Greenwald limit: Difference between revisions

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The Greenwald limit is an operational limit for the density in magnetic confinement devices:
The Greenwald limit is an operational limit for the density in magnetic confinement devices:
<ref>[[doi:10.1088/0741-3335/44/8/201|M. Greenwald, ''Density limits in toroidal plasmas'', Plasma Phys. Control. Fusion '''44''' (2002) R27-R53]]</ref>
<ref>M. Greenwald, ''Density limits in toroidal plasmas'', [[doi:10.1088/0741-3335/44/8/201|Plasma Phys. Control. Fusion '''44''' (2002) R27-R53]]</ref>


:<math>n_G = \frac{I_p}{\pi a^2}</math>
:<math>n_G = \frac{I_p}{\pi a^2}</math>
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where ''n<sub>G</sub>'' is the density in 10<sup>20</sup> m<sup>-3</sup>, ''I<sub>p</sub>'' the plasma current in MA, and ''a'' the minor radius in m.  
where ''n<sub>G</sub>'' is the density in 10<sup>20</sup> m<sup>-3</sup>, ''I<sub>p</sub>'' the plasma current in MA, and ''a'' the minor radius in m.  


In [[tokamak]]s (and [[Reversed Field Pinch]]es<ref>[[doi:10.1063/1.3063060|M.E. Puiatti, P. Scarin, G. Spizzo, et al., ''High density limit in reversed field pinches'', Phys. Plasmas '''16''' (2009) 012505]]</ref>), exceeding the Greenwald limit typically leads to a [[Disruption|disruption]], although sometimes the limit can be crossed without deleterious effects (especially with peaked density profiles). [[Stellarator]]s can typically exceed the Greenwald limit by factors of 2 to 5, or more (replacing ''I<sub>p</sub>'' by an equivalent current corresponding to the magnetic field).
In [[tokamak]]s (and [[Reversed Field Pinch]]es<ref>M.E. Puiatti, P. Scarin, G. Spizzo, et al., ''High density limit in reversed field pinches'', [[doi:10.1063/1.3063060|Phys. Plasmas '''16''' (2009) 012505]]</ref>), exceeding the Greenwald limit typically leads to a [[Disruption|disruption]], although sometimes the limit can be crossed without deleterious effects (especially with peaked density profiles). [[Stellarator]]s can typically exceed the Greenwald limit by factors of 2 to 5, or more (replacing ''I<sub>p</sub>'' 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.
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 island was proposed. <ref>[[doi:10.1103/PhysRevLett.108.165004|D.A. Gates and L. Delgado-Aparicio, ''Origin of Tokamak Density Limit Scalings'', Phys. Rev. Lett. '''108''' (2012) 165004]]</ref>
Recently, an explanation based on the formation of magnetic island was proposed. <ref>D.A. Gates and L. Delgado-Aparicio, ''Origin of Tokamak Density Limit Scalings'', [[doi:10.1103/PhysRevLett.108.165004|Phys. Rev. Lett. '''108''' (2012) 165004]]</ref>


== References ==
== References ==
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