Group-averaged Cross Sections Research Articles

Quasi-Diffusion Method with 3-D Cross Sections for TREAT Core Analysis

The conventional two-step neutronics method used to perform full-core reactor neutronics simulation has been used successfully for light water reactor steady-state and transient analysis. The first step in the method is to generate assembly homogenized few-group cross sections from a lattice transport calculation at the anticipated range of core conditions. The resulting cross sections are then used in the second step to calculate the whole-core flux distribution using nodal diffusion methods. However, when applying this method to small reactors or some experimental reactors such as the Transient Reactor Test (TREAT) Facility, the bias from approximations used in the conventional two-step method can become significant. A large source of error can be the cross sections that are generated from the assembly calculations with reflective boundary conditions since interassembly neutron leakages in small reactors can be significant. Another source of error can be the presence of large void regions such as in the TREAT core. In the work here, the shortcomings of the two-step method were addressed by using the quasi-diffusion method with cross sections obtained from a whole-core three-dimensional Monte Carlo simulation. For the nonvoid region, the group-averaged cross sections were obtained directly from Monte Carlo simulation results, and the directional diffusion coefficients were generated from flux-weighted transport cross sections and the Edington factors directly from the angular flux distribution from the Monte Carlo results. Discontinuity factors were also used in the nodal solution to preserve the neutron currents between nodes based on the Monte Carlo results. For the void region, the directional diffusion coefficients were optimized to minimize the magnitude of the discontinuity factors and thereby mitigate potential numerical problems in the quasi-diffusion method for full-core simulations. The numerical results from the TREAT core steady-state and transient analysis show that the quasi-diffusion method can reproduce the Monte Carlo whole-core results in steady state and that the transient results are in good agreement with experimental measurements.

Treatment of the implicit effect in Shark-X

Shark-X is a set of Perl-based tools build around the deterministic neutron transport code CASMO-5, used to perform uncertainty quantification for lattice calculations at the Paul Scherrer Institut (PSI). While perturbing an input parameter, e.g. a cross section in a given energy range, the resulting perturbation to the effective cross section, e.g. multigroup cross section, can be expressed as the sum of an explicit and implicit component. The implicit term stems from changes in the neutron flux resulting from the cross section perturbation. This effect is neglected when using the standard perturbation theory methodology, even though its importance for uncertainty quantification is reported in the literature.The objectives of the paper are, in view of further enhancing Shark-X, to review a set of existing methods and to propose novel methodologies in order to accurately take the implicit effect into account in the resonance shielding treatment of CASMO-5; as well as to assess the importance of the new tool for typical LWR applications.Amongst the methods considered, those based on an equivalence in dilution allow perturbing the group-averaged cross sections without having to solve the slowing down problem in conjunction with the perturbed point-wise cross sections. However, such methods are found to show only limited improvements as compared to the standard perturbed self-shielded cross sections determined neglecting the implicit effect. As a result, a simpler approach based on the pre-determination of perturbation factors is adopted and implemented into Shark-X and CASMO-5. The new implementation is successfully tested and verified by comparing k-inf sensitivity coefficients computed with Shark-X with those from a Monte-Carlo reference solution, and this for a range of simple homogeneous mixtures as well as for LWR pin cells and lattices.Finally, the paper demonstrates through simple considerations, that the magnitude of the implicit effect is related to the energy group structure in the resolved resonance region, which might be specific to the code used to compute the sensitivity coefficients. The finer is the energy mesh; the smaller is also the impact of the implicit effect, and as such the necessity for a specific treatment.

Verification of the accuracy of Doppler broadened, self-shielded multigroup cross sections for fast power reactor applications

Over the last 5 yr the IAEA nuclear data processing code verification project has attempted to improve the accuracy of the results produced by processing codes. The first round of verification only considered unshielded, cold, group-averaged cross sections. In the second round of verification the effects of Doppler broadening and self-shielding are considered. In this paper we present verification results for Doppler broadening and self-shielding. One of the important results presented in this paper is that the original SIGMA1 method of numerical Doppler broadening as proposed by Cullen and Weisbin (1976) has now been demonstrated to be inaccurate and not capable of producing results to within required accuracies. Fortunately, due to this study, the SIGMA1 method has been significantly improved and the new SIGMA1 is now capable of producing results to within required accuracies. Although this paper presents results based upon using only one code system, it is important to realize that the original SIGMA1 method is presently used in many cross-section processing code systems; the results of this paper indicate that unless these other code systems are updated to include the new SIGMA1 method, the results produced by these code systems could be very inaccurate. In this paper we review the objectives of the IAEA nuclear data processing code verification project as well as the requirements for the accuracy of calculation of Doppler coefficients and the present status of these calculations. Next we present the initial results of Doppler broadening and self-shielding calculations and point out the inconsistency of the results which led to the discovery of errors in the original SIGMA1 method of Doppler broadening. Analysis of the errors found and improvements in the SIGMA1 method are presented. Improved results are presented in order to demonstrate that the new SIGMA1 method can produce results within required accuracies. Guidelines are presented to limit the uncertainty introduced due to cross-section processing in order to balance available computer resources to accuracy requirements. Finally cross-section processing code users are invited to participate in the IAEA processing code verification project in order to verify the accuracy of their calculated results.

