Orbits in asymmetric toroidal magnetic fields

Orbits in an asymmetric toroidal magnetic field are studied for the case in which the local variation of the field strength due to ripple is rapid compared with that due to toroidicity. In this case, to lowest order the poloidal variables are constant and particles move primarily in the toroidal direction. Invariants and averaged equations of motion for the locally passing and locally trapped particles are derived based on this approximation. The equations imply that transitions between the locally trapped and locally passing states occur. The probabilities for these transitions are calculated.