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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]
  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) (SC-24)
OSTI Identifier:
1418995
Alternate Identifier(s):
OSTI ID: 1429578
Grant/Contract Number:  
SC0016106; AC02-09CH11466; FOA-0001386: Early Career Research Program
Resource Type:
Journal Article: 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.
Glasser, Alexander, Kolemen, Egemen, & Glasser, Alan H. Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control. United States. doi:10.1063/1.5007042.
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. doi:10.1063/1.5007042.
@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}
}

Journal Article:
Free Publicly Available Full Text
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