Sensitivity to geometric offsets in the Thomson data

Figure 4.11: Interpreted pressure profile versus $s$ for Thomson input profiles shifted by -5.0mm, -2.5mm, 2.5mm, 5.0mm both without (above) and with (below) matching of kinetic energy content to diamagnetic energy

As previously pointed out, discrepancies between the FP equilibrium fit and the physical flux surfaces identified by the ${p_{\mathrm{e}}}(R)$ fit poses serious difficulties for the interpretation. To illustrate the sensitivity of the procedure to systematic errors, we simulate inconsistent input profiles by rigidly shifting the test equilibrium ${p_{\mathrm{e}}}(R)$ used above by -5mm, -2.5mm, 2.5mm and 5mm in $R$ and examining the effect on the interpreted profile $p(s)$. The upper plot in figure 4.11 show how the shift errors manifest themselves as raising or lowering of the entire interpreted pressure profile, due to the procedure attempting to compensate for the geometrical error by scaling $p(s)$. The shape of the profile remains largely correct, however.

The problem is not alleviated by enforcing a match to the energy content. This is shown in the lower plot of figure 4.11. Although the RMS error in the profile is lower here than with the cases interpreted without matching $W_{\mathrm{p}}$, the profile shapes differ from the actual profile, since the procedure is forced to conserve the integral of $p(s)$ and must redistribute the excess/lack over the profile. This illustrates the dangers of matching to inconsistent data and indicates that the energy content is possibly better used as a cross-check of an interpretation using only the geometry rather than as a rigid criterion.

This is, however, an extreme example of systematic error that could result from a situation such as a misalignment of the Thomson optics. The presence of this or other inconsistencies could be revealed if other appropriate experimental data were available for cross-checking.