Comparison of analytic and full guiding center behavior at a trapped-passing interface in stellarators

The toroidal adiabatic invariant, can be used to describe both trapped and passing particle motion. Analytic expressions have also been developed to treat transitional particles, which are sometimes trapped, and sometimes passing. We have developed analytic descriptions using a non-canonical Hamiltonian formalism. Here we compare analytic approaches with solutions to the full guiding center equations of motion for a model stellarator magnetic and electric field. We also develop the analytic result directly from the equations of motion, since this clarifies some points, particularly for transitional particles.