Benchmark of the code

13.7 Benchmark of the code

To benchmark the numerical code, I set the proﬁle of P and g according to Eqs. (508) and (509) with the parameters c₂ = 0, c₁ = B₀(κ₀² + 1)∕(R₀²κ₀q₀), κ₀ = 1.5, and q₀ = 1.5. The comparison of the analytic and numerical results are shown in Fig. 31.

pict

Fig. 31: Agreement between the magnetic surfaces (contours of Ψ) 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 Ψ = 0.11022 in the Solovev formula (517). Parameters: κ₀ = 1.5, q₀ = 1.5.

Note that the parameter c₀ in the Solovev equilibrium seems to be not needed in the numerical calculation. In fact this impression is wrong: the c₀ parameter is actually needed in determining the boundary magnetic surface of the numerical equilibrium (in the case considered here c₀ is chosen as c₀ = B₀∕(R₀²κ₀q₀)).

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