Bayesian inference and calibration of magnetic diagnostics

The magnetic diagnostics across TAE Technologies’ compact toroid fusion device include 28 internal and 45 external flux loops that measure poloidal flux and axial field strength, 64 three-axis (radial, toroidal, and axial) Mirnov probes, and 22 internal and external, axial-only Mirnov probes. Imperfect construction, installation, and physical constraints required a Bayesian approach for the calibration process to best account for errors in signals. These errors included flux loops not fitted to a perfect circle due to spatial constraints, Mirnov probes not perfectly aligned against their respective axes, and flux pickup that occurred within the insert (feedthrough) of the Mirnov probes. Our model-based calibration is derived from magnetostatic theory and the circuitry of the sensors. These models predicted outputs that were compared against experimental data. Using a simple least-squares optimization, we were able to predict flux loop data within 1% of relative error. For the Mirnov probes, we utilized Bayesian inference to determine three rotation angles and three amplifier gains. The results of this work not only gave our diagnostic measurements physical meaning, but also act as a safeguard to spot when instruments have malfunctioned, or when there is an error in database maintenance. This paper will go into the details of our calibration procedure, our Bayesian modeling, and the accuracy of our results compared to experimental data.