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Burnup Measurement using Bent Crystal Diffraction Spectrometers for Pebble Bed Reactors

Ian Kolaja, Lee Bernstein, Ludovic Jantzen, Eleanor Tubman, Tatiana Siaraferas, Massimiliano Fratoni

TL;DR

This work addresses the challenge of rapid burnup measurement in pebble bed reactors where high discharge pebble activity hampers conventional HPGe gamma spectroscopy. It proposes bent crystal diffraction (BCD) spectrometers as energy-bandpass filters to isolate diagnostic gamma peaks, supported by synthetic spectrum generation with Serpent/HxF, optical modeling in SHADOW3, and regression analysis that achieves up to $R^2\approx0.995$ for burnup prediction. Key findings include the identification of strong burnup indicators from nuclides such as $^{137m}$Ba/$^{137}$Cs, $^{239}$Np, $^{144}$Ce, $^{148m}$Pm, and $^{140}$La, the design of nuclide-specific BCD configurations (e.g., Si(440) for high-energy lines and Si(220) for others), and the feasibility of using lower-cost detectors like scintillators with appropriate filtering. The results imply a practical, faster burnup-monitoring pathway for pebble bed reactors with potential safeguards advantages, while highlighting future work on non-equilibrium operation, shielding optimization, and footprint considerations.

Abstract

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.

Burnup Measurement using Bent Crystal Diffraction Spectrometers for Pebble Bed Reactors

TL;DR

This work addresses the challenge of rapid burnup measurement in pebble bed reactors where high discharge pebble activity hampers conventional HPGe gamma spectroscopy. It proposes bent crystal diffraction (BCD) spectrometers as energy-bandpass filters to isolate diagnostic gamma peaks, supported by synthetic spectrum generation with Serpent/HxF, optical modeling in SHADOW3, and regression analysis that achieves up to for burnup prediction. Key findings include the identification of strong burnup indicators from nuclides such as Ba/Cs, Np, Ce, Pm, and La, the design of nuclide-specific BCD configurations (e.g., Si(440) for high-energy lines and Si(220) for others), and the feasibility of using lower-cost detectors like scintillators with appropriate filtering. The results imply a practical, faster burnup-monitoring pathway for pebble bed reactors with potential safeguards advantages, while highlighting future work on non-equilibrium operation, shielding optimization, and footprint considerations.

Abstract

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, Ba/Cs, Pu, Ce, Pm, and 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 () 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 Ba, while (220) and (440) configurations paired with scintillators were effective for the remaining isotopes.

Paper Structure

This paper contains 13 sections, 10 equations, 15 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Synthetic Spectrum Generation
  3. Pebble Data Generation with HxF
  4. Gamma Transmission to Pebble Surface
  5. Nuclide Selection
  6. Bent Crystal Spectrometer Optical Modeling
  7. Detector Geometry Optimization
  8. Design Evaluation
  9. Final Spectrometer Designs
  10. Simulating Counts
  11. Regression Performance
  12. Gamma Heating Bounding Calculation
  13. Conclusion

Figures (15)

  • Figure 1: Serpent generated plot of the gFHR model in HxF, including the core geometry (left), explicit pebble (top right), and TRISO geometry (bottom right) gfhr.
  • Figure 2: Fraction of gammas emitted from TRISO fuel kernels that exit the pebble's surface at full energy without being absorbed.
  • Figure 3: Calculated feature importance for six target variables: Total pebble burnup, the total concentration of $^{239}$Pu, the total thermal fluence experienced by the pebble, the fast fluence experienced by the pebble on its most recent pass, the average radial pathway of the pebble on its most recent pass, and the power produced by the pebble on its last pass.
  • Figure 4: Plots showing the relationship between fraction of interference and the width of energies making it to the detector via diffraction. The points at which notable contributors to interference drop off are annotated. Targeted measured gammas include 661.7 keV from $^{137m}$Ba, 133.5 keV from $^{144}$Ce, 106.1 keV from $^{239}$Np, and 414.1 keV from $^{148m}$Pm.
  • Figure 5: Illustration of BCD spectrometer in Bragg geometry. The source is a collimated fuel pebble, and the detector has a slit open towards the crystal.
  • ...and 10 more figures