TJ-II:Magnetic coordinates - Revision history

Admin: /* Field direction */

2026-03-19T07:43:27Z

Field direction

← Older revision		Revision as of 09:43, 19 March 2026
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	== Field direction ==		== Field direction ==

	The direction of the dominant toroidal field component is in the <math>-\phi</math> direction (~~clockwise~~, seen from the top), to accommodate the [[TJ-II:Heavy Ion Beam Probe\|Heavy Ion Beam Probe]] diagnostic.		The direction of the dominant toroidal field component is in the <math>\phi</math> direction (anticlockwise, seen from the top), to accommodate the [[TJ-II:Heavy Ion Beam Probe\|Heavy Ion Beam Probe]] diagnostic (except in specific reversed field experiments).

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

Admin at 06:07, 9 November 2025

2025-11-09T06:07:35Z

← Older revision		Revision as of 08:07, 9 November 2025
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	In order to make comparisons between diagnostics, it is useful to convert these real-space coordinates to [[flux coordinates]]. This coordinate transform depends on the particular magnetic configuration used in a given experiment. Two tools are available to do so ([http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ See the on-line documentation] - only internal laboratory access):		In order to make comparisons between diagnostics, it is useful to convert these real-space coordinates to [[flux coordinates]]. This coordinate transform depends on the particular magnetic configuration used in a given experiment. Two tools are available to do so ([http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ See the on-line documentation] - only internal laboratory access):

	First, vacuum equilibrium calculations from [[VMEC]]. These are then used to obtain magnetic flux coordinates <math>(\psi, \theta, \phi)</math>. A set of routines is available to perform the corresponding coordinate transforms.<ref>[[File:TJ2 Library V2.pdf]]: TJ-II Library Manual, Technical report 963, CIEMAT, 2001</ref> ~~The drawback of the VMEC calculations is (a) that magnetic islands are ignored, and (b) that only a limited number of configurations is available.~~<ref>[https://info.fusion.ciemat.es/InternalReport/IR1532.pdf TJ-II Webservices], Technical report 1532, CIEMAT, 2024</ref>		First, vacuum equilibrium calculations from [[VMEC]]. These are then used to obtain magnetic flux coordinates <math>(\psi, \theta, \phi)</math>. A set of routines is available to perform the corresponding coordinate transforms.<ref>[[File:TJ2 Library V2.pdf]]: TJ-II Library Manual, Technical report 963, CIEMAT, 2001</ref><ref>[https://info.fusion.ciemat.es/InternalReport/IR1532.pdf TJ-II Webservices], Technical report 1532, CIEMAT, 2024</ref> The drawback of the VMEC calculations is (a) that magnetic islands are ignored, and (b) that only a limited number of configurations is available.

	Second, magnetic field line calculations using the [[:Wikipedia:Biot_savart\|Biot-Savart Law]]. The approximate magnetic flux is recovered from an interpolation procedure. A set of routines is available to perform the corresponding coordinate transforms. More information can be found in files [http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ g3d_readme.doc and g3d_gridfile.doc]. Since the latter procedure is more flexible and generally applicable than the VMEC-based calculations, the latter is preferred.		Second, magnetic field line calculations using the [[:Wikipedia:Biot_savart\|Biot-Savart Law]]. The approximate magnetic flux is recovered from an interpolation procedure. A set of routines is available to perform the corresponding coordinate transforms. More information can be found in files [http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ g3d_readme.doc and g3d_gridfile.doc]. Since the latter procedure is more flexible and generally applicable than the VMEC-based calculations, the latter is preferred.

Admin at 06:06, 9 November 2025

2025-11-09T06:06:53Z

← Older revision		Revision as of 08:06, 9 November 2025
Line 6:		Line 6:
	In order to make comparisons between diagnostics, it is useful to convert these real-space coordinates to [[flux coordinates]]. This coordinate transform depends on the particular magnetic configuration used in a given experiment. Two tools are available to do so ([http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ See the on-line documentation] - only internal laboratory access):		In order to make comparisons between diagnostics, it is useful to convert these real-space coordinates to [[flux coordinates]]. This coordinate transform depends on the particular magnetic configuration used in a given experiment. Two tools are available to do so ([http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ See the on-line documentation] - only internal laboratory access):

