Greenwald limit

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

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

where n_G is the density in 10²⁰ 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. Recently, an explanation based on the formation of magnetic island was proposed.