Greenwald limit: Difference between revisions
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:<math>n_G = \frac{I_p}{\pi a^2}</math> | :<math>n_G = \frac{I_p}{\pi a^2}</math> | ||
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 line averaged 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>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). | 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) - See [[Sudo limit]]. | ||
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 | Recently, an explanation based on the formation of magnetic islands 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> | ||
== See also == | |||
* [[Sudo limit]] | |||
* [[Beta]] | |||
== References == | == References == | ||
<references /> | <references /> | ||
Latest revision as of 06:18, 23 October 2024
The Greenwald limit is an operational limit for the density in magnetic confinement devices: [1]
where nG is the line averaged 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) - See Sudo limit.
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