Triangularity - Revision history

Eldond: Add simple illustration of shift, elongation, triangularity, and squareness

2023-03-30T21:50:12Z

Add simple illustration of shift, elongation, triangularity, and squareness

← Older revision		Revision as of 23:50, 30 March 2023
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	[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry, including separatrix]]		[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry, including separatrix]]
			[[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. Triangularity is the m=3 perturbation.]]
	The triangularity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] (LCFS) or [[separatrix]] of a [[tokamak]].		The triangularity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] (LCFS) 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>T.C. Luce, [[doi:10.1088/0741-3335/55/9/095009\|Plasma Phys. Control. Fusion '''55''' (2013) 095009 ]]</ref>:

Eldond: Mention how triangularity affects the plasma and mention negative triangularity.

2023-03-28T05:35:51Z

Mention how triangularity affects the plasma and mention negative triangularity.

← Older revision		Revision as of 07:35, 28 March 2023
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	and similar for δ<sub>lower</sub>.		and similar for δ<sub>lower</sub>.
	The overall triangularity is defined as the mean of δ<sub>upper</sub> and δ<sub>lower</sub>.		The overall triangularity is defined as the mean of δ<sub>upper</sub> and δ<sub>lower</sub>.

			Triangularity, especially the triangularity opposite the dominant X-point (so upper triangularity for a lower null plasma), influences the stability and character of the [[pedestal]] and [[Edge Localized Modes\|ELMs]].<ref>[[doi:10.1088/0741-3335/42/5A/319\|T.H. Osborne, et al., Plasma Phys. Control. Fusion '''42''' (2000) A175]]</ref>

			Some devices (TCV and DIII-D) can form plasma cross sections with negative triangularity (the X-points are pushed to larger <math>R</math> than the center of the plasma), which makes H-mode difficult or impossible to access but improves performance of the L-mode.<ref>[[doi:10.1088/1741-4326/abdb95\|W. Han, et al., Nucl. Fusion '''61''' (2021) 034003]]</ref>

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

Admin at 13:24, 17 June 2014

2014-06-17T13:24:00Z

← Older revision		Revision as of 15:24, 17 June 2014
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	* ''R<sub>geo</sub>'' is the geometric major radius, defined as ''(R<sub>max</sub> + R<sub>min</sub>)/2''.		* ''R<sub>geo</sub>'' is the geometric major radius, defined as ''(R<sub>max</sub> + R<sub>min</sub>)/2''.
	* ''a'' is the minor radius of the plasma, defined as ''(R<sub>max</sub> - R<sub>min</sub>)/2''.		* ''a'' is the minor radius of the plasma, defined as ''(R<sub>max</sub> - R<sub>min</sub>)/2''.
	* ''R<sub>upper</sub>'' is the major radius of the highest vertical point of the LCFS.		* ''R<sub>upper</sub>'' is the major radius of the highest vertical point of the LCFS or separatrix.
	* ''R<sub>lower</sub>'' is the major radius of the lowest vertical point of the LCFS.		* ''R<sub>lower</sub>'' is the major radius of the lowest vertical point of the LCFS or separatrix.
	The upper triangularity is then defined as follows:		The upper triangularity is then defined as follows:
	:<math> \delta_{upper} = (R_{geo}-R_{upper})/a</math>		:<math> \delta_{upper} = (R_{geo}-R_{upper})/a</math>

Admin at 13:23, 17 June 2014

2014-06-17T13:23:38Z

← Older revision		Revision as of 15:23, 17 June 2014
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	* ''R<sub>lower</sub>'' is the major radius of the lowest vertical point of the LCFS.		* ''R<sub>lower</sub>'' is the major radius of the lowest vertical point of the LCFS.
	The upper triangularity is then defined as follows:		The upper triangularity is then defined as follows:
	:<math> \delta_{upper} = (~~R_0~~-R_{upper})/a</math>		:<math> \delta_{upper} = (R_{geo}-R_{upper})/a</math>
	and similar for δ<sub>lower</sub>.		and similar for δ<sub>lower</sub>.
	The overall triangularity is defined as the mean of δ<sub>upper</sub> and δ<sub>lower</sub>.		The overall triangularity is defined as the mean of δ<sub>upper</sub> and δ<sub>lower</sub>.

