BEHAVIOR OF THE ADIABATIC INVARIANT NEAR THE SEPARATRIX IN A STELLARATOR

The motion of particles in a stellarator magnetic field is investigated. A new approach is demonstrated by discussing the non-linear oscillator problem for which it is possible to evaluate explicitly the change of the adiabatic invariant due to the crossing of the separatrix. It is found that in the case of the 'fast' crossing, which occurs when the particles cross the separatrix far from the X-point, this change is of the order Of epsilon In (epsilon), where epsilon is a perturbation parameter. Also found is the spectrum of invariants for the 'slow' crossing, which occurs when the particles cross the separatrix near the X-point. A regular procedure is proposed for deriving the invariant for locally trapped particles, with the finite rotational transform per period being taken into account. The trapping probability in stellarators is also calculated.