	First, vacuum equilibrium calculations from [[VMEC]]. These are then used to obtain magnetic flux coordinates <math>(\psi, \theta, \phi)</math>. A set of routines is available to perform the corresponding coordinate transforms.<ref>[[File:TJ2 Library V2.pdf]]: TJ-II Library Manual, ~~Informe Técnico del~~ CIEMAT ~~Nº 963~~</ref> The drawback of the VMEC calculations is (a) that magnetic islands are ignored, and (b) that only a limited number of configurations is available.		First, vacuum equilibrium calculations from [[VMEC]]. These are then used to obtain magnetic flux coordinates <math>(\psi, \theta, \phi)</math>. A set of routines is available to perform the corresponding coordinate transforms.<ref>[[File:TJ2 Library V2.pdf]]: TJ-II Library Manual, Technical report 963, CIEMAT, 2001</ref> The drawback of the VMEC calculations is (a) that magnetic islands are ignored, and (b) that only a limited number of configurations is available.<ref>[https://info.fusion.ciemat.es/InternalReport/IR1532.pdf TJ-II Webservices], Technical report 1532, CIEMAT, 2024</ref>

	Second, magnetic field line calculations using the [[:Wikipedia:Biot_savart\|Biot-Savart Law]]. The approximate magnetic flux is recovered from an interpolation procedure. A set of routines is available to perform the corresponding coordinate transforms. More information can be found in files [http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ g3d_readme.doc and g3d_gridfile.doc]. Since the latter procedure is more flexible and generally applicable than the VMEC-based calculations, the latter is preferred.		Second, magnetic field line calculations using the [[:Wikipedia:Biot_savart\|Biot-Savart Law]]. The approximate magnetic flux is recovered from an interpolation procedure. A set of routines is available to perform the corresponding coordinate transforms. More information can be found in files [http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ g3d_readme.doc and g3d_gridfile.doc]. Since the latter procedure is more flexible and generally applicable than the VMEC-based calculations, the latter is preferred.

Admin at 06:01, 9 November 2025

2025-11-09T06:01:20Z

← Older revision		Revision as of 08:01, 9 November 2025
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	# [[Toroidal coordinates\|Cylindrical]] <math>(R, \phi, Z)</math>, where <math>R^2 = X^2 + Y^2</math> and <math>\tan \phi = Y/X</math>.		# [[Toroidal coordinates\|Cylindrical]] <math>(R, \phi, Z)</math>, where <math>R^2 = X^2 + Y^2</math> and <math>\tan \phi = Y/X</math>.

	In order to make comparisons between diagnostics, it is useful to convert these real-space coordinates to flux coordinates. This coordinate transform depends on the particular magnetic configuration used in a given experiment. Two tools are available to do so ([http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ See the on-line documentation] - only internal laboratory access):		In order to make comparisons between diagnostics, it is useful to convert these real-space coordinates to [[flux coordinates]]. This coordinate transform depends on the particular magnetic configuration used in a given experiment. Two tools are available to do so ([http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ See the on-line documentation] - only internal laboratory access):

	First, vacuum equilibrium calculations from [[VMEC]]. These are then used to obtain magnetic flux coordinates <math>(\psi, \theta, \phi)</math>. A set of routines is available to perform the corresponding coordinate transforms.<ref>[[File:TJ2 Library V2.pdf]]: TJ-II Library Manual, Informe Técnico del CIEMAT Nº 963</ref> The drawback of the VMEC calculations is (a) that magnetic islands are ignored, and (b) that only a limited number of configurations is available.		First, vacuum equilibrium calculations from [[VMEC]]. These are then used to obtain magnetic flux coordinates <math>(\psi, \theta, \phi)</math>. A set of routines is available to perform the corresponding coordinate transforms.<ref>[[File:TJ2 Library V2.pdf]]: TJ-II Library Manual, Informe Técnico del CIEMAT Nº 963</ref> The drawback of the VMEC calculations is (a) that magnetic islands are ignored, and (b) that only a limited number of configurations is available.

Admin: /* Field direction */

2025-11-09T05:59:28Z

Field direction

← Older revision		Revision as of 07:59, 9 November 2025
Line 20:		Line 20:
	== Field direction ==		== Field direction ==

	The direction of the dominant toroidal field component is in the <math>+\phi</math> direction (~~counterclockwise~~, seen from the top), to accommodate the [[TJ-II:Heavy Ion Beam Probe\|Heavy Ion Beam Probe]] diagnostic.		The direction of the dominant toroidal field component is in the <math>-\phi</math> direction (clockwise, seen from the top), to accommodate the [[TJ-II:Heavy Ion Beam Probe\|Heavy Ion Beam Probe]] diagnostic.

