Analysis of Time-Eigenvalue and Eigenfunctions in the CROCUS Benchmark

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.