Nonlinear dynamo mode dynamics in reversed field pinches

Abstract

The nonlinear dynamics of a typical dynamo mode in a reversed field pinch, under the action of the braking torque due to eddy currents excited in a resistive vacuum vessel and the locking torque due to a resonant error-field, is investigated. A simple set of phase evolution equations for the mode is derived: these equations represent an important extension of the well-known equations of Zohm et al. [Europhys. Lett. 11, 745 (1990)] which incorporate a self-consistent calculation of the radial extent of the region of the plasma which corotates with the mode; the width of this region being determined by plasma viscosity. Using these newly developed equations, a comprehensive theory of the influence of a resistive vacuum vessel on error-field locking and unlocking thresholds is developed. Under certain circumstances, a resistive vacuum vessel is found to strongly catalyze locked mode formation. Hopefully, the results obtained in this paper will allow experimentalists to achieve a full understanding of why the so-called “slinky mode” locks in some reversed field pinch devices, but not in others. The locking of the slinky mode is currently an issue of outstanding importance in reversed field pinch research.