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Glossary

Toroidal Field

The magnetic field component that wraps the long way around a torus, confining plasma against radial escape and setting the stage for stable fusion conditions.

Reviewed Last reviewed: 9 Aug 2026 · Category: Glossary

In any toroidal magnetic confinement device—tokamak, stellarator, or spherical torus—the toroidal field (TF) is the component of the magnetic field directed the long way around the doughnut-shaped vacuum vessel. It is the dominant contributor to plasma confinement in most designs and is generated by a set of discrete coils arrayed poloidally around the torus.

How It Works

Each toroidal-field coil carries a large current that produces a magnetic field looping through the bore of the torus. Because the coils are discrete rather than continuous, the field is slightly stronger on the inboard (high-field) side and weaker on the outboard (low-field) side. This 1/R dependence—where R is the major-radial distance from the machine axis—is a fundamental property of toroidal geometry and drives several important drift effects on charged particles.

Key relation: For a set of N coils each carrying current I, the vacuum toroidal field at major radius R is BT = μ0NI / (2πR). In ITER, the 18 superconducting TF coils produce a peak on-axis field of 5.3 T at R = 6.2 m.1

Engineering Considerations

The toroidal-field magnets are typically the largest, heaviest, and most expensive components of a fusion device. They must withstand enormous electromagnetic forces—the centering force that pulls each coil inward toward the machine axis, and the overturning torques generated during plasma disruptions. Modern designs use niobium-tin (Nb3Sn) or rare-earth barium copper oxide (REBCO) high-temperature superconductors to reach fields above 12 T on the conductor, enabling more compact machines.2

Role in Confinement

The toroidal field alone cannot confine a plasma in equilibrium; a poloidal field component is also required to create nested, helical field lines that average out particle drifts. However, the strength of the toroidal field directly sets the achievable plasma pressure through the beta limit: β = 2μ0⟨p⟩ / B2. Higher toroidal fields allow higher absolute pressures at the same normalized beta, which is why high-field approaches—pioneered by MIT's SPARC and Commonwealth Fusion Systems' ARC—have attracted intense interest.3

Scaling insight: Fusion power density scales as B4 at fixed beta, meaning a doubling of the toroidal field yields roughly a 16-fold increase in volumetric power density.4

Ripple and Error Fields

Because real TF coil sets have a finite number of coils, the field exhibits periodic variation known as toroidal-field ripple. Ripple causes enhanced fast-ion losses and can degrade confinement. Designers minimize ripple by increasing the number of coils or adding ferromagnetic inserts between coils, as done in JT-60SA.

Sources

  1. ITER Organization, "Toroidal Field Coils," iter.org/mach/magnets/toroidal-field-coils (2024).
  2. Bromberg, J.L., Fusion: Science, Politics, and the Invention of a New Energy Source, MIT Press (1982), Ch. 4.
  3. Creely, A.J. et al., "Overview of the SPARC tokamak," Journal of Plasma Physics 86, 865860502 (2020).
  4. Wesson, J., Tokamaks, 4th ed., Oxford University Press (2011), §2.3.

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