The Greenwald Limit in Control

How the empirical density limit constrains real-time density control and why staying below it is a scenario design requirement.

The empirical limit

The Greenwald density limit is an empirical scaling: n_G = I_p / (pi a^2), with plasma current I_p in mega-amperes and minor radius a in meters, giving a density in units of 10^20 particles per cubic meter. Operating near or above this line-averaged density strongly correlates with confinement degradation and density-limit disruptions across many tokamaks.

Why it is a control constraint

The limit ties maximum density to plasma current, so as current ramps the allowed density changes with it. A density-control loop must track a reference that stays a safe fraction of n_G at all times, not just at flat-top. During current ramp-down, the falling current lowers the limit, which is a classic setting for density-limit disruptions if fueling is not reduced in step.

Greenwald fraction as a live signal

Control systems compute the Greenwald fraction f_G = n / n_G continuously from the real-time current and density estimates. f_G is a first-class proximity-to-limit signal: as it rises toward one, the scenario layer and disruption predictor become conservative, reducing fueling or backing off the plan before the limit bites.

Not a hard wall

The Greenwald limit is empirical and regime-dependent, not a fundamental cutoff; some scenarios exceed it transiently with strong core fueling and shaping. But it is reliable enough to treat as an operational boundary. Prudent control respects it with margin rather than betting on the exceptions.

Interaction with detachment

The density limit is entangled with edge and divertor physics: high edge density drives radiation and detachment, which can trigger the disruptive chain. So density control, radiated-power control, and detachment control are coupled problems, coordinated so that pushing one does not silently violate another's limit.