Greenwald limit

The Greenwald is a operational limit for the density in magnetic confinement devices:

$n_{G}={\frac {I_{p}}{\pi a^{2}}}$

where n_G is the density in 10¹⁰ m^-3, I_p the plasma current in MA, and a the minor radius in m.

In tokamaks (and RFPs), exceeding the Greenwald limit typically leads to a disruption, although sometimes the limit can be crossed without deleterious effects (especially with peaked density profiles). Stellarators can typically exceed the Greenwald limit by factors of 2 to 5, or more (replacing I_p by an equivalent current corresponding to the magnetic field).

The mechanism behind this phenomenological limit is not understood, but probably associated with edge gradient limits.