Probabilistic locked mode predictor in the presence of a resistive wall and finite island saturation in tokamaks

Akçay, C.; Finn, John M.; Brennan, Dylan P.; Olofsson, K. E. J.; Cole, A. J.

doi:10.1063/5.0177827

Title: Probabilistic locked mode predictor in the presence of a resistive wall and finite island saturation in tokamaks

Journal Article · 03 March 2024 · Physics of Plasmas

DOI: https://doi.org/10.1063/5.0177827 · OSTI ID:2567884

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We present a framework for estimating the probability of locking to an error field in a rotating tokamak plasma. This leverages machine learning methods trained on data from a mode-locking model, including an error field, resistive magnetohydrodynamics modeling of the plasma, a resistive wall, and an external vacuum region, leading to a fifth-order ordinary differential equation (ODE) system. It is an extension of the model without a resistive wall introduced by Akçay et al. [Phys. Plasmas 28, 082106 (2021)]. Tearing mode saturation by a finite island width is also modeled. We vary three pairs of control parameters in our studies: the momentum source plus either the error field, the tearing stability index, or the island saturation term. The order parameters are the time-asymptotic values of the five ODE variables. Normalization of them reduces the system to 2D and facilitates the classification into locked (L) or unlocked (U) states, as illustrated by Akçay et al., [Phys. Plasmas 28, 082106 (2021)]. This classification splits the control space into three regions: L̂, with only L states; Û, with only U states; and a hysteresis (hysteretic) region Ĥ, with both L and U states. In regions L̂ and Û, the cubic equation of torque balance yields one real root. Region Ĥ has three roots, allowing bifurcations between the L and U states. The classification of the ODE solutions into L/U is used to estimate the locking probability, conditional on the pair of the control parameters, using a neural network. We also explore estimating the locking probability for a sparse dataset, using a transfer learning method based on a dense model dataset.

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Research Organization:: General Atomics, San Diego, CA (United States)

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

Grant/Contract Number:: FC02-04ER54698; FG02-95ER54309; SC0019016; SC0022031

OSTI ID:: 2567884

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 3 Vol. 31; ISSN 1070-664X

Publisher:: American Institute of PhysicsCopyright Statement

Country of Publication:: United States

Language:: English

References (53)

