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Glossary

Poloidal Field

The magnetic field component that loops the short way around a torus, essential for plasma equilibrium, shaping, and the helical twist that makes confinement work.

Reviewed Last reviewed: 9 Aug 2026 · Category: Glossary

The poloidal field (PF) is the component of the magnetic field in a toroidal confinement device that circulates in the short direction—around the minor cross-section of the plasma. Together with the toroidal field, it creates the helical magnetic field-line structure required for stable plasma confinement. Without a poloidal component, charged-particle drifts would carry the plasma radially outward in a matter of microseconds.

Sources of the Poloidal Field

In a tokamak, the poloidal field has two distinct sources. The first is the toroidal plasma current itself: a large current (typically several megaamperes) driven around the torus inductively by a central solenoid or non-inductively by radiofrequency waves and neutral-beam injection. This current generates a poloidal field inside and around the plasma column. The second source is a set of external poloidal-field coils—large, horizontal rings stacked above and below the midplane—that provide the vertical field needed to keep the plasma in radial equilibrium and control its cross-sectional shape.1

Equilibrium condition: A conducting ring of current in a toroidal field experiences a net outward "hoop force." The external vertical field Bv must supply an inward J × B force to balance it: Bv ≈ (μ0Ip / 4πR)[ln(8R/a) + βp + li/2 − 3/2], where Ip is the plasma current, R the major radius, a the minor radius, βp the poloidal beta, and li the internal inductance.2

Shaping and Control

Modern tokamaks use multiple independently powered PF coils to sculpt the plasma cross-section into elongated, D-shaped, or even negative-triangularity configurations. Elongation raises the achievable current and beta; triangularity affects edge stability and the behavior of edge-localized modes (ELMs). Active feedback on the PF coil currents is required to stabilize the vertically elongated plasma against the axisymmetric vertical instability, with response times on the order of milliseconds.3

Stellarators: A Different Approach

In a stellarator, the poloidal field is generated entirely by external coils—no plasma current is needed. The coils are twisted into complex three-dimensional shapes (or many modular coils are combined) so that the field lines have the required rotational transform built in. This eliminates the disruption risk inherent in current-driven tokamak plasmas but at the cost of far more complex magnet engineering.4

Diagnostics

The poloidal field at the plasma boundary is routinely measured by arrays of magnetic pickup coils and flux loops embedded in the vacuum vessel wall. These measurements, combined with equilibrium reconstruction codes such as EFIT, allow real-time determination of the plasma shape, current profile, and safety factor.

Sources

  1. Wesson, J., Tokamaks, 4th ed., Oxford University Press (2011), §2.4–2.6.
  2. Freidberg, J.P., Ideal MHD, Cambridge University Press (2014), Ch. 6.
  3. Humphreys, D.A. et al., "Novel aspects of plasma control in ITER," Physics of Plasmas 22, 021806 (2015).
  4. Helander, P. et al., "Stellarator and tokamak plasmas: a comparison," Plasma Physics and Controlled Fusion 54, 124009 (2012).

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