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Title: Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

Abstract

To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescale $$\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.

Authors:
 [1];  [2]; ORCiD logo [3]
+ Show Author Affiliations
  1. Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  3. Fusion Theory and Computation, Inc., Kingston, WA (United States)
Publication Date:
Research Org.:
Fusion Theory and Computation, Inc., Kingston, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES)
OSTI Identifier:
1418995
Alternate Identifier(s):
OSTI ID: 1429578
Grant/Contract Number:  
SC0016106; AC02-09CH11466; FOA-0001386: Early Career Research Program
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 25; Journal Issue: 3; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ideal MHD stability toroidal parallel

Citation Formats

Glasser, Alexander, Kolemen, Egemen, and Glasser, Alan H. Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control. United States: N. p., 2018. Web. doi:10.1063/1.5007042.
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Glasser, Alexander, Kolemen, Egemen, & Glasser, Alan H. Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control. United States. https://doi.org/10.1063/1.5007042
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Glasser, Alexander, Kolemen, Egemen, and Glasser, Alan H. Mon . "Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control". United States. https://doi.org/10.1063/1.5007042. https://www.osti.gov/servlets/purl/1418995.
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@article{osti_1418995,
title = {Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control},
author = {Glasser, Alexander and Kolemen, Egemen and Glasser, Alan H.},
abstractNote = {To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescale $\tau$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.},
doi = {10.1063/1.5007042},
journal = {Physics of Plasmas},
number = 3,
volume = 25,
place = {United States},
year = {Mon Mar 26 00:00:00 EDT 2018},
month = {Mon Mar 26 00:00:00 EDT 2018}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5007042
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Cited by: 9 works
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Figures / Tables:

Fig. 1. Fig. 1.: I) The forward integration of modes without modification exhibits asymmetric behavior near the singular point. On approach to $ψ$=$ψ$s, all modes are dominated by their projection along the asymptotically diverging singular mode and numerically lose their linear independence. II) A reversal of the integration to the left ofmore » the surface restores symmetry and linear independence to the solutions on both sides of the singularity. III) Highlighting the resonant modes ($m$,$m$+$M$) at $ψ$s—i.e., $q$($ψ$s) = $m$/$n$. IV) Integration reversal for $ψ$< $ψ$s and the exclusion of resonant modes.« less
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Works referenced in this record:

The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma
journal, July 2016

A Natural Approach to the Numerical Integration of Riccati Differential Equations
journal, January 1999

Reconstruction of current profile parameters and plasma shapes in tokamaks
journal, November 1985

Linear Stability of Resistive MHD Modes: Axisymmetric Toroidal Computation of the Outer Region Matching Data
journal, December 1994

  • Pletzer, A.; Bondeson, A.; Dewar, R. L.
  • Journal of Computational Physics, Vol. 115, Issue 2
  • DOI: 10.1006/jcph.1994.1215

Numerical Integration of the Differential Riccati Equation and Some Related Issues
journal, June 1992

  • Dieci, Luca
  • SIAM Journal on Numerical Analysis, Vol. 29, Issue 3
  • DOI: 10.1137/0729049

Long pulse high performance discharges in the DIII-D tokamak
journal, November 2001

ELM control strategies and tools: status and potential for ITER
journal, March 2013

Tearing mode analysis in tokamaks, revisited
journal, December 1998

  • Nishimura, Y.; Callen, J. D.; Hegna, C. C.
  • Physics of Plasmas, Vol. 5, Issue 12
  • DOI: 10.1063/1.873166

VODE: A Variable-Coefficient ODE Solver
journal, September 1989

  • Brown, Peter N.; Byrne, George D.; Hindmarsh, Alan C.
  • SIAM Journal on Scientific and Statistical Computing, Vol. 10, Issue 5
  • DOI: 10.1137/0910062

A new eigenvalue problem associated with the two-dimensional Newcomb equation without continuous spectra
journal, August 1999

  • Tokuda, Shinji; Watanabe, Tomoko
  • Physics of Plasmas, Vol. 6, Issue 8
  • DOI: 10.1063/1.873588

OpenMP: an industry standard API for shared-memory programming
journal, January 1998

  • Dagum, L.; Menon, R.
  • IEEE Computational Science and Engineering, Vol. 5, Issue 1
  • DOI: 10.1109/99.660313

The CHEASE code for toroidal MHD equilibria
journal, September 1996

Active control of 2/1 magnetic islands in a tokamak
journal, May 1998

  • Navratil, G. A.; Cates, C.; Mauel, M. E.
  • Physics of Plasmas, Vol. 5, Issue 5
  • DOI: 10.1063/1.872856

Computation of resistive instabilities by matched asymptotic expansions
journal, November 2016

  • Glasser, A. H.; Wang, Z. R.; Park, J. -K.
  • Physics of Plasmas, Vol. 23, Issue 11
  • DOI: 10.1063/1.4967862

Heat flux management via advanced magnetic divertor configurations and divertor detachment
journal, August 2015

Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes
journal, May 2002

  • Snyder, P. B.; Wilson, H. R.; Ferron, J. R.
  • Physics of Plasmas, Vol. 9, Issue 5
  • DOI: 10.1063/1.1449463

Chapter 2: Plasma confinement and transport
journal, December 1999

  • Transport, ITER Physics Expert Group on Confin; Database, ITER Physics Expert Group on Confin; Editors, ITER Physics Basis
  • Nuclear Fusion, Vol. 39, Issue 12
  • DOI: 10.1088/0029-5515/39/12/302

Stationary QH-mode plasmas with high and wide pedestal at low rotation on DIII-D
journal, September 2016

Closed loop control of reversal parameter in RFX-mod
journal, October 2011

Numerical studies of edge localized instabilities in tokamaks
journal, April 2002

  • Wilson, H. R.; Snyder, P. B.; Huysmans, G. T. A.
  • Physics of Plasmas, Vol. 9, Issue 4
  • DOI: 10.1063/1.1459058

The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma
journal, July 2016

Two-dimensional generalizations of the Newcomb equation
journal, April 1990

Efficient matrix-valued algorithms for solving stiff Riccati differential equations
journal, July 1990

  • Choi, C. H.; Laub, A. J.
  • IEEE Transactions on Automatic Control, Vol. 35, Issue 7
  • DOI: 10.1109/9.57015

A Riccati Solution for the Ideal MHD Plasma Response with Applications to Real-time Stability Control
dataset, January 2018

  • Glasser, A.; Kolemen, E.; Glasser, A.
  • Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
  • DOI: 10.11578/1562046

Efficient matrix-valued algorithms for solving stiff Riccati differential equations
conference, January 1989

  • Choi, C. H.; Laub, A. J.
  • Proceedings of the 28th IEEE Conference on Decision and Control
  • DOI: 10.1109/cdc.1989.70248
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    Works referencing / citing this record:

    A robust solution for the resistive MHD toroidal Δ′ matrix in near real-time
    journal, August 2018

    • Glasser, Alexander S.; Kolemen, Egemen
    • Physics of Plasmas, Vol. 25, Issue 8
    • DOI: 10.1063/1.5029477

    Progress in disruption prevention for ITER
    journal, June 2019

    A Riccati Solution for the Ideal MHD Plasma Response with Applications to Real-time Stability Control
    dataset, January 2018

    • Glasser, A.; Kolemen, E.; Glasser, A.
    • Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
    • DOI: 10.11578/1562046
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      Figures / Tables found in this record:

      Fig. 1. (p. 5)figure
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      Fig. 3. (p. 6)figure
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