3 research outputs found
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Onset and Saturation of Ion Heating by Odd-parity Rotating-magnetic-fields in a Field-reversed Configuration
Heating of figure-8 ions by odd-parity rotating magnetic fields (RMFο) applied to an elongated field-reversed configuration (FRC) is investigated. The largest energy gain occurs at resonances (s ≡ ω(sub)R⁄ω) of the RMFο frequency, ω(sub)R, with the figure-8 orbital frequency, ω, and is proportional to s^2 for s – even resonances and to s for s – odd resonances. The threshold for the transition from regular to stochastic orbits explains both the onset and saturation of heating. The FRC magnetic geometry lowers the threshold for heating below that in the tokamak by an order of magnitude
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Regular and Stochastic Orbits of Ions in a Highly Prolate Field-reversed Configuration
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 rho and xi. As a result of separation of time scales of motion, caused by large elongation, there is a conserved adiabatic invariant, J(sub)rho, which breaks down during the crossing of the phase-space separatrix. For integrable motion, which conserves J(sub)rho, 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 xi = 0. The condition for the approach to the separatrix and therefore the breakdown of the adiabatic invariance of J(sub)rho is derived and studied under variation of J(sub)rho and conserved angular momentum, pi(sub)phi. Since repeated violation of J(sub)rho 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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Stochastic Ion Heating in a Field-reversed Configuration Geometry by Rotating Magnetic Fields
Ion heating by application of rotating magnetic fields (RMF) to a prolate field-reversed configuration(FRC) is explored by analytical and numerical techniques. For odd-parity RMF (RMFo), perturbation analysis shows ions in figure-8 orbits gain energy at resonances of the RMFo frequency, ωR, with the figure-8 orbital frequency, ω. Since figure-8 orbits tend to gain the most energy from the RMF and are unlikely to escape in the cusp region (where most losses occur), they are optimal candidates for rapid stochastic heating, as compared to cyclotron and betatron orbits. Comparisons are made between heating caused by even- and odd-parity RMFs and between heating in currently operating and in reactor-scale FRC devices