  Electron orbits are calculated in solitary two-dimensional axisymmetric
electrostatic potential structures, typical of plasma electron holes, in order
to establish the conditions for the particles to remain trapped. Analytic
calculations of the evolution of the parallel energy caused by the perturbing
radial electric field are shown to agree well with full numerical orbit
integration Poincar\'e plots. The predominant mechanism of detrapping is
resonance between the gyro frequency in the parallel magnetic field and
harmonics of the parallel bounce frequency. A region of phase-space adjacent to
the trapped-passing boundary in parallel energy is generally stochastic because
of island overlap of different harmonics, but except for very strong radial
electric field perturbation, more deeply trapped orbits have well-defined
islands and are permanently confined. A simple universal quantitative algorithm
is given, and its results plotted as a function of magnetic field strength and
hole radial scale-length, determining the phase space volume available to
sustain the electron hole by depression of the permanently trapped distribution
function.
