Effect of a resistive vacuum vessel on dynamo mode rotation in reversed field pinches

Abstract

Locked ͑i.e., nonrotating͒ dynamo modes give rise to a serious edge loading problem during the operation of high current reversed field pinches. Rotating dynamo modes generally have a far more benign effect. A simple analytic model is developed in order to investigate the slowing down effect of electromagnetic torques due to eddy currents excited in the vacuum vessel on the rotation of dynamo modes in both the Madison Symmetric Torus ͑MST͒ ͓Fusion Technol. 19, 131 ͑1991͔͒ and the Reversed Field Experiment ͑RFX͒ ͓Fusion Eng. Des. 25, 335 ͑1995͔͒. This model strongly suggests that vacuum vessel eddy currents are the primary cause of the observed lack of mode rotation in RFX. The eddy currents in MST are found to be too weak to cause a similar problem. The crucial difference between RFX and MST is the presence of a thin, highly resistive vacuum vessel in the former device. The MST vacuum vessel is thick and highly conducting. Various locked mode alleviation methods are discussed.

Beyond the Intelligent-shell Concept: the Clean-mode-control for Tearing Perturbations

“…As shown in Fig. 1, the IS control reduces the DFT harmonics of the measurements at a noise level (about 0.1 mT): the larger value observed for the Fourier mode amplitudes is a consequence of the sideband effect represented in formula (2). CMC indeed improves the control on the Fourier mode amplitudes.…”

“…They incorporate the contributions of the non-linear interaction between different TMs, the interactions with the image currents induced onto the shell and with the feedback coils currents. It is a standard result that the electromagnetic torque can be expressed by non-linear combination of the Newcomb's equation solutions for the TMs radial magnetic field perturbations (modes eigenfunctions) [2,14]. The explicit expressions, valid when the plasma is surrounded by a resistive shell, are given in [11] (the zero-pressure condition is assumed for sake of simplicity).…”

“…In fact if the latter were much larger than the former, the cleaning of the measurements with the sideband subtraction would be unfeasible, due to the unavoidable errors and approximations introduced by this procedure. Therefore in a post-processing of the simulation with τ w = 0.1 s and r f = r wi , the sidebands of the m = 1, n = −7 ∼ −19 and m = 0, n = 1 ∼ 12 TMs have been estimated from the coils currents using formulas (4,5), and then added to the respective TMs harmonics according to (2) to obtain an estimate of the measured DFT harmonics. The 'raw' signals b r i, j are then given by the inverse of (1).…”

“…Both in tokamaks and in reversed field pinches (RFP) this determines severe plasma-wall interactions and can lead to premature termination of the discharges. For example, in the RFX-mod reversed field pinch experiment [3] it is not possible to raise the plasma current above 500 kA and to have discharges lasting more than 150 ms, with the only stabilization provided by a shell whose characteristic penetration time, the shell time constant, is 0.1 s. However, we have to underline that the stabilizing effect of this shell on the TMs is reduced by the presence of a far more resistive inner vacuum vessel (3 ms time constant), which decreases to very low amplitude the TMs wall-locking thresholds [2]. RFX-mod has demonstrated the possibility to overcome these limitations with the active control of the edge radial field, made possible by a grid of active coils, placed outside the shell, fully covering the torus.…”

“…However the finite penetration time of the radial magnetic field of any realistic shell determines potentially dangerous MHD phenomena, among which the wall locking of tearing modes (TM) [1,2]. When the amplitude at the resonant surface is above the wall-locking threshold the mode is practically arrested in the laboratory frame and the stabilizing effect of the shell is lost: the TM radial field penetrates the shell and its amplitude considerably increases.…”