Shaping paradigm as a tool for systematic geometry–performance investigations

Demonstrate that the Fourier-mode cross-section shaping framework introduced for axisymmetric and non-axisymmetric ideal-MHD equilibria facilitates systematic investigations into the relationship between general flux-surface geometries and figures of merit.

Background

The authors develop a general method for computing equilibrium cross-section shapes, using symmetry-aligned coordinates and a Fourier modal analysis to quantify shaping modes and their axial rotation via the Fourier-transformed shaping spectrum (FTSS).

From empirical analyses of precise quasi-symmetric configurations and samples from the QUASR database, they observe a spatial resonance between shape complexity and axial rotation correlated with rotational transform and field periods, and conjecture that the proposed shaping paradigm can serve as a systematic framework to relate geometry to performance metrics.