Ideal-Wall and No-Wall Beta Limits

The two pressure ceilings set by external kink stability, with and without a perfectly conducting boundary.

The Kink-Limited Ceiling

Beyond internal instabilities, a tokamak is limited by the external kink mode, a global current- and pressure-driven displacement of the whole plasma column. Its stability depends strongly on the surrounding conducting structure. Two limiting cases bracket reality: no wall (the vacuum extends to infinity) and an ideal wall (a perfect conductor at a finite radius).

No-Wall Limit

With no conducting wall, the external kink sets the no-wall beta limit. Below this normalized pressure the plasma is stable to the ideal external kink even in the absence of any wall. It is the conservative ceiling and is often close to the Troyon-scaling value for standard profiles. Operating below it requires no active stabilization of the kink.

Ideal-Wall Limit

A perfectly conducting wall close to the plasma raises the ceiling: image currents in the wall oppose the kink displacement and stabilize it up to the higher ideal-wall beta limit. Real walls are resistive, not ideal, so between the two limits the plasma is unstable on the slow resistive-wall timescale to the resistive-wall mode, which requires active feedback or rotation to stabilize.

Relevance

The gap between the no-wall and ideal-wall limits is the operating window that advanced scenarios try to exploit, trading higher pressure for the need to control the resistive-wall mode. For the Hyperion breeder concept, wall proximity, profile shaping, and rotation are design levers evaluated against both limits in stability modeling; the machine is a simulation study, and no beta value is a measured hardware result.