Gradient-based optimization of 3D MHD equilibria

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on magnetohydrodynamic (MHD) equilibria (Antonsen et al. , J. Plasma Phys. vol. 85, issue 2, 2019; Paul 86, 1, 2020), we present first example analytic gradient-based optimization fixed-boundary stellarator equilibria. We take advantage gradient information to optimize figures merit relevance design, including rotational transform, magnetic well and quasi-symmetry near axis. With application method, reduce number equilibrium evaluations by dimension space ( ${\sim }50\text {--}500$ ) in comparison with a finite-difference method. discuss regularization objectives optimization, novel method prevents self-intersection plasma boundary. several optimized equilibria, vacuum field very low shear throughout volume.