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TJ-II:Magnetic coordinates: Difference between revisions
TJ-II:Magnetic coordinates (view source)
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The diagnostics perform measurements in real space. The location of points is given in one of these | 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 East, the Y-axis due North, and the ''Z''-axis up. | ||
# [[Toroidal | # [[Toroidal coordinates|Cylindrical]] (''R'', ''φ'', ''Z''), where ''R<sup>2</sup>'' = ''X<sup>2</sup>'' + ''Y<sup>2</sup>'' and tan ''φ'' = ''Y/X''. | ||
In order to make comparisons between diagnostics, it is useful to convert these real-space | 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 | 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. | ||
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 | 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. | ||
It should be noted that these | It should be noted that these coordinate transforms are approximate and not error-free. The errors in the vacuum field calculation are due to three sources: | ||
# The error in the placement of the coils. | # The error in the placement of the coils. | ||