Overlap of Bounce Resonances and the Motion of Ions in a Trapped-Ion Mode

Motion near a separatrix (the boundary between closed and open orbits) is studied both theoretically and numerically for parameters appropriate to the dissipative trapped-ion mode. I observe disappearance of an invariant in a stochastic layer surrounding the separatrix, as a result of overlapping bounce resonances. The fraction of ions lying within the stochastic layer is large even for a mode of relatively small amplitude.