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

Admin: Added field direction

2015-04-17T09:33:24Z

Added field direction

← Older revision		Revision as of 11:33, 17 April 2015
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	The diagnostics perform measurements in real space. The location of points is given in one of these [[Toroidal coordinates\|coordinate systems]] (units according to the S.I. system, m and rad):		The diagnostics perform measurements in real space. The location of points is given in one of these [[Toroidal coordinates\|coordinate systems]] (units according to the S.I. system, m and rad):

	# Cartesian (''X'', ''Y'', ''Z'') with its origin at the centre of the TJ-II device, the X-axis pointing due North, the Y-axis due West, and the ''Z''-axis up (see [[TJ-II:Sectors]]).		# Cartesian <math>(X, Y, Z)</math> with its origin at the centre of the TJ-II device, the ''X''-axis pointing due North, the ''Y''-axis due West, and the ''Z''-axis up (see [[TJ-II:Sectors]]).
	# [[Toroidal coordinates\|Cylindrical]] (''R'', ~~''&~~phi~~;''~~, ''Z''), where ~~''R~~<~~sup~~>2~~</sup>''~~ = ''X~~<sup>~~2~~</sup>''~~ + ''Y~~<sup>~~2</~~sup~~>'' and tan ~~''&~~phi~~;''~~ = ''Y/X''.		# [[Toroidal coordinates\|Cylindrical]] <math>(R, \phi, Z)</math>, where <math>R^2 = X^2 + Y^2</math> and <math>\tan \phi = Y/X</math>.

	In order to make comparisons between diagnostics, it is useful to convert these real-space coordinates to flux coordinates. This coordinate transform depends on the particular magnetic configuration used in a given experiment. Two tools are available to do so ([http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ See the on-line documentation] - only internal laboratory access):		In order to make comparisons between diagnostics, it is useful to convert these real-space coordinates to flux coordinates. This coordinate transform depends on the particular magnetic configuration used in a given experiment. Two tools are available to do so ([http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ See the on-line documentation] - only internal laboratory access):

	First, vacuum equilibrium calculations from [[VMEC]]. These are then used to obtain magnetic flux coordinates ''(ψ, θ, φ)''. A set of routines is available to perform the corresponding coordinate transforms.<ref>[[File:TJ2 Library V2.pdf]]: TJ-II Library Manual, Informe Técnico del CIEMAT Nº 963</ref> The drawback of the VMEC calculations is (a) that magnetic islands are ignored, and (b) that only a limited number of configurations is available.		First, vacuum equilibrium calculations from [[VMEC]]. These are then used to obtain magnetic flux coordinates <math>(\psi, \theta, \phi)</math>. A set of routines is available to perform the corresponding coordinate transforms.<ref>[[File:TJ2 Library V2.pdf]]: TJ-II Library Manual, Informe Técnico del CIEMAT Nº 963</ref> The drawback of the VMEC calculations is (a) that magnetic islands are ignored, and (b) that only a limited number of configurations is available.

	Second, magnetic field line calculations using the [[:Wikipedia:Biot_savart\|Biot-Savart Law]]. The approximate magnetic flux is recovered from an interpolation procedure. A set of routines is available to perform the corresponding coordinate transforms. More information can be found in files [http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ g3d_readme.doc and g3d_gridfile.doc]. Since the latter procedure is more flexible and generally applicable than the VMEC-based calculations, the latter is preferred.		Second, magnetic field line calculations using the [[:Wikipedia:Biot_savart\|Biot-Savart Law]]. The approximate magnetic flux is recovered from an interpolation procedure. A set of routines is available to perform the corresponding coordinate transforms. More information can be found in files [http://www-fusion.ciemat.es/cgi-bin/dir/dirnew.cgi?manuals/geometry_TJII/ g3d_readme.doc and g3d_gridfile.doc]. Since the latter procedure is more flexible and generally applicable than the VMEC-based calculations, the latter is preferred.
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	Additional errors are due to finite-pressure effects (estimated to be quite small in TJ-II) and net plasma currents.		Additional errors are due to finite-pressure effects (estimated to be quite small in TJ-II) and net plasma currents.

			== Field direction ==

			The direction of the dominant toroidal field component is in the <math>+\phi</math> direction (counterclockwise, seen from the top), to accommodate the [[TJ-II:Heavy Ion Beam Probe\|Heavy Ion Beam Probe]] diagnostic.

