# TJ-II:Magnetic coordinates

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 North, the*Y*-axis due West, and the*Z*-axis up (see TJ-II:Sectors). - Cylindrical $ (R, \phi, Z) $, where $ R^2 = X^2 + Y^2 $ and $ \tan \phi = Y/X $.

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 (See the on-line documentation - only internal laboratory access):

First, vacuum equilibrium calculations from VMEC. These are then used to obtain magnetic flux coordinates $ (\psi, \theta, \phi) $. A set of routines is available to perform the corresponding coordinate transforms.^{[1]} 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 coordinate transforms. More information can be found in files 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 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 value of the currents flowing through the coils.
- The error due to the fact that the model uses a finite amount of filaments to model the current in the coils (which has a continuous distribution).

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 $ +\phi $ direction (counterclockwise, seen from the top), to accommodate the Heavy Ion Beam Probe diagnostic.

## See also

- Toroidal coordinates
- MHD equilibrium
- Flux surface
- Effective plasma radius
- TJ-II Magnetic field (visual examples)

## References

- ↑ File:TJ2 Library V2.pdf: TJ-II Library Manual, Informe Técnico del CIEMAT Nº 963