Greenwald limit - Revision history

Admin at 05:18, 23 October 2024

2024-10-23T05:18:09Z

← Older revision		Revision as of 07:18, 23 October 2024
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	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.		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.
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	== See also ==		== See also ==

	[[Beta]]		* [[Sudo limit]]
			* [[Beta]]

	== References ==		== References ==
	<references />		<references />

Esolano at 08:42, 9 July 2020

2020-07-09T08:42:52Z

← Older revision		Revision as of 10:42, 9 July 2020
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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).

Admin at 10:46, 30 October 2015

2015-10-30T10:46:05Z

← Older revision		Revision as of 12:46, 30 October 2015
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	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>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>		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 ==		== See also ==

Admin at 10:40, 30 October 2015

2015-10-30T10:40:59Z

← Older revision		Revision as of 12:40, 30 October 2015
Line 10:		Line 10:
	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>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>		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>

			== See also ==

			[[Beta]]

	== References ==		== References ==
	<references />		<references />

Admin: Updated reference links

2015-10-30T10:18:59Z

Updated reference links

← Older revision		Revision as of 12:18, 30 October 2015
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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>
Line 6:		Line 6:
	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 ==
	<references />		<references />

Admin at 06:46, 17 July 2012

2012-07-17T06:46:08Z

← Older revision		Revision as of 08:46, 17 July 2012
Line 6:		Line 6:
	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 ~~tokamaks~~ (and ~~RFPs~~), 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). ~~Stellarators~~ 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>[[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).

	The mechanism behind this phenomenological limit is not 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>[[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>

	~~== See also ==~~

	* High density limit in [[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>

	== References ==		== References ==
	<references />		<references />

Admin at 06:42, 17 July 2012

2012-07-17T06:42:40Z

← Older revision		Revision as of 08:42, 17 July 2012
Line 10:		Line 10:
	The mechanism behind this phenomenological limit is not understood, but probably associated with edge gradient limits.		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. <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>[[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>

			== See also ==

			* High density limit in [[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>

	== References ==		== References ==
	<references />		<references />

Admin at 12:14, 11 July 2012

2012-07-11T12:14:07Z

← Older revision		Revision as of 14:14, 11 July 2012
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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>[~~http~~:~~//dx.doi.org/~~10.1088/0741-3335/44/8/201 M. Greenwald, ''Density limits in toroidal plasmas'', Plasma Phys. Control. Fusion '''44''' (2002) R27-R53]</ref>		<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>

	:<math>n_G = \frac{I_p}{\pi a^2}</math>		:<math>n_G = \frac{I_p}{\pi a^2}</math>
Line 9:		Line 9:

	The mechanism behind this phenomenological limit is not understood, but probably associated with edge gradient limits.		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. <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>

	== References ==		== References ==
	<references />		<references />

Admin: Reverted edits by 193.4.57.122 (Talk) to last revision by Admin

2011-05-18T17:34:07Z

Reverted edits by 193.4.57.122 (Talk) to last revision by Admin

← Older revision		Revision as of 19:34, 18 May 2011
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	~~HHIS~~ I ~~shulod have thought~~ of ~~that!~~		The Greenwald limit is an operational limit for the density in magnetic confinement devices:
			<ref>[http://dx.doi.org/10.1088/0741-3335/44/8/201 M. Greenwald, ''Density limits in toroidal plasmas'', Plasma Phys. Control. Fusion '''44''' (2002) R27-R53]</ref>

			:<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.

			In tokamaks (and RFPs), 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). Stellarators 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 understood, but probably associated with edge gradient limits.

			== References ==
			<references />

193.4.57.122: VwvDUISWXhVtNBjwst

2011-05-18T07:59:33Z

VwvDUISWXhVtNBjwst

← Older revision		Revision as of 09:59, 18 May 2011
Line 1:		Line 1:
	~~The Greenwald limit is an operational limit for the density in magnetic confinement devices:~~		HHIS I shulod have thought of that!
	~~<ref>[http://dx.doi.org/10.1088/0741-3335/44/8/201 M. Greenwald, ''Density limits in toroidal plasmas'', Plasma Phys. Control. Fusion '''44''' (2002) R27-R53]</ref>~~

	~~:<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.~~

	In tokamaks (and RFPs), 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). Stellarators 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 understood, but probably associated with edge gradient limits.~~

	~~== References ==~~
	~~<references />~~