magnetic flux surface is one of the nested, doughnut-shaped surfaces traced out by the magnetic field lines inside a confinement device, on which plasma pressure and temperature equalize.
The picture to hold is an onion bent into a torus. In a well-confined 📝plasma, each helical field line winds around and around the torus without ever leaving an invisible surface, and those surfaces nest inside one another from the hot core out to the edge. Because charged particles stream freely along field lines but cross them only slowly, anything that equalizes quickly — pressure, temperature, density — becomes effectively constant on each surface. The plasma's profile is then a stack of values, one per surface, and confinement quality is the question of how slowly heat leaks from one onion layer to the next.
The idealization is also the failure map. Where field lines reconnect, a 📝magnetic island tears open a flux surface and short-circuits the layers it spans, letting heat skip across; where surfaces are destroyed wholesale, transport becomes rapid. The outermost intact surface — the separatrix in a diverted 📝Tokamak — marks the boundary of confinement itself: inside it, field lines close on themselves and hold plasma; beyond it, they run into material surfaces. Designing and controlling the shape of the flux surfaces, from the near-circular core to the shaped edge, is the working geometry of every magnetic confinement device.