# 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 *n _{G}* is the density in 10

^{20}m

^{-3},

*I*the plasma current in MA, and

_{p}*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 *I _{p}* 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]}

## See also

## References

- ↑ M. Greenwald,
*Density limits in toroidal plasmas*, Plasma Phys. Control. Fusion**44**(2002) R27-R53 - ↑ M.E. Puiatti, P. Scarin, G. Spizzo, et al.,
*High density limit in reversed field pinches*, Phys. Plasmas**16**(2009) 012505 - ↑ D.A. Gates and L. Delgado-Aparicio,
*Origin of Tokamak Density Limit Scalings*, Phys. Rev. Lett.**108**(2012) 165004