The total magnetic field threading through a surface — the quantity that governs induction, confinement geometry, and every volt of transformer action in a tokamak
Magnetic flux, denoted ΦB, quantifies the total amount of magnetic field passing through a given surface. Formally it is the surface integral of the magnetic field vector B over an area A: ΦB = ∫B·dA. The SI unit is the weber (Wb), equivalent to one volt-second. A uniform field of one tesla threading one square metre produces exactly one weber of flux.[1]
Flux is a scalar quantity, but its sign carries physical meaning: it indicates which side of the surface the net field emerges from. When the field is uniform and perpendicular to the surface the expression simplifies to ΦB = BA, but in most plasma devices the field varies spatially, making the full integral essential.
In a tokamak the central solenoid stores magnetic flux and then swings it to drive the toroidal plasma current by transformer action. The total available flux swing — measured in volt-seconds — sets an upper bound on how long an inductively driven plasma discharge can last. Devices pursuing steady-state operation must supplement the solenoid with non-inductive current-drive methods precisely because the solenoid’s flux is finite.[2]
Poloidal flux surfaces, defined as contours of constant poloidal magnetic flux ψ, form the nested surfaces on which plasma pressure and current density are approximately constant. These flux surfaces are the backbone of magnetohydrodynamic (MHD) equilibrium theory and determine the shape, elongation, and triangularity of the plasma cross-section.[3]
Flux loops — simple wire loops placed at known locations around the vacuum vessel — measure the time derivative of magnetic flux via Faraday’s law. Integrating the induced voltage over time recovers the flux itself. Arrays of flux loops, combined with magnetic pickup coils, feed the real-time equilibrium reconstruction codes (such as EFIT) that operators rely on to control plasma shape and position during a discharge.[4]
Because magnetic flux is conserved in a perfectly conducting plasma, it also underpins the concept of “frozen-in” flux in ideal MHD: field lines move with the plasma as though they were embedded in it, a simplification that breaks down only where resistivity or reconnection becomes important.