error field is a small departure from perfect axisymmetry in a tokamak's magnetic field, left by imperfect coil winding and alignment, that can penetrate the 📝plasma, tear open a magnetic island, and lock it to the wall.
A 📝Tokamak's confining field is designed to look identical at every toroidal angle, and real hardware never does. Millimetre-scale misalignments in the 📝toroidal field coils and 📝poloidal field coils, together with asymmetric joints and feeders, leave a residual non-axisymmetric field, conventionally decomposed into helical components labelled by poloidal and toroidal mode numbers m/n. Where a component's helicity matches the plasma's own — an n = 1, m = 2 field at the surface where the 📝safety factor (q) equals 2 — the perturbation resonates. 📝plasma rotation normally shields that surface, but below a threshold in density and rotation the field penetrates, opens a 📝magnetic island by the same mechanism as a 📝tearing mode, and the island stops rotating. That locked mode degrades confinement, brakes the plasma further, and frequently ends in 📝disruption — a leading termination path at low density and during current 📝ramp-up.
The tolerance is measured rather than theoretical. Buttery and co-authors compared error-field penetration thresholds on 📝JET, COMPASS-D and 📝DIII-D in 1999 and extrapolated to 📝ITER: the JET data give a threshold 2/1 field near 1.25 × 10⁻⁴ of the 📝toroidal field at ITER reference parameters, the DIII-D data near 2.0 × 10⁻⁴. Correction coils cancel what assembly cannot. An error field is not a 📝resonant magnetic perturbation (RMP) — the same kind of non-axisymmetric field, applied deliberately — nor a 📝neoclassical tearing mode, whose island is sustained by lost 📝bootstrap current rather than driven from outside.
For machines that do not yet exist, the figure is a specification. 📝Nils Leuthold's 2026 📝magnetohydrodynamics paper places 📝ARC's error-field tolerance between 📝SPARC's and ITER's by scaling, and specifies correction coils that would also serve to suppress 📝edge localized mode (ELM)s — modelling, for a plant that has not been built.