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TJ-II:Magnetic coordinates: Difference between revisions
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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 [[Toroidal coordinates|coordinate systems]] (units according to the S.I. system, m and rad): | ||
# Cartesian ( | # 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]]). | ||
# Cylindrical ( | # [[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 | 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 <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 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. | ||
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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 == | |||
* [[Toroidal coordinates]] | |||
* [[MHD equilibrium]] | |||
* [[Flux surface]] | |||
* [[Effective plasma radius]] | |||
* [[TJ-II:Magnetic field|TJ-II Magnetic field]] (visual examples) | |||
== References == | == References == | ||
<references /> | <references /> | ||