Self-consistency test for the interpretive procedure

Here, we check that the pressure profile from a known equilibrium is correctly reproduced by the interpretive procedure. From an FP equilibrium from outside the FP equilibrium database, we can simulate an idealized noise-free Thomson profile, since the pressure is a known function of major radius $R$. This is then used as an input to the interpretive procedure and the resulting interpreted $p(s)$ is compared to the known $p(s)$.

It has been shown in [65] that for non-circular tokamak plasmas (where there are two free profiles $p(s)$ and $J_{\rm {pol}}(s)$), knowledge of the shape of the magnetic surfaces is sufficient to determine the current distribution. In our case we have only a single free profile $p(s)$ and we implicitly assume that there is a unique pressure profile that produces a given set of flux surfaces.

Figure 4.9: Top row: flux geometry for the FP equilibrium reconstruction in the Thomson $\phi =0$ plane and its interpreted pressure profile versus $s$. Bottom row: exact and recovered Thomson profile ${p_{\mathrm{e}}}$ versus $R$ [m] and absolute difference between exact and interpreted pressures versus $s$.

The flux surface geometry of a sample FP equilibrium in the $\phi =0$ symmetry plane, its simulated Thomson data and the pressure profile returned by the interpretive procedure with deviations from the actual profile are shown in figure 4.9. The known input pressure $p(s)$ is closely reproduced within tight error bounds. This was found to hold for all equilibria tested in this way, verifying that correct results are obtained when the input ${p_{\mathrm{e}}}(R)$ profile corresponds exactly to an FP equilibrium in the absence of noise.