Single-stage stellarator optimization: combining coils with fixed boundary equilibria

Abstract

We introduce a novel approach for the simultaneous optimization of plasma and coil engineering objectives in a fixed-boundary equilibrium that is computationally efficient and applicable to a broad range of vacuum and finite plasma pressure scenarios. Our approach treats plasma boundary and coil shapes as independently optimized variables, penalizing the mismatch between the two using a quadratic flux term in the objective function. Four use cases are presented to demonstrate the effectiveness of the approach, including simple and complex stellarator geometries. As it is shown here, this method outperforms previous 2-stage approaches, achieving smaller plasma objective function values when coils are taken into account.

Constructing precisely quasi-isodynamic magnetic fields

“…Including both MHD and gyrokinetic stability metrics in the target function will be necessary when designing a viable fusion reactor. Finding a set of coils with reasonable properties would also be a valuable project, as was done in Jorge et al (2023). The optimization approach in this paper also seems to be sensitive to initial conditions: we were unable to find any good configurations n fp > 1, except for those initialized from a solution found using NAE.…”

Understanding trade-offs in stellarator design with multi-objective optimization

“…Part of the loss of quasi-symmetry is inherent to the two-stage approach to coil design: the coils are optimized to reproduce a target magnetic field, but not to generate a quasi-symmetric field. Single-stage optimization approaches (Giuliani et al 2022a,b ;Jorge et al 2023), however, directly optimize coils for quasi-symmetry, ensuring that they achieve optimal quasi-symmetry levels over the space of coils satisfying the coil length constraint. Single-stage approaches would hence improve the unfortunate trade-off between coil length and quasi-symmetry.…”

The magnetic gradient scale length explains why certain plasmas require close external magnetic coils

“…Conversely, increasing plasma-coil separation at a fixed coil complexity results in coils that do not reproduce the target plasma shape to a high enough level of accuracy. A partial solution to this issue may be to perform single-stage optimization, in which both the plasma shape and coil shapes are optimized together [8][9][10][11]. However, single-stage optimization can be computationally challenging.…”