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Title: Optimal design of feedback coils for the control of external modes in tokamaks

Abstract

A formalism is developed for optimizing the design of feedback coils placed around a tokamak plasma in order to control the resistive shell mode. It is found that feedback schemes for controlling the resistive shell mode fail whenever the distortion of the mode structure by the currents circulating in the feedback coils becomes too strong, in which case the mode escapes through the gaps between the coils, or through the centers of the coils. The main aim of the optimization process is to reduce this distortion by minimizing the coupling of different Fourier harmonics due to the feedback currents. It is possible to define a quantity {alpha}{sub 0} which parametrizes the strength of the coupling. Feedback fails for {alpha}{sub 0}{ge}1. The optimization procedure consists of minimizing {alpha}{sub 0} subject to practical constraints. If there are very many evenly spaced feedback coils surrounding the plasma in the poloidal direction then the optimization can be performed analytically. Otherwise, the optimization must be performed numerically. The optimal configuration is to have many, large, overlapping coils in the poloidal direction. {copyright} {ital 1998 American Institute of Physics.}

Authors:
;  [1]
  1. Institute for Fusion Studies, Department of Physics, The University of Texas at Austin, Austin, Texas78712 (United States)
Publication Date:
OSTI Identifier:
616863
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 5; Journal Issue: 6; Other Information: PBD: Jun 1998
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION; PLASMA INSTABILITY; FEEDBACK; TOKAMAK DEVICES; OPTIMIZATION; SHELLS; PLASMA CONFINEMENT; BETA RATIO

Citation Formats

Fitzpatrick, R., and Yu, E.P.. Optimal design of feedback coils for the control of external modes in tokamaks. United States: N. p., 1998. Web. doi:10.1063/1.872908.
Fitzpatrick, R., & Yu, E.P.. Optimal design of feedback coils for the control of external modes in tokamaks. United States. doi:10.1063/1.872908.
Fitzpatrick, R., and Yu, E.P.. 1998. "Optimal design of feedback coils for the control of external modes in tokamaks". United States. doi:10.1063/1.872908.
@article{osti_616863,
title = {Optimal design of feedback coils for the control of external modes in tokamaks},
author = {Fitzpatrick, R. and Yu, E.P.},
abstractNote = {A formalism is developed for optimizing the design of feedback coils placed around a tokamak plasma in order to control the resistive shell mode. It is found that feedback schemes for controlling the resistive shell mode fail whenever the distortion of the mode structure by the currents circulating in the feedback coils becomes too strong, in which case the mode escapes through the gaps between the coils, or through the centers of the coils. The main aim of the optimization process is to reduce this distortion by minimizing the coupling of different Fourier harmonics due to the feedback currents. It is possible to define a quantity {alpha}{sub 0} which parametrizes the strength of the coupling. Feedback fails for {alpha}{sub 0}{ge}1. The optimization procedure consists of minimizing {alpha}{sub 0} subject to practical constraints. If there are very many evenly spaced feedback coils surrounding the plasma in the poloidal direction then the optimization can be performed analytically. Otherwise, the optimization must be performed numerically. The optimal configuration is to have many, large, overlapping coils in the poloidal direction. {copyright} {ital 1998 American Institute of Physics.}},
doi = {10.1063/1.872908},
journal = {Physics of Plasmas},
number = 6,
volume = 5,
place = {United States},
year = 1998,
month = 6
}
  • An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least-square method with exponential forgetting factor and covariance resetting is used to identify (experimentally determine) the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time-dependent RWM in a slowly evolving tokamakmore » discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.« less
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  • No abstract prepared.
  • A quadratic dispersion relation is derived which governs the feedback-modified stability of the resistive shell mode in a large-aspect ratio, low-{beta} tokamak plasma. The effectiveness of a given feedback scheme is determined by a single parameter, {alpha}{sub 0}, which measures the coupling of different poloidal harmonics due to the nonsinusoidal nature of the feedback currents. Feedback fails when this parameter becomes either too positive or too negative. Feedback schemes can be classified into three groups, depending on the relative values of the poloidal mode number, m{sub 0}, of the intrinsically unstable resistive shell mode, and the number, M, of feedbackmore » coils in the poloidal direction. Group I corresponds to M{<=}2m{sub 0} and M{ne}m{sub 0}; group II corresponds to M=m{sub 0}; finally, group III corresponds to M>2m{sub 0}. The optimal group I feedback scheme is characterized by extremely narrow detector loops placed as close as possible to the plasma, i.e., well inside the resistive shell. Of course, such a scheme would be somewhat impractical. The optimal group II feedback scheme is characterized by large, nonoverlapping detector loops, and moderately large, nonoverlapping feedback coils. Such a scheme is 100% effective (i.e., it makes the resistive shell appear superconducting) when the detector loops are located just outside the shell. Unfortunately, the scheme only works efficiently for resistive shell modes possessing one particular poloidal mode number. The optimal group III feedback scheme is characterized by slightly overlapping detector loops, and strongly overlapping feedback coils. Such a scheme is 100% effective when the detector loops are located just outside the shell. In addition, the scheme works efficiently for resistive shell modes with a range of different poloidal mode numbers.« less