Flux surface

Since the magnetic field is divergence-free (and magnetic nulls are undesirable), the Poincare-Hopf theorem implies that such a surface must be either a torus, or a knot.

Flux surfaces can either be rational or irrational, depending on the behavior of magnetic field lines on the flux surface.

Rational surfaces have magnetic field lines are which are periodic; the magnetic field line closes back on itself.

Conversely irrational surfaces have magnetic field lines which do not close back on themselves, and a magnetic field line traces out the entire flux surface (the magnetic field line comes arbitrarily close to each point on the flux surface).

[2][3] Flux surfaces are not guaranteed to exist; the magnetic field line can fill a volume chaotically.

A part of a flux surface (yellow), and the magnetic axis (black). The magnetic flux passing through the red and blue surface is called the poloidal and toroidal flux, respectively. There is furthermore a rational magnetic field line (green) on the flux surface.