TJ-II:Magnetic coordinates: Difference between revisions

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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>.

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><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.

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== 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 ==

@@ Line 4: / Line 4: @@
 # [[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, 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.
@@ Line 20: / Line 20: @@
 == 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 ==