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

References in corpus (4)

• An improved current potential method for fast computation of stellarator coil shapes
• An adjoint method for determining the sensitivity of island size to magnetic field variations
• Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary
• Single-stage gradient-based stellarator coil design: Optimization for near-axis quasi-symmetry

Cited by in corpus (13)

• Direct stellarator coil design using global optimization: application to a comprehensive exploration of quasi-axisymmetric devices
• Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry
• Permanent magnet optimization for stellarators as sparse regression
• Stochastic and a posteriori optimization to mitigate coil manufacturing errors in stellarator design
• Stellarator coil optimization supporting multiple magnetic configurations
• Global Stochastic Optimization of Stellarator Coil Configurations
• Adjoint methods for quasisymmetry of vacuum fields on a surface
• Consistency of Monte Carlo Estimators for Risk-Neutral PDE-Constrained Optimization
• Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization
• Asymptotic Consistency for Nonconvex Risk-Averse Stochastic Optimization with Infinite Dimensional Decision Spaces
• Efficient Computation of Stellarator Coils with an Augmented Lagrangian Optimization Method
• Flexible Stellarator Physics Facility
• Performance Bounds for PDE-Constrained Optimization under Uncertainty