Calibration Of Magnetic Diagnostics Using Markov Chain Monte Carlo

TAE Technologies' C-2W experiment (named "Norman") requires accurate measurements of magnetic fields to control, optimize and understand the Field-Reversed Configuration (FRC). On Norman, the hundreds of magnetic probes use a calibration model derived from electrodynamic theory and the circuitry of the sensors. The focus of this study will be the Mirnov probes, 64 three-axis (radial, toroidal, axial) chip inductors. For these probes, we need to model their physical misalignments and the magnetic noise within the feedthrough section. Our non-linear model contains 6 physical parameters of interest: 3 amplifier gains and 3 angles of rotation. In our previous calibration methodology, we rearranged this model into a linear form¹. This required us to solve for 9 terms in a two-step process: Bayesian maximum a posteriori estimation, and least-squares optimization for parameter decoupling. Here, we present an updated method using the Markov Chain Monte Carlo Metropolis-Hastings algorithm. This approach simplifies the process computationally by direct sampling of the posterior distributions for the 6 physical parameters without the need to linearize. We derived parameter values that not only satisfied physical constraints, but also provided better agreement between probe predictions and experimental data.

¹Rev. Sci. Instrum. 93, 113553 (2022)