Burnup Measurement using Bent Crystal Diffraction Spectrometers for Pebble Bed Reactors

Burnup measurement is essential for monitoring and controlling pebble bed reactors (PBRs), where fuel pebbles circulate rapidly through the core. However, conventional gamma spectroscopy using high purity germanium (HPGe) detectors is difficult due to high activity levels in discharge pebbles, leading to excessive dead time and Compton scattering. This study explores the use of bent crystal diffraction (BCD) spectrometers to filter the emitted gamma spectrum and isolate key peaks for improved measurement accuracy and speed. Pebble wise depletion calculations were performed and the resulting spectra were analyzed using ray tracing (SHADOW3) and gamma response modeling (GADRAS). Key isotopes, $^{137m}$Ba/$^{137}$Cs, $^{239}$Pu, $^{144}$Ce, $^{148m}$Pm, and $^{140}$La, were found to strongly correlate with burnup, residence time, core passes, plutonium production, and fluence. Machine learning regression models applied to simulated spectra achieved a coefficient of determination ($R^2$) as high as 0.995 for burnup prediction. Among various BCD configurations, mosaic silicon crystals in the (440) orientation combined with an HPGe detector provided optimal performance for $^{137m}$Ba, while (220) and (440) configurations paired with scintillators were effective for the remaining isotopes.