Finding Robust Operating Points for Burning Plasma Tokamaks Accounting for Empirical Model Uncertainty*

This work shows that a tokamak design robust to our current uncertainties in plasma performance differs from traditionally optimized designs. Plasma Operating CONtours (POPCONs) based on empirical confinement models are widely used for scoping tokamak design (Creely, et al., JPP, 2020). However, reasonable variations in the assumed confinement, radial shape of kinetic profiles, and impurities can give vastly different performance predictions (Rodriguez-Fernandez, et al., NF, 2024). SPARC is a tokamak under construction with the goal of achieving a burning plasma, which leverages POPCONs as a part of its scenario planning (Rodriguez-Fernandez, et al., NF, 2022). Here, we shift to maximizing its probability of success, rather than maximizing its fusion gain. To do this, a Monte Carlo analysis is performed for reasonable variations in assumption parameters. We find a different optimal operating point when considering robustness than deterministic POPCONs would suggest. To offset the expense of Monte Carlo analysis, we use Bayesian Optimization to intelligently sample the operational space. This allows the maximum success probability to be found two orders of magnitude more quickly than using a brute force approach. Additional efficiency is achieved by using multi-fidelity techniques. This work leads us to believe a further reduction of uncertainty in tokamak design would be feasible by optimizing directly with physics-based models.