Bdot probe and Rogowski coil cross-calibration and sensor fusion in pulsed direct current capacitor discharges

Bdot probes and Rogowski coils are used in the measurement of transient magnetic fields and currents, respectively. They both share the mechanism of creating an induced electromotive force response via Faraday's law, which scales linearly with the pulsed magnetic field. High power capacitor direct current (DC) discharge systems release a single pulse of current that is both very high and very fast (≲1 ms). To capture these transient data and characterize these systems, high current tolerant and fast response time sensors are required. While these measuring devices have been well studied and utilized for almost 100 years, a comprehensive and detailed description of the custom design, calibration, and sensor fusion application of these tools for use in various pulsed DC capacitor value discharges is largely missing in the literature. Using robust analytical calculations, finite element analyses, and empirical methods, we have developed a sensor fusion protocol for current and magnetic field probes (with relative errors of ±13% and ±15%, respectively) for use in any geometry of high speed pulsed DC current calibrated capacitor discharge systems. This paper comprehensively outlines the design and sensor fusion methodologies that allow for the deployment of in-house built Bdot probes and Rogowski coils to a wide range of pulsed DC systems and demonstrates their use in a characteristic plasma environment.