Theoretical investigation of field-line quality in a driven spheromak

Theoretical studies aimed at predicting and diagnosing field-line quality in a spheromak are described. These include nonlinear three-dimensional MHD simulations and analyses of confinement in spheromaks dominated by either open (stochastic) field lines or approximate flux surfaces. Three-dimensional nonlinear MHD simulations confirm that field lines are predominantly open when there is a large-amplitude toroidal-mode-number n = 1 mode. However, an appreciable volume of good flux surfaces can be obtained either during the drive-off phase of a scheme with periodic pulsed drive or for an extended period under driven conditions, with oscillating volume, when the odd-n modes are suppressed. If a configuration with radially localized perturbations can be achieved, a scaling analysis for a Rosenbluth-Bussac spheromak equilibrium indicates a favourable (1/Lundquist number) scaling to larger, higher-field devices. A hyper-resistivity analysis, which also assumes small-scale perturbations, reproduces well magnetic probe data in the sustained spheromak physics experiment, while an analysis of the same experiment based on one-dimensional transport along open field lines contradicts experimental observations in several key ways. The scaling analysis is also applied to reversed-field pinches and indicates that a completely determined scaling can be obtained with less approximation to the resistive MHD equations than indicated in the previous literature.