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Multi-Machine Scalings of Thresholds for N=1 and N=2 Error Field Correction

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Multi-Machine Scalings of Thresholds for N=1 and N=2 Error Field Correction Multi-machine Scalings of Thresholds for n=1 and n=2 Error Field Correction N.C. Logan1, J.-K. Park2, Q. Hu2, S. Yang2, T. Markovic3, M. Maraschek4, L. Piron5,6, P. Piovesan6, Y. In7, H. Wang8, S. Wolfe9, C. Paz-Soldan10,11, E.J. Strait10, S. Munaretto10 1 Lawrence Livermore National Laboratory 2 Princeton Plasma Physics Laboratory 3 IPP Czech Academy of Sciences 4 Max-Planck Institut für Plasmaphysik 5 Universit`a degli Studi di Padova 6 Consorzio RFX 7 Ulsan National Inst. of Sci. & Tech.8 IPP Chinese Academy of Sciences 9 Massachusetts Inst. of Tech. (retired) 10 General Atomics 11 Columbia University Presented at the 28th IAEA Fusion Energy Conference Virtual, 10-15 May 2021 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344, Princeton Plasma Physics Laboratory under contract DE-AC02-09CH11466, and DIII-D under contract DE-FC02-04ER5469. This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore 1 National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes. Simple error field penetration scalings set the tolerances & correction-coil designs for new machines like ITER ▪ Nonaxisymmetric fields cause tearing, locking, and disruptions ▪ A large database has been accumulated for n=1 penetration threshold scaling ▪ EFC criterion scale a robust coupling metric with basic equilibrium parameters ▪ Initial data shows n=2 thresholds can have similar magnitude & scaling Fig. from Strait, et. al, Nucl. Fusion, 54, 2014 N.C. Logan / IAEA FEC / 05.2021 2 This poster shows how simple scalings have been developed for multi-machine databases for n=1 and n=2 Error Fields Factor of 2 ▪ EF magnitude “δ” determined by ideal MHD resonance β ℓ ▪ Broad scaling done using simplest possible 0D parameters: ne, BT, R0, N/ i ▪ Robustly describes thresholds spanning factor of ~20 within a factor of ~2 N.C. Logan / IAEA FEC / 05.2021 3 Error field magnitude parameterized by ideal MHD resonance 4 Ideal MHD is used to identify the most dangerous component of the Error Field ▪ Error Fields (EFs) drive natural modes of the plasma response that amplify or shield the external perturbations and an effective EF metric for avoidance of core tearing modes should incorporate this plasma response ▪ A broadly validated model of the detailed nonlinear response and penetration across all machines has proven difficult due to the complexity of this physics — Modeling requires (and is sensitive to) detailed kinetic profile information not always available ▪ We use the ideal MHD plasma response to represent the "outer layer" away from the resonant surfaces and empirical scalings to represent the more complex "inner layer" dynamics at the rational surface — Use “overlap” metric (next page) rather than 2/1 resonant field to maximize robustness — Fundamental 0D plasma parameters are used in this scaling to maximize the utility for design of future tokamaks for which accurate knowledge of detailed profiles may not be available — 0D is also necessary when incorporating Ohmic discharges with limited profile measurements N.C. Logan / IAEA FEC / 05.2021 5 This approach scales a external field metric that includes some knowledge of the plasma response Experiment → δres(bext, q95, κ, ...) ≤ δpen(ne, BT, R0, βN, ω, ...) ← Scaling 3D equilibrium on the fast ideal Nonlinear, resistive, resonant layer MHD time scale evolution on slower time scales Experimental evaluation of Relies on empirical scaling “dangerous” EF calculated by GPEC1 1 J.-K. Park, A.H. Boozer, J.E. Menard, and M.J. Schaffer, Nuclear Fusion 48, 45006 (2008). N.C. Logan / IAEA FEC / 05.2021 6 This approach scales an external field metric that includes some knowledge of the plasma response δres(bext, q95, κ, ...) ≤ δpen(ne, BT, R0, βN, ω, ...) 3D equilibrium on the fast ideal Example: Dangerous EF MHD time scale looks similar across machines in similar q95 v1 is first right singular plasmas vector of C: robust bres = C· bext ~ e1v1 · bext feature of equilibrium with q95, and shaping dependences Linear coupling between Eigenvalue e can be external 3D field 1 more sensitive to and total details of equilibrium resonant field reconstruction including the plasma response N.C. Logan / IAEA FEC / 05.2021 7 This approach scales an external field metric that includes some knowledge of the plasma response δres(bext, q95, κ, ...) ≤ δpen(ne, BT, R0, βN, ω, ...) 