Ellipticity - Revision history

Eldond: Add a figure with simple illustrations of Shafranov shift, elongation, triangularity, and squareness.

2023-03-30T21:47:45Z

Add a figure with simple illustrations of Shafranov shift, elongation, triangularity, and squareness.

← Older revision		Revision as of 23:47, 30 March 2023
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	[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry]]		[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry]]
			[[File:Cross_section_1shift_2elong_3triang_4square.png\|400px\|thumb\|right\|Illustration of the m=1,2,3, and 4 perturbations to a tokamak plasma cross section. Ellipticity/elongation is the m=2 perturbation (second from the left).]]
	The ellipticity (also referred to as elongation<ref name="Luce2013">T.C. Luce, [[doi:10.1088/0741-3335/55/9/095009\|Plasma Phys. Control. Fusion '''55''' (2013) 095009 ]]</ref>) refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].		The ellipticity (also referred to as elongation<ref name="Luce2013">T.C. Luce, [[doi:10.1088/0741-3335/55/9/095009\|Plasma Phys. Control. Fusion '''55''' (2013) 095009 ]]</ref>) refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].

Eldond: Mention typical max kappa value

2023-03-27T17:42:47Z

Mention typical max kappa value

← Older revision		Revision as of 19:42, 27 March 2023
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	Higher elongation is beneficial for fusion performance, but comes with increased vertical instability growth rate and thus increased risk of vertical displacement event (VDE) type disruptions.<ref>D.A. Humphreys, et al., ''Experimental vertical stability studies for ITER performance and design guidance'' [[doi:10.1088/0029-5515/49/11/115003\|Nucl. Fusion '''49''' (2009) 115003]]</ref>		Higher elongation is beneficial for fusion performance, but comes with increased vertical instability growth rate and thus increased risk of vertical displacement event (VDE) type disruptions.<ref>D.A. Humphreys, et al., ''Experimental vertical stability studies for ITER performance and design guidance'' [[doi:10.1088/0029-5515/49/11/115003\|Nucl. Fusion '''49''' (2009) 115003]]</ref>
			Because of vertical stability constraints, <math>\kappa</math> is usually limited to a value close to about 1.8.

	== See also ==		== See also ==

Eldond: Mention the effects of increasing elongation

2023-03-27T17:40:24Z

Mention the effects of increasing elongation

← Older revision		Revision as of 19:40, 27 March 2023
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	The ellipticity is then defined as follows:		The ellipticity is then defined as follows:
	:<math> \kappa = (Z_{max}-Z_{min})/2a</math>		:<math> \kappa = (Z_{max}-Z_{min})/2a</math>

			Higher elongation is beneficial for fusion performance, but comes with increased vertical instability growth rate and thus increased risk of vertical displacement event (VDE) type disruptions.<ref>D.A. Humphreys, et al., ''Experimental vertical stability studies for ITER performance and design guidance'' [[doi:10.1088/0029-5515/49/11/115003\|Nucl. Fusion '''49''' (2009) 115003]]</ref>

	== See also ==		== See also ==

Akoehn: added expression "elongation"

2020-05-29T10:40:08Z

added expression "elongation"

← Older revision		Revision as of 12:40, 29 May 2020
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	[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry]]		[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry]]
	The ellipticity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].		The ellipticity (also referred to as elongation<ref name="Luce2013">T.C. Luce, [[doi:10.1088/0741-3335/55/9/095009\|Plasma Phys. Control. Fusion '''55''' (2013) 095009 ]]</ref>) refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].

	Assuming<ref~~>T.C. Luce, [[doi:10.1088~~/~~0741-3335/55/9/095009\|Plasma Phys. Control. Fusion '''55''' (2013) 095009 ]]</ref~~>:		Assuming<ref name="Luce2013" />:
	* ''R<sub>max</sub>'' is the maximum value of ''R'' along the LCFS or separatrix.		* ''R<sub>max</sub>'' is the maximum value of ''R'' along the LCFS or separatrix.
	* ''R<sub>min</sub>'' is the minimum value of ''R'' along the LCFS or separatrix.		* ''R<sub>min</sub>'' is the minimum value of ''R'' along the LCFS or separatrix.

