ANALYSIS OF TIME-EIGENVALUE AND EIGENFUNCTIONS IN THE CROCUS BENCHMARK

Yasushi Nauchi,Alexis Jinaphanh,Andrea Zoia,M Margulis,P Blaise

doi:10.1051/epjconf/202124704011

Abstract

Time-dependent neutron transport in non-critical state can be expressed by the natural mode equation. In order to estimate the dominant eigenvalue and eigenfunction of the natural mode, CEA had extended the α-k method and developed the generalized iterated fission probability method (G-IFP) in the TRIPOLI-4® code. CRIEPI has chosen to compute those quantities by a time-dependent neutron transport calculation, and has thus developed a time-dependent neutron transport technique based on k-power iteration (TDPI) in MCNP-5. In this work, we compare the two approaches by computing the dominant eigenvalue and the direct and adjoint eigenfunctions for the CROCUS benchmark. The model has previously been qualified for keffs and kinetic parameters by TRIPOLI-4 and MCNP-5. The eigenvalues of the natural mode equations by α-k and TDPI are in good agreement with each other, and closely follow those predicted by the inhour equation. Neutron spectra and spatial distributions (flux and fission neutron emission) obtained by the two methods are also in good agreement. Similar results are also obtained for the adjoint fundamental eigenfunctions. These findings substantiate the coherence of both calculation strategies for natural mode.

Highlights

Over the last ten years, there has been a growing interest for bias and uncertainty quantification in reactor physics calculation based on Monte Carlo methods
Similar efforts have been carried out at CRIEPI, by resorting to a different approach: the direct and adjoint αeigenfunction can be obtained by observing the neutron population for sufficiently long time after a source is placed at the initial position [11]: the distribution of the neutron population at the final time represents the fundamental direct mode; the asymptotic population can be used to assess the importance of the initial point-source, and in this respect it acts as an estimator of the adjoint flux for the natural mode equation
CRIEPI has developed the technique based on k-power iteration (TDPI) technique, which was implemented in MCNP-5

Summary

INTRODUCTION

Over the last ten years, there has been a growing interest for bias and uncertainty quantification in reactor physics calculation based on Monte Carlo methods In this respect, the discovery of the Iterated Fission Probability (IFP) method has been a major breakthrough for continuous-energy Monte Carlo transport [1,2], enabling the deployment of rigorous first-order reactivity perturbation theory and k-eigenvalue sensitivity analysis [3,4]. We further extend this preliminary investigation by considering full-scale three-dimensional and continuous-energy problems For this purpose, CEA has implemented the α-k and the G-IFP methods in the development version of the TRIPOLI-4® code [13], whereas CRIEPI has developed a time-dependent neutron transport technique based on the k-power iteration (TDPI) [14] and implemented it into the MCNP-5 code [15]. To the best of our knowledge, this is the first time that similar comparisons are attempted

Generalized Iterated Fission Probability Method

Time-Dependent Neutron Transport

Description of the CROCUS Benchmark

Direct calculations: dominant α-eigenvalue and eigenfunctions

Adjoint calculations: dominant α eigenfunctions

CONCLUSIONS