On the distribution of points in a cube and the approximate evaluation of integrals Sobol', I. M. USSR Computational Mathematics and Mathematical Physics, Vol. 7, Issue 4 https://doi.org/10.1016/0041-5553(67)90144-9	journal	January 1967
Hazard function exploration of tokamak tearing mode stability boundaries Olofsson, K. E. J.; Sammuli, B. S.; Humphreys, D. A. Fusion Engineering and Design, Vol. 146 https://doi.org/10.1016/j.fusengdes.2019.02.109	journal	September 2019
Database-wide hazard modelling of the onset of DIII-D tearing modes with field features Olofsson, K. E. J.; Akçay, C.; Sammuli, B. S. Journal of Plasma Physics, Vol. 88, Issue 5 https://doi.org/10.1017/S0022377822001003	journal	October 2022
Predicting disruptive instabilities in controlled fusion plasmas through deep learning Kates-Harbeck, Julian; Svyatkovskiy, Alexey; Tang, William Nature, Vol. 568, Issue 7753 https://doi.org/10.1038/s41586-019-1116-4	journal	April 2019
The interaction of error fields and resistive wall modes Gimblett, C. G.; Hastie, R. J. Physics of Plasmas, Vol. 11, Issue 3 https://doi.org/10.1063/1.1639155	journal	March 2004
Finite-Resistivity Instabilities of a Sheet Pinch Furth, Harold P.; Killeen, John; Rosenbluth, Marshall N. Physics of Fluids, Vol. 6, Issue 4 https://doi.org/10.1063/1.1706761	journal	January 1963
Hyperresistivity due to viscous tearing mode turbulence Finn, John M. Physics of Plasmas, Vol. 12, Issue 9 https://doi.org/10.1063/1.2048887	journal	September 2005
Drift-magnetohydrodynamical model of error-field penetration in tokamak plasmas Cole, A.; Fitzpatrick, R. Physics of Plasmas, Vol. 13, Issue 3 https://doi.org/10.1063/1.2178167	journal	March 2006
The influence of rotation on the βN threshold for the 2∕1 neoclassical tearing mode in DIII-D Buttery, R. J.; La Haye, R. J.; Gohil, P. Physics of Plasmas, Vol. 15, Issue 5 https://doi.org/10.1063/1.2894215	journal	May 2008
Predictive simulations of ITER including neutral beam driven toroidal rotation Halpern, Federico D.; Kritz, Arnold H.; Bateman, Glenn Physics of Plasmas, Vol. 15, Issue 6 https://doi.org/10.1063/1.2931037	journal	June 2008
Variational principles with Padé approximants for tearing mode analysis Cole, Andrew J.; Finn, John M. Physics of Plasmas, Vol. 21, Issue 3 https://doi.org/10.1063/1.4868861	journal	March 2014
Control of linear modes in cylindrical resistive magnetohydrodynamics with a resistive wall, plasma rotation, and complex gain Brennan, D. P.; Finn, J. M. Physics of Plasmas, Vol. 21, Issue 10 https://doi.org/10.1063/1.4896712	journal	October 2014
Phase locking of multi-helicity neoclassical tearing modes in tokamak plasmas Fitzpatrick, Richard Physics of Plasmas, Vol. 22, Issue 4 https://doi.org/10.1063/1.4919030	journal	April 2015
Forces and moments within layers of driven tearing modes with sheared rotation Cole, A. J.; Finn, J. M.; Hegna, C. C. Physics of Plasmas, Vol. 22, Issue 10 https://doi.org/10.1063/1.4932991	journal	October 2015
Real frequency tearing layers with parallel dynamics and the effect on error field locking and resistive wall modes Finn, J. M.; Cole, A. J.; Brennan, D. P. Physics of Plasmas, Vol. 26, Issue 10 https://doi.org/10.1063/1.5124490	journal	October 2019
Machine learning control for disruption and tearing mode avoidance Fu, Yichen; Eldon, David; Erickson, Keith Physics of Plasmas, Vol. 27, Issue 2 https://doi.org/10.1063/1.5125581	journal	February 2020
Nonlinear error field response in the presence of plasma rotation and real frequencies due to favorable curvature Akçay, Cihan; Finn, John M.; Cole, Andrew J. Physics of Plasmas, Vol. 27, Issue 3 https://doi.org/10.1063/1.5144470	journal	March 2020