Admin at 13:15, 17 June 2014

2014-06-17T13:15:38Z

← Older revision		Revision as of 15:15, 17 June 2014
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	[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry]]		[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry]]
	The ellipticity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].		The ellipticity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].
	It is ~~defined as~~ the maximum ~~vertical height~~ of the ~~cross section (2~~''b''~~) divided by~~ the maximum ~~horizontal width~~ of the ~~cross section (2~~''a'').
			Assuming<ref>T.C. Luce, [[doi:10.1088/0741-3335/55/9/095009\|Plasma Phys. Control. Fusion '''55''' (2013) 095009 ]]</ref>:
			* ''R<sub>max</sub>'' is the maximum value of ''R'' along the LCFS or separatrix.
			* ''R<sub>min</sub>'' is the minimum value of ''R'' along the LCFS or separatrix.
			* ''Z<sub>max</sub>'' is the maximum value of ''Z'' along the LCFS or separatrix.
			* ''Z<sub>min</sub>'' is the minimum value of ''Z'' along the LCFS or separatrix.
			* ''a'' is the minor radius of the plasma, defined as ''(R<sub>max</sub> - R<sub>min</sub>)/2''.
			The ellipticity is then defined as follows:
			:<math> \kappa = (Z_{max}-Z_{min})/2a</math>

	== See also ==		== See also ==
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	* [[Toroidal coordinates]]		* [[Toroidal coordinates]]
	* [[Effective plasma radius]]		* [[Effective plasma radius]]

			== References ==
			<references />

Admin at 09:57, 12 June 2014

2014-06-12T09:57:09Z

← Older revision		Revision as of 11:57, 12 June 2014
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			[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry]]
	The ellipticity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].		The ellipticity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].
	It is defined as the maximum vertical height of the cross section (2''b'') divided by the maximum horizontal width of the cross section (2''a'').		It is defined as the maximum vertical height of the cross section (2''b'') divided by the maximum horizontal width of the cross section (2''a'').

Admin at 06:58, 12 June 2014

2014-06-12T06:58:25Z

← Older revision		Revision as of 08:58, 12 June 2014
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	The ellipticity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].		The ellipticity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].
	It is defined as the ~~total~~ vertical height of the cross section (2''b'') divided by the ~~total~~ horizontal width of the cross section (2''a'').		It is defined as the maximum vertical height of the cross section (2''b'') divided by the maximum horizontal width of the cross section (2''a'').

	== See also ==		== See also ==

Admin: /* See also */

2014-06-11T13:44:41Z

Admin: /* See also */

2014-06-11T13:43:37Z

Admin: Created page with "The ellipticity refers to the shape of the poloidal cross section of the Last Closed Flux surface or separatrix of a tokamak. It is defined as the total vertical h..."

2014-06-11T08:19:08Z

Created page with "The ellipticity refers to the shape of the poloidal cross section of the Last Closed Flux surface or separatrix of a tokamak. It is defined as the total vertical h..."

New page

The ellipticity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].
It is defined as the total vertical height of the cross section (2''b'') divided by the total horizontal width of the cross section (2''a'').

== See also ==

* [[Triangularity]]

← Older revision		Revision as of 23:47, 30 March 2023
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	[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry]]		[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry]]
			[[File:Cross_section_1shift_2elong_3triang_4square.png\|400px\|thumb\|right\|Illustration of the m=1,2,3, and 4 perturbations to a tokamak plasma cross section. Ellipticity/elongation is the m=2 perturbation (second from the left).]]
	The ellipticity (also referred to as elongation<ref name="Luce2013">T.C. Luce, [[doi:10.1088/0741-3335/55/9/095009\|Plasma Phys. Control. Fusion '''55''' (2013) 095009 ]]</ref>) refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].		The ellipticity (also referred to as elongation<ref name="Luce2013">T.C. Luce, [[doi:10.1088/0741-3335/55/9/095009\|Plasma Phys. Control. Fusion '''55''' (2013) 095009 ]]</ref>) refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] or [[separatrix]] of a [[tokamak]].

← Older revision		Revision as of 15:44, 11 June 2014
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	* [[Triangularity]]		* [[Triangularity]]
	* [[Toroidal coordinates]]		* [[Toroidal coordinates]]
			* [[Effective plasma radius]]

← Older revision		Revision as of 15:43, 11 June 2014
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	* [[Triangularity]]		* [[Triangularity]]
			* [[Toroidal coordinates]]