TJ-II:Magnetic coordinates: Difference between revisions

The diagnostics perform measurements in real space. The location of points is given in one of these co-ordinate systems (units according to the S.I. system, m and rad):

# [[Toroidal co-ordinates|Cylindrical]] (''R'', ''φ'', ''Z''), where ''R²'' = ''X²'' + ''Y²'' and tan ''φ'' = ''Y/X''.

In order to make comparisons between diagnostics, it is useful to convert these real-space co-ordinates to flux co-ordinates. This co-ordinate 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 co-ordinates ''(&psi;, &theta;, &phi;)''. A set of routines is available to perform the corresponding co-ordinate 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 co-ordinate 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 co-ordinate transforms are approximate and not error-free. The errors in the vacuum field calculation are due to three sources: