SPARC Tokamak Error Field Expectations and Physics-Based Correction Coil Design

TL;DR

SPARC addresses the risk of error-field (EF) induced locked modes by combining a physics-based dominant-mode EF metric with empirical multi-machine scaling to project core EF thresholds. The approach identifies the dangerous EF spectrum via a dominant n=1 core coupling mode obtained from a truncated, SVD-ranked coupling matrix, and accounts for nonresonant effects (subdominant core coupling, edge resonances, NTV braking) using conservative models and probabilistic risk. A Monte Carlo framework propagates coil-tolerances, assembly misalignments, and intrinsic coil asymmetries to produce EF PDFs and locking-risk distributions, guiding tolerance schemes that balance engineering feasibility with physics margins. The SPARC 3x6 EFCC system is designed to maximize core-resonant coupling (optimal midplane placement, ~57% baseline overlap in L-mode, up to 81% with phasing) while maintaining nonresonant pollution within acceptable limits and preserving the ability to exercise n=2 EFC or RMP for future control. This physics-driven design enables operation in high-field, high-performance regimes and informs assembly tolerances and future ARC-scale devices through quantified EF risk and corrective capabilities.

Abstract

Non-axisymmetric magnetic field coils have been designed to provide efficient error field correction and suppress edge localized modes in SPARC - a compact high-field tokamak that is presently under construction at Commonwealth Fusion Systems. These designs utilize the Generalized Perturbed Equilibrium Code's (GPEC's) representation of the multi-modal, non-axisymmetric plasma response to optimize the geometric coupling between 3D coil arrays and the desired core or edge plasma response. Error field correction coils are designed to couple to the plasma-amplified kink that dominates the drive of core resonances. The maximum allowable error field is projected to SPARC using an empirical scaling that is consistent with linear and nonlinear MHD modeling expectations. Asymmetric construction and assembly tolerances are then balanced against the corresponding kA-turns needed for correction to levels below the allowable limit. These physics-driven coil designs provide confidence in our ability to operate SPARC in new high field tokamak regimes without error field induced locked modes.

Figures (17)

• Figure 1: SPARC PRD safety factor (a), temperature (b), pressure (c), density (d), $\mathbf{E}$$\times$$\mathbf{B}$ precession frequency (e), and ion diamagnetic frequency (f) profiles for the representative L (blue) and H (orange) mode times of 7 and 14 seconds respectively.
• Figure 2: Dominant mode structure of the representative SPARC PRD (a) L-mode and (b) H-mode times. The upper (U), midplane (M) and lower (L) EFCCs are shown in magenta. Core rational surfaces are shown in purple.
• Figure 3: (a) The weighted least squares ITPA EF threshold scaling plotted against the actual data in the ohmic, L-mode and H-mode database using in the fit. (b) Histogram of the empirical threshold data with SPARC scenario projections marked. Note the SPARC L-mode projection uses a scaling law fit to only Ohmic and L-mode data.
• Figure 4: (a) Probability distribution function of dominant mode overlap thresholds and (b) corresponding risk of locking for a given EF value in the scenarios defined in Table \ref{['tab:equil_scalars']}. Dashed vertical lines mark the threshold using the nominal value of each exponent in the corresponding scaling law.
• Figure 5: The lowest density accessible with EFC (open bar) and without EFC (closed bar) for a number of published EFC studies. The densities have been normalized to the density at which REs are expected (which was directly determined for DIII-D in Paz-Soldan2016TheLimit). As such, no amount of EFC can enable access below 1.