added, the bilateral symmetry of the flux surfaces—and hence the blocked and passing particles—are modified. Localized particles are affected through stochastic transitions, and particle orbits are globally ergodic.