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.

Full particle orbit effects in regular and stochastic magnetic fields

“…To be more specific, we shall consider the motion of a charged particle in a fixed external magnetic field, and deal with the case in which the assumption of the guiding center theory breaks down. Similar phenomena have been discussed by Landsman et al 5 , and more recently by Cambon et al 6 .…”

Interpreting electron-momentum distributions and nonadiabaticity in strong-field ionization

“…f (t) describes the envelope of the pulse with maximum f (0) = 1. This field, due to the absence of spatial dependence and magnetic fields which both considerably complicate the dynamics [23][24][25], allows for easy interpretation of classical trajectories [26,27].…”

Stochastic Ion Heating in a Field-reversed Configuration Geometry by Rotating Magnetic Fields

“…RM F at negative Ω pushes π φ to lower, eventually negative, values which results in axial losses across the separatix. 15 For even parity, loss rates were less for positive Ω. One feature in the RM F code is the ability to shut off E φ , E z , and/or E r arbitrarily, to explore which electric field components cause appreciable heating.…”

“…This approximation is both useful and representative because many figure-8 orbits, especially higher energy ones, are confined close to the z = 0 plane. 15 The energy gained from the RM F o field is then used to derive a condition for the transition from regular to ergodic orbits by applying the criterion for the exponential separation of trajectories, hence heating. 16 Section IV presents numerical results obtained with the RM F code.…”