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

Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

doi:10.1063/1.5007042

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

Journal Article · Mon Mar 26 00:00:00 EDT 2018 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5007042· OSTI ID:1418995

Glasser, Alexander ^[1]; Kolemen, Egemen ^[2]; ^[3]

Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Fusion Theory and Computation, Inc.
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Fusion Theory and Computation, Inc., Kingston, WA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Fusion Theory and Computation, Inc., Kingston, WA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

Grant/Contract Number:: AC02-09CH11466; SC0016106

OSTI ID:: 1418995

Alternate ID(s):: OSTI ID: 1429578

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 3 Vol. 25; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (25)

The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma Glasser, A. H. Physics of Plasmas, Vol. 23, Issue 7 https://doi.org/10.1063/1.4958328	journal	July 2016
A Riccati Solution for the Ideal MHD Plasma Response with Applications to Real-time Stability Control Glasser, A.; Kolemen, E.; Glasser, A. Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States) https://doi.org/10.11578/1562046	dataset	January 2018
Linear Stability of Resistive MHD Modes: Axisymmetric Toroidal Computation of the Outer Region Matching Data Pletzer, A.; Bondeson, A.; Dewar, R. L. Journal of Computational Physics, Vol. 115, Issue 2 https://doi.org/10.1006/jcph.1994.1215	journal	December 1994
The CHEASE code for toroidal MHD equilibria Lütjens, H.; Bondeson, A.; Sauter, O. Computer Physics Communications, Vol. 97, Issue 3 https://doi.org/10.1016/0010-4655(96)00046-X	journal	September 1996
Closed loop control of reversal parameter in RFX-mod Barp, Marco; Cavazzana, Roberto; Marchiori, Giuseppe Fusion Engineering and Design, Vol. 86, Issue 6-8 https://doi.org/10.1016/j.fusengdes.2011.03.048	journal	October 2011
Heat flux management via advanced magnetic divertor configurations and divertor detachment Kolemen, E.; Allen, S. L.; Bray, B. D. Journal of Nuclear Materials, Vol. 463 https://doi.org/10.1016/j.jnucmat.2014.11.099	journal	August 2015
Two-dimensional generalizations of the Newcomb equation Dewar, R. L.; Pletzer, A. Journal of Plasma Physics, Vol. 43, Issue 2 https://doi.org/10.1017/S002237780001480X	journal	April 1990
Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes Snyder, P. B.; Wilson, H. R.; Ferron, J. R. Physics of Plasmas, Vol. 9, Issue 5 https://doi.org/10.1063/1.1449463	journal	May 2002
Numerical studies of edge localized instabilities in tokamaks Wilson, H. R.; Snyder, P. B.; Huysmans, G. T. A. Physics of Plasmas, Vol. 9, Issue 4 https://doi.org/10.1063/1.1459058	journal	April 2002
Computation of resistive instabilities by matched asymptotic expansions Glasser, A. H.; Wang, Z. R.; Park, J. -K. Physics of Plasmas, Vol. 23, Issue 11 https://doi.org/10.1063/1.4967862	journal	November 2016
Active control of 2/1 magnetic islands in a tokamak Navratil, G. A.; Cates, C.; Mauel, M. E. Physics of Plasmas, Vol. 5, Issue 5 https://doi.org/10.1063/1.872856	journal	May 1998
Tearing mode analysis in tokamaks, revisited Nishimura, Y.; Callen, J. D.; Hegna, C. C. Physics of Plasmas, Vol. 5, Issue 12 https://doi.org/10.1063/1.873166	journal	December 1998