Admin at 13:15, 17 June 2014

2014-06-17T13:15:54Z

← Older revision		Revision as of 15:15, 17 June 2014
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	* ''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.
	* ''R<sub>geo</sub>'' is the geometric major radius, defined as ''(R<sub>max</sub> + R<sub>min</sub>)/2''.		* ''R<sub>geo</sub>'' is the geometric major radius, defined as ''(R<sub>max</sub> + R<sub>min</sub>)/2''.
	* ''a'' is the minor radius of the plasma, defined ''(R<sub>max</sub> - R<sub>min</sub>)/2''.		* ''a'' is the minor radius of the plasma, defined as ''(R<sub>max</sub> - R<sub>min</sub>)/2''.
	* ''R<sub>upper</sub>'' is the major radius of the highest vertical point of the LCFS.		* ''R<sub>upper</sub>'' is the major radius of the highest vertical point of the LCFS.
	* ''R<sub>lower</sub>'' is the major radius of the lowest vertical point of the LCFS.		* ''R<sub>lower</sub>'' is the major radius of the lowest vertical point of the LCFS.

Admin at 13:11, 17 June 2014

2014-06-17T13:11:32Z

← Older revision		Revision as of 15:11, 17 June 2014
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	[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry, including separatrix]]		[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry, including separatrix]]
	The triangularity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] (LCFS) or [[separatrix]] of a [[tokamak]].		The triangularity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] (LCFS) or [[separatrix]] of a [[tokamak]].
	Assuming:		Assuming<ref>T.C. Luce, [[doi:10.1088/0741-3335/55/9/095009\|Plasma Phys. Control. Fusion '''55''' (2013) 095009 ]]</ref>:
	* ''R<sub>0</sub>'' is the ~~major radius~~ of the ~~midpoint of~~ the ~~2 intersections~~ of the LCFS or separatrix ~~with~~ the ~~equatorial plane (~~''Z'' ~~= 0)~~.		* ''R<sub>max</sub>'' is the maximum value of ''R'' along the LCFS or separatrix.
	* ''a'' is the minor radius of the plasma, defined ~~as the radial difference between the 2 intersections of the LCFS or separatrix with the equatorial plane (~~''Z'' ~~= 0), divided by 2~~.		* ''R<sub>min</sub>'' is the minimum value of ''R'' along the LCFS or separatrix.
			* ''R<sub>geo</sub>'' is the geometric major radius, defined as ''(R<sub>max</sub> + R<sub>min</sub>)/2''.
			* ''a'' is the minor radius of the plasma, defined ''(R<sub>max</sub> - R<sub>min</sub>)/2''.
	* ''R<sub>upper</sub>'' is the major radius of the highest vertical point of the LCFS.		* ''R<sub>upper</sub>'' is the major radius of the highest vertical point of the LCFS.
	* ''R<sub>lower</sub>'' is the major radius of the lowest vertical point of the LCFS.		* ''R<sub>lower</sub>'' is the major radius of the lowest vertical point of the LCFS.
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	* [[Toroidal coordinates]]		* [[Toroidal coordinates]]
	* [[Effective plasma radius]]		* [[Effective plasma radius]]

			== References ==
			<references />

Admin at 10:00, 12 June 2014

2014-06-12T10:00:48Z

← Older revision		Revision as of 12:00, 12 June 2014
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	* ''R<sub>0</sub>'' is the major radius of the midpoint of the 2 intersections of the LCFS or separatrix with the equatorial plane (''Z'' = 0).		* ''R<sub>0</sub>'' is the major radius of the midpoint of the 2 intersections of the LCFS or separatrix with the equatorial plane (''Z'' = 0).
	* ''a'' is the minor radius of the plasma, defined as the radial difference between the 2 intersections of the LCFS or separatrix with the equatorial plane (''Z'' = 0), divided by 2.		* ''a'' is the minor radius of the plasma, defined as the radial difference between the 2 intersections of the LCFS or separatrix with the equatorial plane (''Z'' = 0), divided by 2.
	* ''R<sub>upper</sub>'' is the major radius ~~of the upper X-point (in case it exists) or~~ of the highest vertical point of the LCFS.		* ''R<sub>upper</sub>'' is the major radius of the highest vertical point of the LCFS.
	* ''R<sub>lower</sub>'' is the major radius ~~of the lower X-point (in case it exists) or~~ of the lowest vertical point of the LCFS.		* ''R<sub>lower</sub>'' is the major radius of the lowest vertical point of the LCFS.
	The upper triangularity is then defined as follows:		The upper triangularity is then defined as follows:
	:<math> \delta_{upper} = (R_0-R_{upper})/a</math>		:<math> \delta_{upper} = (R_0-R_{upper})/a</math>

