Model for relaxation in reversed-field pinch plasmas

Abstract

In this article, a model for anomalous ion heating, a dynamo current-sustained edge toroidal field, and a sawtooth oscillation during the relaxation in the reversed-field pinch (RFP) plasma is presented. The dynamo (α), the turbulent resistivity (β) and viscosity (χ), dependent on the magnetohydrodynamics (MHD) fluctuations, are incorporated into the model. Turbulent viscous dissipation of the fluctuation energy is proposed as the mechanism of the anomalous ion heating. This is a straightforward corollary of the turbulent viscosity heating of ions in that the temperature of the heavier ions is higher than that of the lighter ions and that the ion temperature increases with the MHD fluctuation level. Correspondingly, the turbulent resistivity heats electrons anomalously. It is shown that the dynamo current, generated by the back-transfer of fluctuating magnetic field helicity to mean magnetic field, sustains the RFP magnetic configuration. In the edge the total current density is approximately equal to the dynamo current density, while at the core the dynamo current opposes the applied electric-field-driven current, flattening the current profile. Provided the α dynamo has a periodic behavior in time, the physical quantities of the RFP plasma have a sawtooth time dependence. The local poloidal current density in the edge increases during the sawtooth crash and peaks at the end of the crash, as do the ion and electron temperatures. In contrast, the toroidal current density at the core decreases during the crash and arrives at its minimum at the end of the crash. Qualitatively, the conclusions drawn from the present model are in good agreement with many of the experimental results [Scime et al., Phys. Rev. Lett. 68, 2165 (1992); Ji et al., ibid. 73, 668 (1994)] and the numerical simulations.