A new eigenvalue problem associated with the two-dimensional Newcomb equation without continuous spectra Tokuda, Shinji; Watanabe, Tomoko Physics of Plasmas, Vol. 6, Issue 8 https://doi.org/10.1063/1.873588	journal	August 1999
Reconstruction of current profile parameters and plasma shapes in tokamaks Lao, L. L.; St. John, H.; Stambaugh, R. D. Nuclear Fusion, Vol. 25, Issue 11 https://doi.org/10.1088/0029-5515/25/11/007	journal	November 1985
Chapter 2: Plasma confinement and transport Transport, ITER Physics Expert Group on Confin; Database, ITER Physics Expert Group on Confin; Editors, ITER Physics Basis Nuclear Fusion, Vol. 39, Issue 12 https://doi.org/10.1088/0029-5515/39/12/302	journal	December 1999
Long pulse high performance discharges in the DIII-D tokamak Luce, T. C.; Wade, M. R.; Politzer, P. A. Nuclear Fusion, Vol. 41, Issue 11 https://doi.org/10.1088/0029-5515/41/11/308	journal	November 2001
ELM control strategies and tools: status and potential for ITER Lang, P. T.; Loarte, A.; Saibene, G. Nuclear Fusion, Vol. 53, Issue 4 https://doi.org/10.1088/0029-5515/53/4/043004	journal	March 2013
State-of-the-art neoclassical tearing mode control in DIII-D using real-time steerable electron cyclotron current drive launchers Kolemen, E.; Welander, A. S.; La Haye, R. J. Nuclear Fusion, Vol. 54, Issue 7 https://doi.org/10.1088/0029-5515/54/7/073020	journal	May 2014
Stationary QH-mode plasmas with high and wide pedestal at low rotation on DIII-D Chen, Xi; Burrell, K. H.; Osborne, T. H. Nuclear Fusion, Vol. 57, Issue 2 https://doi.org/10.1088/0029-5515/57/2/022007	journal	September 2016
Efficient matrix-valued algorithms for solving stiff Riccati differential equations Choi, C. H.; Laub, A. J. IEEE Transactions on Automatic Control, Vol. 35, Issue 7 https://doi.org/10.1109/9.57015	journal	July 1990
OpenMP: an industry standard API for shared-memory programming Dagum, L.; Menon, R. IEEE Computational Science and Engineering, Vol. 5, Issue 1 https://doi.org/10.1109/99.660313	journal	January 1998
Efficient matrix-valued algorithms for solving stiff Riccati differential equations Choi, C. H.; Laub, A. J. Proceedings of the 28th IEEE Conference on Decision and Control https://doi.org/10.1109/cdc.1989.70248	conference	January 1989
Numerical Integration of the Differential Riccati Equation and Some Related Issues Dieci, Luca SIAM Journal on Numerical Analysis, Vol. 29, Issue 3 https://doi.org/10.1137/0729049	journal	June 1992
VODE: A Variable-Coefficient ODE Solver Brown, Peter N.; Byrne, George D.; Hindmarsh, Alan C. SIAM Journal on Scientific and Statistical Computing, Vol. 10, Issue 5 https://doi.org/10.1137/0910062	journal	September 1989
A Natural Approach to the Numerical Integration of Riccati Differential Equations Schiff, Jeremy; Shnider, S. SIAM Journal on Numerical Analysis, Vol. 36, Issue 5 https://doi.org/10.1137/S0036142996307946	journal	January 1999

Cited By (3)

A Riccati Solution for the Ideal MHD Plasma Response with Applications to Real-time Stability Control Glasser, A.; Kolemen, E.; Glasser, A. Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States) https://doi.org/10.11578/1562046	dataset	January 2018
A robust solution for the resistive MHD toroidal Δ′ matrix in near real-time Glasser, Alexander S.; Kolemen, Egemen Physics of Plasmas, Vol. 25, Issue 8 https://doi.org/10.1063/1.5029477	journal	August 2018
Progress in disruption prevention for ITER Strait, E. J.; Barr, J. L.; Baruzzo, M. Nuclear Fusion, Vol. 59, Issue 11 https://doi.org/10.1088/1741-4326/ab15de	journal	June 2019