Equilibrium calculation

An equilibrium in MRxMHD simultaneously satisfies the Beltrami equation and the interface force balance condition:

\[\begin{split}\nabla \times \mathbf{B} = \mu \mathbf{B} \\ \mathbf{F}_l = [p + B^2/2\mu_0]_l\end{split}\]

An equilibrium is found by minimizing the Force in an iterative loop which involves solving the Beltrami equation and adjusting interface geometry.

The minimization is performed using the script scripts/calc_spectre_eq.py which takes a TOML file as input. The output will be an HDF5 file containing the optimal interface geometry, along with the resulting Beltrami field, and other postprocessing information. The output can be analyzed as described in the postprocessing section. During force minimization, the output is piped to a text file, where each iteration of the minimization is logged, along with extra information.

Example calculations

• Fixed-boundary QA vacuum
• Free-boundary W7-X vacuum