Regular and stochastic orbits of ions in a highly prolate field-reversed configuration

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.