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Glossary

Error Field

Unwanted magnetic field asymmetries from coil misalignment that brake plasma rotation and trigger locked modes

Reviewed Last reviewed: 9 Aug 2026 · Category: Glossary

What Is an Error Field?

An error field is any component of the magnetic field that breaks the designed axisymmetry of a tokamak. These asymmetries arise primarily from manufacturing and assembly tolerances: coil misalignments of a few millimeters, deviations in coil winding geometry, bus-bar and lead asymmetries, and ferromagnetic structural components. Even fractional departures of order δB/B ∼ 10−4 can profoundly affect plasma behavior because the plasma amplifies the external perturbation through resonant response at rational magnetic surfaces.1

Locked Modes and Disruptions

The most dangerous consequence of an error field is the locked mode. When the error field at a rational surface (typically q = 2) exceeds a critical threshold, electromagnetic torque from the non-axisymmetric perturbation brakes the local plasma rotation to zero. The resulting stationary magnetic island grows rapidly because it loses the stabilizing influence of rotation-induced shielding. Locked modes flatten the local temperature and pressure profiles and frequently trigger major disruptions, particularly at low density where the error-field penetration threshold is smallest.2

Error-field sensitivity scales unfavorably with machine size. The penetration threshold drops roughly as βN−1 ne−1/3, meaning that ITER—with its tight operational windows—requires error fields below δB2,1/BT ∼ 2 × 10−5 at the q = 2 surface.

Error-Field Correction

Because mechanical tolerances can never be made arbitrarily small, all modern tokamaks employ error-field correction (EFC) coils—sets of non-axisymmetric trim coils that generate a compensating field to cancel the intrinsic error. EFC is performed either in feed-forward mode, using coil-current optimization based on magnetic measurements and compass scans, or in real-time feedback using locked-mode detector signals. ITER will use 27 in-vessel EFC coils (9 upper, 9 equatorial, 9 lower) originally designed for ELM control but also tasked with error-field correction to the n = 1 and n = 2 components.3

Measurement and Characterization

The intrinsic error field of a machine is measured by a compass scan: the applied correction field is systematically varied in amplitude and phase, and the critical density for locked-mode onset is recorded. The correction that maximizes the locked-mode-free operating space identifies the optimal EFC. Overlap criteria developed by Park and others decompose the 3D field into components resonant at each rational surface, enabling systematic correction prioritized by the most dangerous harmonic.4

Sources

  1. Buttery, R.J. et al., 'Error field mode studies on JET, COMPASS-D and DIII-D, and implications for ITER,' Nuclear Fusion 39(11), 1827–1835 (1999).
  2. La Haye, R.J. et al., 'Critical error fields for locked mode instability in tokamaks,' Physics of Fluids B 4(7), 2098–2103 (1992).
  3. Park, J.-K. et al., 'Error field correction in ITER,' Nuclear Fusion 48(4), 045006 (2008).
  4. Schaffer, M.J. et al., 'ITER error field correction coil design,' Fusion Engineering and Design 107, 77–86 (2016).

Related

Plasma Rotation Locked Mode Disruption Resistive Wall Mode Magnetic Perturbation