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In MA sample irradiation test data calculations, the neutron fluence during irradiation period is generally scaled by using dosimetry data in order to improve calculation accuracy. In such a case, appropriate correction is required to burnup sensitivity coefficients obtained by the conventional generalized perturbation theory because some cancellations occur in the burnup sensitivity coefficients. Therefore, a new formula for the burnup sensitivity coefficient has been derived with the consideration of the neutron fluence scaling (NFS) effect. In addition, the cross-section-induced uncertainty is evaluated by using the obtained burnup sensitivity coefficients and the covariance data based on the JENDL-4.0.

The effect of feedback reactivity on the safety of a fast reactor has been studied based on the asymptotic approximation for unprotected transients. The asymptotic approximation adopts the steady state heat transfer equation for calculating temperatures of coolant and fuel with the use of the relevant core power and mass flow. The feedback reactivity can be approximately estimated from the temperatures. This approximation is applied to the UTOP (unprotected transient overpower) and ULOF (unprotected loss of flow) accidents of a sodium-cooled fast reactor with a sodium plenum and GEM (gas expansion module). The reactivity feedback has been estimated, and the constraints of the feedback reactivity for maintaining the safety of the core have been predicted. For the UTOP accident the constraint for the control rod reactivity and the Doppler (+fuel expansion) reactivity coefficient is presented to prevent the fuel melting. For the ULOF accident the constraint of the parameter R is introduced which is the normalized ratio of the power to mass flow rate. The parameter does not exceed the critical point corresponding to the onset of the coolant boiling, and the coolant boiling does not occur because of the large negative reactivity insertion by the GEM. Thus the core safety can be approximately estimated by the present method without detailed calculations, though the accurate analyses are required by the use of transient analyses.

The uncertainty of minor actinides transmutation in fast reactors has been estimated for individual nuclides of minor actinides (MA). The burn-up dependent sensitivities of MA number densities are calculated using the generalized perturbation theory, and a method is derived to transform the sensitivities to the sensitivities of minor actinides transmutation. The sensitivities are used to obtain the uncertainties of minor actinides transmutation together with the cross-section covariance data of JENDL-4. The method is applied to the two MA transmutation fast reactor cores with MA content of 6% and 11%. It is seen that the uncertainties of the total MA transmutation amounts are about 3% and 4% for the two cores because the uncertainties of Np-237 and Am-241 transmutations which mainly contribute the total transmutation are small (about 3%). The contribution to the uncertainties is mainly caused by the Np-237 and Am-241 capture cross-sections. The transmutation uncertainties for Np-239, Am-233, Cm-243, and Cm-245 are rather large. However the transmutation amounts of these nuclides are very small, and the large uncertainties are not the problem in practice. However, it is found that the transmutation amount of Cm-244 has large uncertainties of 10% and 13% for the cores with MA content of 6% and 11%, and this large uncertainties have to be considered when MA fuels are fabricated and reprocessed because Cm-244 produces large decay heat and neutron emission.

Based on the great works of Massimo Salvatores the research studies on the cross-section covariance data and the cross-section adjustment have been revisited, and the important issues and the remaining future tasks have been discussed. On the covariance studies the estimation of the covariance data suitable to predicting neutronics parameters uncertainty has been discussed, and it was found that for MA nuclides covariance data there is a case where the conventional covariance data should be increased. On the adjustment studies the Salvatores report indicated that the negative correlation of after-adjustment covariance data has large effects from numerical calculations, and in this paper the negative correlation effect has been discussed from the theoretical point of view.

Results obtained in the project named “Study on Minor Actinides Transmutation using Monju Data”, which has been sponsored by the Ministry of Education, Culture, Sports, Science and Technology in Japan (MEXT) are described. In order to physically understand transmutation of individual MA nuclides in fast reactors, a new method was developed in which the MAs transmutation is interpreted by two formulas. One corresponds to the difference of individual MA nuclides amounts before and after a burnup period, and the other is the sum of amount of fission of a relevant MA nuclide and the net plutonium production from the MA nuclide during a burnup period. The method has been applied to two fast reactors with MA fuels loaded in cores homogeneously and in a blanket region heterogeneously. Numerical results of MA transmutation for the two reactors are shown.

The purpose of this paper is to apply our improved method for calculating sensitivities and uncertainties of reactivity responses for UO 2 and MOX ( ThO 2 – UO 2 and PuO 2 – UO 2 ) fueled pressurized water reactor cells. The improved method has been used to calculate sensitivity coefficients relative to infinite dilution cross-sections with self-shielding effect taken into account. Two types of reactivities are considered: Doppler reactivity and coolant void reactivity. For each type of reactivity, the sensitivities are calculated for small and large changes of reactivity. The results have demonstrated that the sensitivities are dependent on the changes of reactivity, and the reactivity variation uncertainty is larger than the eigenvalue uncertainty. In addition, the uncertainty of coolant void reactivity is much greater than Doppler reactivity especially for large changes of reactivity because the contribution of U-238 inelastic scattering becomes large. The sensitivity coefficients and uncertainties of both reactivities were verified by comparing with SCALE code results using ENDF/B-VII library and good agreements have been found.