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

Admin at 09:04, 13 January 2010

2010-01-13T09:04:08Z

← Older revision		Revision as of 11:04, 13 January 2010
Line 1:		Line 1:
	The diagnostics perform measurements in real space. The location of points is given in one of these [[Toroidal coordinates\|coordinate systems]] (units according to the S.I. system, m and rad):		The diagnostics perform measurements in real space. The location of points is given in one of these [[Toroidal coordinates\|coordinate systems]] (units according to the S.I. system, m and rad):

	# Cartesian (''X'', ''Y'', ''Z'') with its origin at the centre of the TJ-II device, the X-axis pointing due ~~West~~, the Y-axis due ~~South~~, and the ''Z''-axis up (see [[TJ-II:Sectors]]).		# Cartesian (''X'', ''Y'', ''Z'') with its origin at the centre of the TJ-II device, the X-axis pointing due North, the Y-axis due West, and the ''Z''-axis up (see [[TJ-II:Sectors]]).
	# [[Toroidal coordinates\|Cylindrical]] (''R'', ''φ'', ''Z''), where ''R<sup>2</sup>'' = ''X<sup>2</sup>'' + ''Y<sup>2</sup>'' and tan ''φ'' = ''Y/X''.		# [[Toroidal coordinates\|Cylindrical]] (''R'', ''φ'', ''Z''), where ''R<sup>2</sup>'' = ''X<sup>2</sup>'' + ''Y<sup>2</sup>'' and tan ''φ'' = ''Y/X''.

Admin at 08:58, 4 December 2009

2009-12-04T08:58:50Z

← Older revision		Revision as of 10:58, 4 December 2009
Line 1:		Line 1:
	The diagnostics perform measurements in real space. The location of points is given in one of these coordinate systems (units according to the S.I. system, m and rad):		The diagnostics perform measurements in real space. The location of points is given in one of these [[Toroidal coordinates\|coordinate systems]] (units according to the S.I. system, m and rad):

	# Cartesian (''X'', ''Y'', ''Z'') with its origin at the centre of the TJ-II device, the X-axis pointing due West, the Y-axis due South, and the ''Z''-axis up (see [[TJ-II:Sectors]]).		# Cartesian (''X'', ''Y'', ''Z'') with its origin at the centre of the TJ-II device, the X-axis pointing due West, the Y-axis due South, and the ''Z''-axis up (see [[TJ-II:Sectors]]).
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	== See also ==		== See also ==

			* [[Toroidal coordinates]]
	* [[MHD equilibrium]]		* [[MHD equilibrium]]
			* [[Flux surface]]
	* [[Effective plasma radius]]		* [[Effective plasma radius]]
	* [[TJ-II:Magnetic field\|TJ-II Magnetic field]] (visual examples)		* [[TJ-II:Magnetic field\|TJ-II Magnetic field]] (visual examples)

Admin at 12:27, 11 October 2009

2009-10-11T12:27:47Z

← Older revision		Revision as of 14:27, 11 October 2009
Line 1:		Line 1:
	The diagnostics perform measurements in real space. The location of points is given in one of these coordinate systems (units according to the S.I. system, m and rad):		The diagnostics perform measurements in real space. The location of points is given in one of these coordinate systems (units according to the S.I. system, m and rad):

	# Cartesian (''X'', ''Y'', ''Z'') with its origin at the centre of the TJ-II device, the X-axis pointing due ~~East~~, the Y-axis due ~~North~~, and the ''Z''-axis up.		# Cartesian (''X'', ''Y'', ''Z'') with its origin at the centre of the TJ-II device, the X-axis pointing due West, the Y-axis due South, and the ''Z''-axis up (see [[TJ-II:Sectors]]).
	# [[Toroidal coordinates\|Cylindrical]] (''R'', ''φ'', ''Z''), where ''R<sup>2</sup>'' = ''X<sup>2</sup>'' + ''Y<sup>2</sup>'' and tan ''φ'' = ''Y/X''.		# [[Toroidal coordinates\|Cylindrical]] (''R'', ''φ'', ''Z''), where ''R<sup>2</sup>'' = ''X<sup>2</sup>'' + ''Y<sup>2</sup>'' and tan ''φ'' = ''Y/X''.

Admin: /* See also */

2009-10-11T09:59:31Z

← Older revision		Revision as of 11:59, 11 October 2009
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	* [[MHD equilibrium]]		* [[MHD equilibrium]]
	* [[Effective plasma radius]]		* [[Effective plasma radius]]
			* [[TJ-II:Magnetic field\|TJ-II Magnetic field]] (visual examples)

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