3D equilibrium on the fast ideal MHD time scale v1 robust, with Ires = C· bext ~ e1v1 · bext common structure “Overlap” metric easily δ = v · b / B Example: 270° 1 ext T obtained from arbitrary phasing coils are vacuum EF more dangerous than 90° ones in this DIII-D plasma - have Ideal MHD quantifies the dangerous part of higher overlap the vacuum EF that drives resonances in the plasma N.C. Logan / IAEA FEC / 05.2021 8 The overlap metric, δ, unifies the many different coils and their different couplings to various plasma scenarios ITER DIII-D COMPASS NSTX* KSTAR *Including potential off-mid-plane coil design N.C. Logan / IAEA FEC / 05.2021 9 Scalings fit using multivariable regression on experimental database of thresholds built by applying intentional error fields 10 Multivariate regression on large databases requires large amounts of experimental data on many machines ▪ Decades of individual experimental work has reported a wide range of scaling exponents for common dependencies — Density scaling exponents ranging from ~0.5 to ~1.0 [1,2] — Toroidal field exponents ranging from negative to positive [3] ▪ Data from 7 machines has been collected into a common database as part of a ITPA joint experiment effort (MDC-19) ▪ Experiments performed/published in the last 2 years expanded this database to include toroidal mode number n=2 [4] — Fits are separated by n number in this work — Combined fits suggest a linear dependence on n due to less amplification of the least stable n=2 and deeper location of the 3/2 surface, but recent KSTAR results suggest details of the unconstrained rotation can alter this [5] ▪ Multivariate regressions on these databases are used to project thresholds to ITER 1 Buttery, Nucl. Fusion 2000 2 Lazzaro, Phys. Plasmas 2002 3 Wang, Nucl. Fusion 2020 4 Logan, Nucl. Fusion 2020 4 Yang, Nucl. Fusion 2021 (submitted) N.C. Logan / IAEA FEC / 05.2021 11 Experiments in each machine explore thresholds in applied error fields using 3D coils DIII-D ▪ Fixed 3D coil configuration ramped in amplitude until penetration — Time identified by density, rotation & magnetics Locking — Expect ~10% error from coil current & penetration time identification ▪ Devoted scans of ne, BT, PINJ, etc. done in various machines — Majority used upper single null Ohmic/L-modes N.C. Logan / IAEA FEC / 05.2021 12 Diverse scalings in different experiments / conditions exemplify dangers of single-experiment trends DIII-D L-mode 1T 2T Independent fits ▪ Single scan is often ~4-8 shots → fits may give varied scalings — Access to low range of scan variable is essential — Compensating for other variables (BT, R0, βN/ℓi) does not collapse individual scalings ▪ Resulted in a wide variety of density and toroidal field scalings reported by individual machines in the past N.C. Logan / IAEA FEC / 05.2021 13 Combining all data into a single, multidimensional regression aligns discrepancies and reduces the uncertainties DIII-D L-mode 1T 2T Single fit ▪ Takeaway: Need large database in variety of conditions for robust scaling ▪ This is even more true when including multiple machines! — Luckily, the ITPA MDC-19 joint experiment has built a large multi-machine database N.C. Logan / IAEA FEC / 05.2021 14 Performing multivariate regression on the ITPA database, threshold scalings look promising for ITER so far ITER ▪ Projected ITER EF thresholds are comparable or larger than those ITER commonly dealt Factor of 2 with on existing Logan, Nucl. Fusion 2020 Logan, 1 devices1 -3.7±0.03 0.6±0.06 -1.1±0.07 0.1±0.07 -0.2±0.05 δn=1 ≤ 10 ne BT R0 (βN/ℓi) → δITER,n=1 = 1.37±0.36 x10-4 -3.4±0.06 1.1±0.1 -1.5±0.2 1.5±0.1 0.4±0.1 -3 * δn=2 ≤ 10 ne BT R0 (βN/ℓi) → δITER,n=2 = 8.8±4.4 x10 -4 * n=2 database includes only 2 sizes,and lacks H-mode EF amplification physics. Removing R from the regression results in δITER= 1.7 x10 N.C. Logan / IAEA FEC / 05.2021 15 Large database regressions focus on broad trends, not local dynamics 16 The goal of these database scalings is to provide a robust, trustworthy projection of the allowable EF for future machines ▪ Distribution of experimental data is not even across the explored parameters — Large number of experimental data points available from recent experiments on similarly sized DIII-D, EAST and
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