One task of the regulatory body during the review and assessment process is the quantification of uncertainty and sensitivity (U&S) during normal and accident conditions. Nowadays there are many codes having the capability of estimating U&S, but few of them can estimate uncertainty and sensitivity during severe accident conditions. The IRSN uncertainty propagation and sensitivity analysis tool named SUNSET is considered one of the most important tools used in U&S analysis, where it is coupled with ASTEC software package (Accident Source Term Evaluation Code) for computing U&S during severe accident condition. Unfortunately, the SUNSET tool cannot perform U&S analyses during all the transient time. The SUNSET software can only calculate U&S parameters for maximum, minimum, and last output values, therefore it was necessary to modify the SUNSET tool to calculate U&S during the whole transient time. The main objective of this study is to develop a Python script to replace the SUNSET post-processing step, extract the results, and perform U&S analysis. ASTEC code has been used for the simulation of a loss of coolant accident in the cold leg of the primary circuit of the FPT-1 test. The obtained results indicate the efficiency of the modified SUNSET tools to calculate the uncertainty during severe accidents. In general, it was found that the code is capable to model the main severe accident phenomena. SUNSET package shows good agreement with the experimental data, for the whole calculation period, until thermocouples failure moment. The obtained results show that the main safety parameters are very sensitive to the power multiplier.

A covariance data which represents the uncertainty of the difference between the evaluated cross section data and the true data has been discussed and estimated. The two methods of estimating the covariance data suitable for predicting neutronics parameters uncertainty is proposed. One is the method to use the scatter of bias factors, the ratio of the measured neutronics parameters to the calculated ones, among different critical assemblies and the other is the method to use the difference between the bias factors and the true value (unity). The features of the methods is discussed. As a preliminary application the two methods have been used to the criticality problem of thermal reactors with uranium fuel. The covariance data suitable for k-eff uncertainty prediction has been estimated using the data of 65 thermal critical assemblies. From the numerical results, it has been found that the conventional covariance data should be reduced by a factor of 4–16 for predicting k-eff uncertainty. Though the result is preliminary because the covariance data for individual nuclides is not explicitly considered, one can conceive how the proposed methods could be generalized to obtain a new covariance data which could be used for practical uncertainty prediction.

A transient analysis code based on three-dimensional Sn nodal transport theory was developed for accurate transient analysis of the fast reactor. The time-dependent flux is factorized into the amplitude function and the shape function by the improved quasi-static approximation. The direct extension of the Sn nodal transport theory leads to the angular-dependent source term and requires much computer memory. To avoid direct treatment of angular-dependent source term, a new treatment was derived for the source term. The results of steady-state calculations were compared with that obtained by NSHEX for the verification of transport solver. For the verification of reactivity calculation based on perturbation theory, the reactivity was compared with that obtained from the multiplication factor by using the adiabatic approximation. The result with Sn transport calculation was compared with that with the diffusion calculation in Monju core. The results show the discrepancy of reactivity mainly comes from the absorption term.

This paper discusses the improvement of a method for calculating sensitivity coefficients of neutronics parameters relative to infinite dilution cross-sections because the conventional method neglects resonance self-shielding effect. In this study, the self-shielding effect is taken into account by using the intermediate resonance approximation in order to get accurate results in both high and low energy groups. The improved method is applied to calculate sensitivity coefficients and uncertainties of eigenvalue responses for UO 2 and MOX ( ThO 2 – UO 2 and PuO 2 – UO 2 ) fueled pressurized water reactor cells. The verification of the improved method was performed by comparing the sensitivities with MCNP6 and TSUNAMI-1D. For uncertainty, calculation comparisons were done with TSUNAMI-1D, and we demonstrate that the differences are caused by the use of different covariance matrices.

In order to perform sensitivity analyzes in light water reactors where self-shielding effect becomes important, a new method has been developed for calculating sensitivity coefficient of core characteristics relative to the infinite dilution cross-sections instead of the effective cross-sections. This method considers the change of the self-shielding factor due to cross-section perturbation for different nuclides and reactions. SRAC and SAINT codes are used to calculate the improved sensitivity; while the accuracy of the present method has been verified by MCNP code and good agreement has been found.

Neutron cross-section and their covariance at higher energies are generated by nuclear model parameters. The model based covariance exhibit a large systematic errors as compared to experimentally generated covariance. In the absence of probability distribution for the systematic errors, we propose the representativity factor approach to minimize these errors by simulating the upper and lower bounds by the Technique of Determinant Inequalities developed by us. We demonstrate the utility of our approach in simulating optical model covariance parameters for fluorine with reduced systematic errors.

