Calibration of Superconducting Radio-Frequency cavity forward and reflected channels based on stored energy dynamics

Modern superconducting radio-frequency linear accelerators require the cavity bandwidth and detuning to be within a specified range to maximize the efficiency of the machine. To correctly estimate these states during operation, the measured RF signals should be calibrated. Due to the finite isolation of the waveguide directional couplers, cross-coupling effects in the forward and reflected channels complicate the calibration of the RF signals in Low-Level RF control systems. Past work proposed a compensation method employing least-squares optimization. This method requires the directivity of the directional couplers to be much higher than one. Additionally, the algorithm requires a tuning parameter to optimize the calculated calibration. However, for some accelerating systems, finding an acceptable value for such a parameter is challenging and time-consuming. Other methods strongly depend on the forward-reflected ratio during the field decay phase. This, in some circumstances, may decrease the accuracy due to noise or systematic errors. In this paper, we present a way to overcome these limitations by performing a global nonlinear least square optimization constrained by energy conservation laws. The method is tested with L-band superconducting resonators at loaded quality factors of 4 . 6 ⋅ 1 0 6 and 2 . 8 ⋅ 1 0 7 .