Investigations with an idealized diagnostic setup

Following the demonstration of FP recoveries using various sets of the experimentally available magnetic measurements in chapter 3, it is pertinent to place the earlier results in context with what can be achieved assuming comprehensive knowledge of the plasma-induced magnetic field in the vacuum region. For our database of equilibria, we evaluate the field due to the plasma on a fine grid covering the vacuum vessel contour and assess the limits of information contained in this large dataset through parametric regressions. We consider direct recovery of $p(s)$, the pressure profile as a function of normalized toroidal flux, in terms of external magnetic information alone. A parallel subsequently emerges between pressure and geometric information, and we show that knowledge of the flux surface geometry enables the pressure profile to be recovered very accurately over the database. This leads to a scheme for optimizing the magnetic diagnostic setup on W7-AS in which we pay particular attention to the impact of nuisance error fields on the FP reconstructions.