The interaction of resonant magnetic perturbations with rotating plasmas Fitzpatrick, R.; Hender, T. C. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 3 https://doi.org/10.1063/1.859863	journal	March 1991
Saturation of the tearing mode White, Roscoe B.; Monticello, D. A.; Rosenbluth, Marshall N. Physics of Fluids, Vol. 20, Issue 5 https://doi.org/10.1063/1.861939	journal	January 1977
Energy balance of the collisional tearing mode Bondeson, Anders; Sobel, J. R. Physics of Fluids, Vol. 27, Issue 8 https://doi.org/10.1063/1.864858	journal	January 1984
Viscous resistive magnetic reconnection Porcelli, Francesco Physics of Fluids, Vol. 30, Issue 6 https://doi.org/10.1063/1.866240	journal	January 1987
Nonlinear tearing modes in the presence of resistive wall and rotation Finn, John M.; Sovinec, Carl R. Physics of Plasmas, Vol. 5, Issue 2 https://doi.org/10.1063/1.872730	journal	February 1998
Machine learning methods for probabilistic locked-mode predictors in tokamak plasmas Akçay, Cihan; Finn, John M.; Brennan, Dylan P. Physics of Plasmas, Vol. 28, Issue 8 https://doi.org/10.1063/5.0053670	journal	August 2021
Disruption event characterization and forecasting in tokamaks Sabbagh, S. A.; Berkery, J. W.; Park, Y. S. Physics of Plasmas, Vol. 30, Issue 3 https://doi.org/10.1063/5.0133825	journal	March 2023
Progress Toward Interpretable Machine Learning–Based Disruption Predictors Across Tokamaks Rea, C.; Montes, K. J.; Pau, A. Fusion Science and Technology, Vol. 76, Issue 8 https://doi.org/10.1080/15361055.2020.1798589	journal	September 2020
Mode locking in tokamaks Nave, M. F. F.; Wesson, J. A. Nuclear Fusion, Vol. 30, Issue 12 https://doi.org/10.1088/0029-5515/30/12/011	journal	December 1990
Interaction of tearing modes with external structures in cylindrical geometry (plasma) Fitzpatrick, R. Nuclear Fusion, Vol. 33, Issue 7 https://doi.org/10.1088/0029-5515/33/7/I08	journal	July 1993
Forecasting disruptions in the ADITYA tokamak using neural networks Sengupta, A.; Ranjan, P. Nuclear Fusion, Vol. 40, Issue 12 https://doi.org/10.1088/0029-5515/40/12/304	journal	December 2000
Prediction of density limit disruption boundaries from diagnostic signals using neural networks Sengupta, A.; Ranjan, P. Nuclear Fusion, Vol. 41, Issue 5 https://doi.org/10.1088/0029-5515/41/5/302	journal	May 2001
On-line prediction and mitigation of disruptions in ASDEX Upgrade Pautasso, G.; Tichmann, C.; Egorov, S. Nuclear Fusion, Vol. 42, Issue 1 https://doi.org/10.1088/0029-5515/42/1/314	journal	January 2002
A cross-tokamak neural network disruption predictor for the JET and ASDEX Upgrade tokamaks Windsor, C. G.; Pautasso, G.; Tichmann, C. Nuclear Fusion, Vol. 45, Issue 5 https://doi.org/10.1088/0029-5515/45/5/004	journal	April 2005
A prediction tool for real-time application in the disruption protection system at JET Cannas, B.; Fanni, A.; Sonato, P. Nuclear Fusion, Vol. 47, Issue 11 https://doi.org/10.1088/0029-5515/47/11/018	journal	October 2007
Prototype of an adaptive disruption predictor for JET based on fuzzy logic and regression trees Murari, A.; Vagliasindi, G.; Arena, P. Nuclear Fusion, Vol. 48, Issue 3 https://doi.org/10.1088/0029-5515/48/3/035010	journal	February 2008
Unbiased and non-supervised learning methods for disruption prediction at JET Murari, A.; Vega, J.; Rattá, G. A. Nuclear Fusion, Vol. 49, Issue 5 https://doi.org/10.1088/0029-5515/49/5/055028	journal	April 2009
Advances in global MHD mode stabilization research on NSTX Sabbagh, S. A.; Berkery, J. W.; Bell, R. E. Nuclear Fusion, Vol. 50, Issue 2 https://doi.org/10.1088/0029-5515/50/2/025020	journal	January 2010
On the roles of direct feedback and error field correction in stabilizing resistive-wall modes In, Y.; Bogatu, I. N.; Garofalo, A. M. Nuclear Fusion, Vol. 50, Issue 4 https://doi.org/10.1088/0029-5515/50/4/042001	journal	March 2010
