Improved flux-surface parameterization through constrained nonlinear optimization

Parameterization of magnetic flux-surfaces is often used for magnetohydrodynamic stability analysis and microturbulence modeling in tokamaks. Shape parameters such local parameterization a (numerical) equilibrium are traditionally computed analytically using geometrically derived quantities. However, the shape approximated by average values different sections flux-surface contour or truncated series, which does not guarantee an optimal fit. Here, instead nonlinear least squares optimization to compute these parameters, with weighted sum squared error cost function that robust outliers. This method results lower total absolute both poloidal field density than current methods several parameterizations based on well-known “Miller geometry.” Furthermore, rapid convergence achieved, no approximate geometric measurements needed, applicable any analytical parameterization. Validation local, linear gyrokinetic simulations optimized showed reduced root mean square errors growth rate frequency spectra when compared numerical equilibria. In particular, popular Turnbull–Miller benefits from this approach, extending its usability closer toward last-closed cases minor up-down asymmetry.