Ion dynamics in a field-reversed configuration are explored for a highly elongated device, with emphasis placed on ions having positive canonical angular momentum. Due to angular invariance, the equations of motion are that of a two degree-of-freedom system with spatial variables ρ and ζ. As a result of separation of time scales of motion caused by large elongation, there is a conserved adiabatic invariant, Jρ, which breaks down during the crossing of the phase-space separatrix. For integrable motion, which conserves Jρ, an approximate one-dimensional effective potential was obtained by averaging over the fast radial motion. This averaged potential has the shape of either a double or single symmetric well centered about ζ=0. The condition for the approach to the separatrix and therefore the breakdown of the adiabatic invariance of Jρ is derived and studied under variation of Jρ and conserved angular momentum, πφ. Since repeated violation of Jρ results in chaotic motion, this condition can be used to predict whether an ion (or distribution of ions) with given initial conditions will undergo chaotic motion.

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