# Greenwald limit

The Greenwald limit is an operational limit for the density in magnetic confinement devices: [1]

$n_G = \frac{I_p}{\pi a^2}$

where nG is the density in 1020 m-3, Ip the plasma current in MA, and a the minor radius in m.

In tokamaks (and Reversed Field Pinches[2]), 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 Ip by an equivalent current corresponding to the magnetic field).

The mechanism behind this phenomenological limit is not fully understood, but probably associated with edge gradient limits. Recently, an explanation based on the formation of magnetic islands was proposed. [3]