Admin at 09:59, 12 June 2014

2014-06-12T09:59:44Z

← Older revision		Revision as of 11:59, 12 June 2014
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			[[File:Geometry.png\|400px\|thumb\|right\|Sketch of tokamak geometry, including separatrix]]
	The triangularity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] (LCFS) or [[separatrix]] of a [[tokamak]].		The triangularity refers to the shape of the poloidal cross section of the Last Closed [[Flux surface]] (LCFS) or [[separatrix]] of a [[tokamak]].
	Assuming:		Assuming:
	* ''R<sub>0</sub>'' is the major radius of the midpoint of the 2 intersections of the LCFS or separatrix with the equatorial plane (''Z'' = 0).		* ''R<sub>0</sub>'' is the major radius of the midpoint of the 2 intersections of the LCFS or separatrix with the equatorial plane (''Z'' = 0).
	* ''a'' is the minor radius of the plasma, defined as the radial difference between the 2 intersections of the LCFS or separatrix with the equatorial plane (''Z'' = 0), divided by 2.		* ''a'' is the minor radius of the plasma, defined as the radial difference between the 2 intersections of the LCFS or separatrix with the equatorial plane (''Z'' = 0), divided by 2.
	* ''R<sub>up</sub>'' is the major radius of the upper X-point (in case it exists) or of the highest vertical point of the LCFS.		* ''R<sub>upper</sub>'' is the major radius of the upper X-point (in case it exists) or of the highest vertical point of the LCFS.
	* ''R<sub>~~down~~</sub>'' is the major radius of the lower X-point (in case it exists) or of the lowest vertical point of the LCFS.		* ''R<sub>lower</sub>'' is the major radius of the lower X-point (in case it exists) or of the lowest vertical point of the LCFS.
	The upper triangularity is then defined as follows:		The upper triangularity is then defined as follows:
	:<math> \delta_{up} = (R_0-R_{up})/a</math>		:<math> \delta_{upper} = (R_0-R_{upper})/a</math>
	and similar for δ<sub>~~down~~</sub>.		and similar for δ<sub>lower</sub>.
	The overall triangularity is defined as the mean of δ<sub>up</sub> and δ<sub>~~down~~</sub>.		The overall triangularity is defined as the mean of δ<sub>upper</sub> and δ<sub>lower</sub>.

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

Admin: /* See also */

2014-06-11T13:44:55Z

Admin at 13:08, 11 June 2014

2014-06-11T13:08:24Z

← Older revision		Revision as of 15:08, 11 June 2014
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	* ''R<sub>down</sub>'' is the major radius of the lower X-point (in case it exists) or of the lowest vertical point of the LCFS.		* ''R<sub>down</sub>'' is the major radius of the lower X-point (in case it exists) or of the lowest vertical point of the LCFS.
	The upper triangularity is then defined as follows:		The upper triangularity is then defined as follows:
	:<math> \~~kappa_~~{up} = (R_0-R_{up})/a</math>		:<math> \delta_{up} = (R_0-R_{up})/a</math>
	and similar for &~~kappa~~;<sub>down</sub>.		and similar for δ<sub>down</sub>.
	The overall triangularity is defined as the mean of &~~kappa~~;<sub>up</sub> and &~~kappa~~;<sub>down</sub>.		The overall triangularity is defined as the mean of δ<sub>up</sub> and δ<sub>down</sub>.

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

	* [[Ellipticity]]		* [[Ellipticity]]
			* [[Toroidal coordinates]]

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