Some New Applications of Neutron Slowing Down Time Spectrometry

A lead neutron slowing-down-time spectrometer LESP (LEad Standard Pile or LEad neutron SPectrometer) with a number of novel features was devised. It was applied to measurements on the effective sensitivity of counters and on the effective absorption and total cross sections of reactor materials. The basic principle of this method centers around the correlation that exists between the average neutron energy and the neutron slowing-down-time after fast neutrons are pulsed into a block of heavy medium with small neutron absorption such as a large lead assembly. This is analogous to the well established time-of-flight spectrometry. The proposed method of spectrometry should be suitable for measurement of such effects as the resonance self and mutual shielding and geometrical heterogeneity. As trial experiment, the effective efficiency of a 235U fission chamber was measured and found to correspond fairly well with BNL-325 data. As another example, blocks of heavy resonance material such as natural uranium, antimony and tungsten were placed in the LESP for producing the standard neutron spectrum fields of these materials, and the neutron spectra and effective cross sections measured on these materials were compared with calculation. It is concluded that these new applications of the method are quite practical for measurements of such properties as the effective efficiency of neutron counters and group averaged cross sections.

Measurement of Fissions Produced in Bulk Plutonium-239 by 2-eV to 10-keV Neutrons

This experiment was conducted to obtain data to be used in calculating the number of fissions produced by neutrons in bulk 239Pu as a function of neutron energy. The data provide a consistent set of group-averaged cross sections and self-shielding factors. Although self-shielding factors have been calculated from cross-section data, no previous experiments to measure the energy dependence of 239 Pu self shielding exist. A consistent set of cross sections is possible because of the wide neutron energy range over which this experiment was done. No attempt was made to determine resonance parameters, since in this experiment poor energy resolution was used to improve statistics. (Resonance parameters are, in fact, unnecessary to determine group-averaged cross sections and room-temperature self-shielding factors.) Good-geometry self-shielding factors were measured by a plutonium fission counter shielded by various thicknesses of plutonium. Average fission cross sections, total cross sections, and self-shielding factors have been determined in 11 energy groups whose end points are in the ratio of 2.15-to-1. The energy range was 2.15 eV to 10 keV. The LRL Linac neutron time-of-flight facility was used, with a neutron resolution of 0.18 μsec/m. The detector consisted of a spark chamber that was sensitive to fission fragments, facing a 0.4 mg/cm2 plutonium-239 foil. Seven Pu absorber foils ranging from 0.06 to 3 g/cm2 were used in the self-shielding measurements. This range of absorber thickness yields an adequate description of the resonance-produced surface-absorption effect throughout the above energy region.

Effects of Low-Lying Europium Resonances on the Temperature Defect in Water-Moderated Reactors

The selection of appropriate epithermal group-averaged cross sections for use in a few-group criticality calculation is particularly difficult when resonance absorbers are present. However, by use of the SOFOCATE code for the calculation of thermal spectra in hydrogenous media, it is now practical to include low-lying resonances below 2 ev in the thermal group. Since the SOFOCATE code, which is based on the Wigner-Wilkins differential equation for monatomic hydrogen thermalization, has yielded good agreement with measured spectra in water, it is felt that use of this code and inclusion of low-lying resonances in the thermal group constitute a more accurate and convenient method of treating these resonances than other procedures. As an application of the method, a study has been made of some of the effects associated with the use of Eu as a means of reducing the temperature defect in water-moderated reactors. It is shown that the use of natural, unshielded Eu would reduce the temperature defect provided the spectral hardening introduced by the core absorption is sufficiently small. It is also shown that the strong dependence on spectral hardening is due to the presence of the Eu resonances at about 0.4 ev.