Adjoint flux calculation of natural mode equation by time dependent neutron transport

ABSTRACT

The physical implication of the eigenfunction of the adjoint of the natural mode equation is studied. The eigenfunction at a phase space position is theoretically derived to be proportional to the amplitude of the neutron flux sufficiently long time after a source is placed at the position. Meanwhile, the time change rate and distribution of the neutron flux originated in the source must converge to those of the fundamental mode of the natural mode equation. Based on the proportional relation, the adjoint flux is calculated for a MOX- and UO₂-fueled lattice by a continuous-energy Monte Carlo time-dependent neutron transport calculation. The calculated distributions of the adjoint flux agree well with those of the iterated fission probability both in the prompt and delayed critical states.     

Application of correction technique using leakage index combined with SPH or discontinuity factors for energy collapsing on pin-by-pin BWR core analysis

A correction technique to capture the spectral interference effect on collapsed cross sections is combined with the superhomogenization (SPH) factor or the discontinuity factor (DF) and is applied to the pin-by-pin core analysis for boiling water reactors (BWRs). The spectral interference effect has relationship with variations of neutron leakage in each pin-cell from the viewpoint of neutron balance. In order to correct collapsed cross sections, a new correction technique, in which the neutron leakage in each pin-cell is used as a correction index, was proposed in the previous study. By this correction technique, the reference coarse group cross sections are well reproduced and the calculation accuracies are improved. However, the reference fine group calculation results could not be reproduced since the correction technique cannot reduce energy collapsing errors. Thus, we combine the correction technique with the SPH factor or the DF to reduce energy collapsing errors. In order to verify and discuss the applicability of the correction technique with the SPH factor or the DF, two-dimensional benchmark calculations considering typical characteristics of BWR cores are carried out. The correction technique with the DF more accurately reproduces the reference fine group calculation results than that with the SPH factor.