The field component that wraps the short way around a tokamak cross-section — generated by the plasma current itself and essential for twisting field lines into confining helices
In a tokamak two orthogonal field components combine to confine the plasma. The toroidal field, produced by external coils, runs the long way around the torus. The poloidal field, denoted Bθ, circles the short way around each plasma cross-section. By Ampère’s law the poloidal field is generated primarily by the toroidal plasma current flowing through the plasma column: at a distance r from the magnetic axis the poloidal field strength is approximately Bθ = μ0I(r)/(2πr), where I(r) is the current enclosed within that radius.[1]
External poloidal field coils also contribute, principally to shape and position the plasma (elongation, triangularity, vertical stability) rather than to create the primary confining twist.
A purely toroidal field cannot confine a plasma. The curvature and gradient of such a field cause systematic vertical drifts that separate ions and electrons, producing an electric field that drives the plasma radially outward. Adding a poloidal field component twists the field lines into helices so that each field line samples both the inboard and outboard sides of the torus. This averaging cancels the charge separation and restores confinement. The degree of twist is parameterised by the safety factor q, defined as the number of toroidal transits a field line makes for each poloidal transit.[2]
Contours of constant poloidal flux ψ define the nested flux surfaces on which the equilibrium quantities — pressure, current density, safety factor — are approximately constant. The Grad–Shafranov equation governs the two-dimensional MHD equilibrium by balancing the pressure gradient and the magnetic forces, with the poloidal flux function as the central unknown. Solving this equation is fundamental to designing the coil sets and predicting the plasma shape of any tokamak.[3]
The poloidal field is measured outside the plasma by arrays of magnetic pickup coils (Mirnov coils) mounted on the vacuum vessel wall. Internal poloidal field measurements rely on the motional Stark effect or Faraday rotation polarimetry, which resolve the local pitch angle of the total magnetic field and thereby separate the poloidal and toroidal components.[4]