Regular and Stochastic Orbits of Ions in a Highly Prolate Field-reversed Configuration

Abstract

Ion dynamics in a field-reversed configuration (FRC) 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, J ρ , which breaks down during the crossing of the phase-space separatrix. For integrable motion, which conserves J ρ , 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 break-down of the adiabatic invariance of J ρ is derived and studied under variation of J ρ and conserved angular momentum, π φ . Since repeated violation of J ρ 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.