Beta-Limit Control
Keeping the plasma pressure below the stability ceiling set by pressure-driven magnetohydrodynamic modes.
What beta measures
Beta is the ratio of plasma pressure to magnetic pressure - a measure of how efficiently the magnetic field confines the plasma. Higher beta means more fusion power for a given field, so it is desirable, but pressure-driven MHD instabilities set a ceiling. Operating near that ceiling maximizes performance and risk together, which is why beta needs active control.
The normalized limit
The stability ceiling is expressed through normalized beta, beta_N, which folds out the trivial dependence on current, field, and size. Empirically, beta_N above a critical value (the Troyon-type limit, around 3-4 in conventional tokamaks, higher in some configurations) triggers pressure-driven modes. Beta-limit control keeps beta_N below its regime-specific ceiling with margin.
The instabilities involved
- Ideal external kink modes at the beta ceiling
- Resistive-wall modes when a wall slows the kink
- Ballooning modes driven by pressure gradient and curvature
- Neoclassical tearing modes seeded at high beta
The control levers
Beta is regulated by controlling heating power and fueling, which set the pressure. When beta approaches the limit, the controller reduces heating or backs off density to lower pressure. Because some high-beta modes are wall-stabilizable, beta-limit control works together with resistive-wall-mode control and rotation control to safely access the region above the no-wall limit.
A proximity signal
Beta_N relative to its limit is a live proximity-to-instability signal, like the Greenwald fraction for density. It feeds the disruption predictor and avoidance logic: as beta_N nears the ceiling, the stack becomes conservative, trimming pressure before a pressure-driven mode can grow. Staying below the limit with margin is safer than chasing the last increment of performance.