Single-stage gradient-based stellarator coil design: stochastic optimization

We extend the single-stage stellarator coil design approach for quasi-symmetry on axis from [Giuliani et al, 2020] to additionally take into account manufacturing errors. By modeling errors independently discretization, we have flexibility consider realistic forms of The corresponding stochastic optimization problems are formulated using a risk-neutral and risk-averse approaches. present an efficient, gradient-based descent algorithm which relies analytical derivatives solve these problems. In comprehensive numerical study, compare designs resulting deterministic find that formulation results in more robust configurations reduces number local minima problem. also approaches terms away magnetic axis, confinement particles released close axis. Finally, show consider, objective Conditional Value-at-Risk leads similar objective.