Progress in understanding error-field physics in NSTX spherical torus plasmas Menard, J. E.; Bell, R. E.; Gates, D. A. Nuclear Fusion, Vol. 50, Issue 4 https://doi.org/10.1088/0029-5515/50/4/045008	journal	March 2010
Modifications to ideal stability by kinetic effects in NSTX Berkery, J. W.; Sabbagh, S. A.; Bell, R. E. Nuclear Fusion, Vol. 55, Issue 12 https://doi.org/10.1088/0029-5515/55/12/123007	journal	October 2015
Effect of thick blanket modules on neoclassical tearing mode locking in ITER La Haye, R. J.; Paz-Soldan, C.; Liu, Y. Q. Nuclear Fusion, Vol. 57, Issue 1 https://doi.org/10.1088/0029-5515/57/1/014004	journal	November 2016
Statistical analysis of m / n = 2/1 locked and quasi-stationary modes with rotating precursors at DIII-D Sweeney, R.; Choi, W.; La Haye, R. J. Nuclear Fusion, Vol. 57, Issue 1 https://doi.org/10.1088/0029-5515/57/1/016019	journal	November 2016
Electromechanical modelling and design for phase control of locked modes in the DIII-D tokamak Olofsson, K. E. J.; Choi, W.; Humphreys, D. A. Plasma Physics and Controlled Fusion, Vol. 58, Issue 4 https://doi.org/10.1088/0741-3335/58/4/045008	journal	February 2016
Event hazard function learning and survival analysis for tearing mode onset characterization Olofsson, K. E. J.; Humphreys, D. A.; Haye, R. J. La Plasma Physics and Controlled Fusion, Vol. 60, Issue 8 https://doi.org/10.1088/1361-6587/aac662	journal	June 2018
Disruption prediction investigations using Machine Learning tools on DIII-D and Alcator C-Mod Rea, C.; Granetz, R. S.; Montes, K. Plasma Physics and Controlled Fusion, Vol. 60, Issue 8 https://doi.org/10.1088/1361-6587/aac7fe	journal	June 2018
Disruption predictor based on neural network and anomaly detection on J-TEXT Zheng, W.; Wu, Q. Q.; Zhang, M. Plasma Physics and Controlled Fusion, Vol. 62, Issue 4 https://doi.org/10.1088/1361-6587/ab6b02	journal	February 2020
Disruption prediction using a full convolutional neural network on EAST Guo, B. H.; Shen, B.; Chen, D. L. Plasma Physics and Controlled Fusion, Vol. 63, Issue 2 https://doi.org/10.1088/1361-6587/abcbab	journal	December 2020
Adaptive predictors based on probabilistic SVM for real time disruption mitigation on JET Murari, A.; Lungaroni, M.; Peluso, E. Nuclear Fusion, Vol. 58, Issue 5 https://doi.org/10.1088/1741-4326/aaaf9c	journal	March 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
Machine learning for disruption warnings on Alcator C-Mod, DIII-D, and EAST Montes, K. J.; Rea, C.; Granetz, R. S. Nuclear Fusion, Vol. 59, Issue 9 https://doi.org/10.1088/1741-4326/ab1df4	journal	July 2019
A real-time machine learning-based disruption predictor in DIII-D Rea, C.; Montes, K. J.; Erickson, K. G. Nuclear Fusion, Vol. 59, Issue 9 https://doi.org/10.1088/1741-4326/ab28bf	journal	July 2019
A disruption predictor based on a 1.5-dimensional convolutional neural network in HL-2A Yang, Zongyu; Xia, Fan; Song, Xianming Nuclear Fusion, Vol. 60, Issue 1 https://doi.org/10.1088/1741-4326/ab4b6f	journal	November 2019
Neoclassical Tearing Mode Seeding by Nonlinear Three-Wave Interactions in Tokamaks Bardóczi, L.; Logan, N. C.; Strait, E. J. Physical Review Letters, Vol. 127, Issue 5 https://doi.org/10.1103/PhysRevLett.127.055002	journal	July 2021
A Survey on Transfer Learning Pan, Sinno Jialin; Yang, Qiang IEEE Transactions on Knowledge and Data Engineering, Vol. 22, Issue 10 https://doi.org/10.1109/TKDE.2009.191	journal	October 2010
Reminder of the First Paper on Transfer Learning in Neural Networks, 1976 Bozinovski, Stevo Informatica, Vol. 44, Issue 3 https://doi.org/10.31449/inf.v44i3.2828	journal	September 2020

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