Control and diagnostic uses of feedback

Abstract

Recent results on multimode feedback control of magnetohydrodynamic (MHD) modes and a variety of diagnostic uses of feedback are summarized. First, is the report on reduction and scaling of transport under feedback. By controlling the fluctuation amplitudes and consequently the transport via feedback, it is found that the scaling of the diffusion coefficient is linear with root-mean-square rms fluctuation level. The scaling appears not to agree with any generic theory. A variety of other diagnostic uses of feedback have been developed. The primary goal is an experimental methodology for the determination of dynamic models of plasma turbulence, both for better transport understanding and more credible feedback controller designs. A specific motivation is to search for a low-order dynamic model, suitable for the convenient study of both transport and feedback. First, the time series analysis method is used for the determination of chaotic attractor dimension of plasma fluctuations. For E×B rotational flute modes it is found to be close to three, indicating that a low-order dynamic model may be adequate for transport prediction and feedback controller design. Second, a new method for direct experimental determination of nonlinear dynamical models of plasma turbulence using feedback has been developed. Specifically, the process begins with a standard three-wave coupling model and introduces a variable feedback gain. The power spectrum, delayed power spectrum, and bispectrum of fluctuations are then experimentally obtained. By varying the feedback gain continuously, an arbitrary number of numerical equations for a fixed number of unknowns can be generated. Their numerical solution yields the linear dispersion, as well as nonlinear coupling coefficients. This method has been successfully applied for E×B rotationally driven flute modes.

Fluctuation induced transport of driven drift waves: I. Monochromatic waves

“…A suppression of broadband fluctuations has therefore not been achieved. Till today this technique has been refined and tested in fusion experiments [6,7], but the observed reduction of fluctuations is localized and the efficiency is not satisfying. More promising results are obtained with biasing experiments, which aim to generate sheared flows by radial currents between electrodes inserted into the plasma and the vessel wall [8].…”

Chaos control and taming of turbulence in plasma devices

“…We note that the present approach conceptually differs from earlier works on feedback control of plasmas, where the emphasis was put on the suppression of instabilities by comparatively strong parameter variations. 7,8 For example, the suppression of edge turbulence was the goal of a series of experiments performed in the Texas Experimental Tokamak ͑TEXT͒. 9 An electric exciter probe inserted in the plasma edge region was driven by a phase-shifted feedback signal picked up with a different probe at a different toroidal position.…”

Kinetic enhancement of Raman backscatter, and electron acoustic Thomson scatter

“…[40] is an early example). Although we do not pursue it here, bispectral techniques can give estimates of the coupling coefficients and mode growth rates [41][42][43].…”