Magnetic Flux Surfaces
The nested toroidal surfaces traced by field lines, on which pressure and temperature are constant.
Nested surfaces
In a well-confined toroidal plasma, magnetic field lines lie on nested toroidal surfaces of constant poloidal flux psi. Because heat and particles flow far faster along field lines than across them, pressure, temperature, and density are nearly constant on each surface. Flux surfaces are therefore the natural coordinate for describing a confined plasma.
Flux-surface labels
Any monotonic function of psi can label the surfaces; common choices are the normalized poloidal flux, the toroidal flux, or the volume enclosed. Transport equations are written as one-dimensional equations in such a label after averaging over each surface, which is why toroidal confinement reduces to essentially radial transport.
When surfaces break
- At rational surfaces, resonant perturbations can tear field lines into magnetic islands
- Overlapping islands destroy surfaces and create stochastic (chaotic) field regions
- The last closed flux surface (separatrix or limiter surface) bounds the confined plasma
The magnetic axis and separatrix
The innermost degenerate surface is the magnetic axis; the outermost closed surface is the separatrix, which in a divertor configuration passes through an X-point. Outside it, field lines strike material surfaces in the scrape-off layer. The quality of the nested-surface structure directly determines confinement quality.
How they are found
Flux surfaces are contours of psi from the Grad-Shafranov equilibrium. Field-line tracing and Poincare plots reveal whether surfaces are intact or broken. Preserving good flux surfaces, especially avoiding island overlap, is central to confinement in every magnetic device, including the Hyperion breeder spherical tokamak, whose strong shaping and negative triangularity are defined relative to these surfaces.