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

TL;DR

This paper enhances stellarator coil design by incorporating coil manufacturing errors into a stochastic, gradient-based optimization framework, improving robustness and reducing local minima in coil configurations.

Contribution

It introduces a flexible stochastic optimization approach accounting for coil errors, with analytical derivatives, and compares risk-neutral and risk-averse formulations for improved coil design robustness.

Findings

Risk-neutral optimization yields more robust coil configurations.

Inclusion of coil errors reduces local minima in the design space.

Risk-averse CVaR approach produces similar results to risk-neutral optimization.

Abstract

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