Benchmark of the code

To benchmark the numerical code, I set the profile of $P$ and $g$ according to Eqs. (69) and (70) with the parameters $c_2 = 0$, $c_1 = B_0 (\kappa_0^2 + 1) / (R_0^2 \kappa_0 q_0)$, $\kappa _0 = 1.5$, and $q_0 = 1.5$. The comparison of the analytic and numerical results are shown in Fig. 31.

Figure 31: Agreement between the magnetic surfaces (contours of $\Psi$) given by the Solovev analytic formula and those calculated by the numerical code. The two sets of magnetic surfaces are indistinguishable at this scale. The boundary magnetic surface is selected by the requirement that $\overline {\Psi } = 0.11022$ in the Solovev formula (78). Parameters: $\kappa _0 = 1.5$, $q_0 = 1.5$.

Note that the parameter $c_0$ in the Solovev equilibrium seems to be not needed in the numerical calculation. In fact this impression is wrong: the $c_0$ parameter is actually needed in determining the boundary magnetic surface of the numerical equilibrium (in the case considered here $c_0$ is chosen as $c_0 = B_0 / (R_0^2 \kappa_0 q_0)$).