Numerical studies of confinement scalings for the dynamo-free reversed-field pinch

Abstract

In the reversed-field pinch (RFP), tearing modes associated with the dynamo are responsible for reduced energyand particle confinement. In this study, it is observed that by implementing current profile control (CPC) in the RFP, a dynamo-free state can be achieved. The effect of CPC in the RFP is examined by the use of numerical simulations, and scaling laws are presented for confinement parameters. The model is nonlinear MHD in 3D including finite resistivity and pressure. A linear regression analysis is performed on simulation data from a series of computer runs for a set of initial parameter values. Scaling laws are determined for radial magnetic field, energy confinement time, poloidal beta and temperature. Confinement is improved substantially as compared with the conventional RFP-the temperature reaches reactor relevant levels by ohmic heating alone. It is observed that the configuration spontaneously develops into a quasi single helicity state. The CPC scheme is designed to eliminate the fluctuating electric dynamo field E f = − v × B , using feedback of an externally imposed electric field. The focus of this study is on obtaining principal theoretical optimization of confinement in the RFP by implementing CPC and to formulate scaling laws for confinement parameters, thus investigating the reactor viability of the concept.

Static current profile control and RFP confinement

“…Interestingly, confinement improvement of high-beta RFP plasmas, somewhat beyond the results presented in this paper, was attained using a different numerical CPC model, based on feedback replacement of the naturally generated E f by an internal electric field [6,7]. By simulation of a large number of scenarios, scaling laws for magnetic field fluctuations, on-axis temperature, poloidal beta and energy confinement time were obtained.…”

“…The use of poloidal current drive or feedback systems (using PPCD or radio frequency waves) to improve energy confinement in the RFP has been discussed extensively in the literature, both numerically and experimentally [3,4,[6][7][8][9][10][11].…”

Filamentary current structures in the Madison Symmetric Torus

“…This may be due to the fact that finite pressure effects are not included in a selfconsistent way in these codes. Interestingly recent nonlinear simulations of pulsed parallel current drive (PPCD) plasmas made with DEBSP, a version of DEBS including pressure, show that the m = 0 modes are not efficiently stabilized by PPCD and continue to have a finite amplitude, probably due to the strong edge pressure gradient associated with EC conditions [25,26]. These results suggest that pressure driven modes may play a significant role in EC plasmas.…”

Ultra-high beta in numerical simulations of a tearing-mode reduced reversed-field pinch

“…Other authors have examined the introduction of static auxiliary fields [16]. In this and previous studies by the authors the auxiliary field is derived by a feedback function [3][4][5][6], which uses the dynamo field E f as an input signal. The feedback signal is then calculated for the objective of eliminating the dynamo field, which thus results in an auxiliary field that will consequently be tailored radially and temporally exactly right to perform the task.…”

“…In earlier work by the authors [3][4][5][6], a numerical model was examined in which an externally applied auxiliary electric field E a was applied to control the current profile. The field was automatically adjusted for continual elimination of the dynamo field E f = − v × B (brackets indicate mean over periodic coordinates) through a feedback routine.…”