The Resistive-Wall Mode

A slow external kink that grows on the wall's resistive timescale in the gap between the no-wall and ideal-wall limits.

The Mode

The resistive-wall mode is the external kink modified by a resistive, rather than perfectly conducting, wall. A perfect wall would fully stabilize the kink up to the ideal-wall beta limit; a resistive wall only delays it. In the beta range between the no-wall and ideal-wall limits, the mode cannot be fully stabilized and grows slowly, on the timescale of magnetic flux diffusion through the wall rather than the fast Alfven time.

Growth Timescale

Because the instability must push flux through the resistive wall to grow, its growth rate is set by the wall's resistive time, which is milliseconds to seconds, far slower than an ideal kink. This slowness is both a curse and an opportunity: the mode is persistent and will terminate a high-beta discharge if unchecked, but its leisurely growth makes it amenable to active feedback control.

Stabilization

Two mechanisms suppress the resistive-wall mode. Plasma rotation above a critical fraction of the Alfven speed couples the mode to the stabilizing effect of the wall through kinetic dissipation, effectively converting it back toward a stable state. Alternatively, active feedback coils detect the mode's field and drive currents to oppose it. Real scenarios use a combination of rotation and feedback.

Relevance

Accessing the high-beta region above the no-wall limit, where fusion performance is best, requires controlling the resistive-wall mode. For the Hyperion breeder concept, wall proximity, achievable rotation, and feedback capability are design-stage levers evaluated against the no-wall and ideal-wall limits; all such analysis is computational for a simulated device.