The anisotropic scattering effect to keff is studied for UO2 and MOX fueled BWR assemblies. The anisotropic scattering effect increases the assembly k∞ by 0.44% Δk for the UO2 assembly with 0% void fraction, and by 0.21% Δk for the MOX assembly with 0% void fraction. This is because the anisotropic scattering effect flattens the intra-assembly thermal flux, and the absorption rate in the surrounding water gap is decreased, but the absorption rates in the MOX fuel rods are increased compared to the UO2 rods. Therefore, the total decrease in absorption rates in the UO2 assembly is relatively large, and the k∞ is increased in the UO2 assembly. The dependence of the anisotropic scattering effect on the void fraction is investigated, and the significant difference of 0.62% Δk/k is found for the 0% and the 80% void fractions. The BWR assemblies with Gd rods are also considered. Furthermore, the usefulness of the transport cross section is investigated, and it is found that the transport cross section gives reasonable anisotropic scattering effect, though not satisfactory.

The one-point kinetic equations with numerical errors induced by the explicit, implicit and Crank–Nicolson integration methods are derived. The zero-power transfer functions based on the present equations are demonstrated to investigate the numerical stability of the discretized systems. These demonstrations indicate unconditional stability for the implicit and Crank–Nicolson methods but present the possibility of numerical instability for the explicit method. An upper limit of time mesh spacing for the stability is formulated and several numerical calculations are made to confirm the validity of this formula.

An analytical method to obtain the amplitude of limit-cycle inphase oscillation in boiling water reactors is proposed, which is applicable to small-amplitude limit cycles actually observed in various stability tests. The expression of a zero-power transfer function including the limit-cycle amplitude can be derived by considering higher-order nonlinear interaction between neutron density and feedback reactivity. In a limit-cycle oscillation, the gainand phase-margin of the open-loop transfer function, which is defined by the product of the zero-power and a feedback transfer function, must be zero. From this requirement the oscillation amplitude and resonance frequency can be determined. A numerical example indicates that the fifth-order nonlinear approximation is adequate for the evaluation of the amplitude and that the resonance frequency is only slightly dependent on the amplitude. Assuming the independence of the resonance frequency from the amplitude, a simple formula can also be derived. When a resonance frequency is obtained by linear stability analysis, the oscillation amplitude can be readily determined from the formula expressed as a function of the amplitude by a polynomial.

The commonly used transmutation rate of minor actinides in nuclear reactors is decomposed into four components, overall fission rate, Pu production rate, MA production rate, and element production rate. The physical meanings of these factors are described. The transmutation rates of minor actinides in two types of highly-moderated PWRs, a MOX fueled Na cooled fast reactor, and a metal fueled Pb cooled fast reactor are interpreted using the four components. The metal fueled Pb cooled fast reactor can incinerate minor actinides most (79 kg GWth·year−1), and this amount is about four times larger than the thermal reactors. The thermal reactors have large relative overall fission rates for 241Am and have a potential for the incineration of 241Am.

The transmutation of minor actinides (MAs) has been investigated in thermal reactor cells using mixed oxide fuel with MAs. The effect of neutron spectra on transmutation is studied by changing the neutron spectra. Five transmutation rates are compared: direct fission incineration rate, capture transmutation rate, consumption rate, overall fission incineration rate and inventory difference transmutation rate. The relations between these transmutation rates and their dependence on the neutron spectrum were investigated. To effectively incinerate MAs it is necessary to maximize the overall fission incineration rate and the inventory difference transmutation rate. These transmutation rates become maximum when the fraction of neutrons below 1 eV is about 8% for the case where the MA addition is 1–3%. When the MA addition is over 5%, the transmutation rates become maximum for very hard neutron spectrum.

A neutronic model for linear multichannel analysis of out-of-phase (regional) instability in a BWR core is derived. In this model, the zero-power transfer function of a spatial-harmonic mode, the nodal component of the harmonic amplitude and the node-wise feedback coefficients for the mode appear. Applying the modal expansion technique to a transient flux, we can formulate the above transfer function, nodal component and feedback coefficients. When the λ-mode eigenvalues, eigenfunctions and adjoint-eigenfunctions are numerically obtained by a three-dimensional calculation, these quantities can be evaluated. We derive a lumped neutronic model by the reduction of the present multi-channel model. Consequently, the lumped feedback coefficients for the first-harmonic mode and the nodal component of the harmonic amplitude can be explicitly expressed.

An effective one-group coarse-mesh method for calculating three-dimensional power distribution in fast reactors has been developed. This method uses direction dependent one-group diffusion coefficients in each region so as to preserve neutron leakage rates before and after energy condensation. Furthermore, to correct coarse meshes of one point per hexagonal assembly used in the three-dimensional diffusion calculation, one-group cross-sections are modified by applying Askew's method. Based upon this method an effective three-dimensional diffusion code has been made. Results obtained in test cases on a prototype fast reactor indicate that this method is as accurate as six-group fine-mesh diffusion calculations using six mesh points per assembly in each radial plane and the solution of this method is a factor of 40 faster than the six-group fine-mesh calculations.

An effective homogenization method has been developed for heterogeneous assemblies such as fuel assemblies with and without control blades in BWR and control-rod channels in FBR. Effective homogenized cross sections are calculated so as to preserve the integrated reaction rates in a heterogeneous assembly in each group by iteratively changing the cross section used in homogeneous super-cell calculations in a model composed of the heterogeneous assembly and a fuel region. The method has been applied to the rod-worth calculation for pin rods in the fast critical assembly ZPPR-10 and to the power-density calculation of a test BWR core.