A note on database scalings

In generating the database as outlined in section 3.3, allowing all 4 external coil currents to vary means that there is a free scaling factor for the magnetic field strength which has no effect on the vacuum flux surface topology [62]. We therefore choose to keep the modular coil current $I_{\mathrm{mod}}$ constant at 15.5 kA and vary only the current ratios $I_{\mathrm{s}}/I_{\mathrm{mod}}$, $I_{\mathrm{tor}}/I_{\mathrm{mod}}$ and $I_{\mathrm{vert}}/I_{\mathrm{mod}}$, thereby eliminating one unnecessary degree of freedom and reducing the size requirements of the database. Reconstructions of the flux surface geometry can still be performed for other values of $I_{\mathrm{mod}}$ if the appropriate scaling is introduced. The plasma-induced deformations of the vacuum flux surfaces depend on $\beta$ rather than the absolute energy content, thus the magnetic signals to be used in reconstructions should be scaled by (15.5/ $I_{\mathrm{mod}}$ [kA]) to obtain correct results. This is obvious in the case of the diamagnetic signal (see equation 2.75) and in fact holds for all diagnostics listed above. For $\cos(m=2)/\cos(m=1)$ no scaling is necessary, since this is already a normalized quantity.