Neutronics calculation methods

The methods used for reactor calculations can be considered in three categories, the accurate reference calculation methods, the routine methods used for operating reactors, such as SUPER-PHENIX, and those used for exploratory design studies. 

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Studies of solvent structure are usually carried out by analyzing radial distribution functions that are obtained by X-ray or neutron diffraction methods. Monte Carlo (MC) or molecular dynamics (MD) calculations are also used. Studies of the structure of lion-aqueous and mixed solvents are not extensive yet but some of the results have been reviewed. Pure and mixed solvents included in the reviews... 

During the last two decades, studies on ion solvation and electrolyte solutions have made remarkable progress by the interplay of experiments and theories. Experimentally, X-ray and neutron diffraction methods and sophisticated EXAFS, IR, Raman, NMR and dielectric relaxation spectroscopies have been used successfully to obtain structural and/or dynamic information about ion-solvent and ion-ion interactions. Theoretically, microscopic or molecular approaches to the study of ion solvation and electrolyte solutions were made by Monte Carlo and molecular dynamics calculations/simulations, as well as by improved statistical mechanics treatments. Some topics that are essential to this book, are included in this chapter. For more details of recent progress, see Ref. [1]. 

The neutron inelastic scattering spectra of 2,4-dinitroimidazole have been registered and calculated by solid-slate calculation methods at BLYP/dnd, BP/dnd, and PWC/dnd theory levels [682], Comparison of the observed and calculated neutron spectra reveals that the BLYP/dnd calculations provide the best description of the experimental spectrum. 

K. Holdema-Natkaniec, A. Szyczewski, I. Natkaniec, V.D. Khaviyutchenko A. Pawlukojc (2002). Appl. Phys. A [Suppl.], 74, S1274-S1276. Progesterone and testosterone studies by neutron-scattering methods and quantum chemisby calculations. 

Proton Wave Functions in Palladium Studied by Ab Initio Calculations and Inelastic Neutron Scattering Methods... 

The precision of the neutron activation method for 18 elements can be seen from the data in Table 5.7. The standard deviations listed have been calculated from replicate determinations of these elements in a California oil. Except for Au, the relative standard deviation for all elements is less than 12%. The value of 57.1% for the relative standard deviation of the Au concentration is due possibly to adsorption of Au on the container walls during irradiation because Au was observed in some of the irradiation vials after removal of the sample. 

A full scale critical experiment is important to evaluate the calculated results such as reactivity coefficients and critical conditions. As neutron leakage is enhanced in the 4S core, the conventional calculation method is not sufficient to accurately predict the core characteristics. A critical experiment is thus the most urgent R D item. 

Calculational methods used to determine the neutron multiplication should be validated, preferably against applicable measured data (see Appendix VII). For irradiated nuclear fuel this vahdation should include comparison with measured radionuclide data. The results of this validation should be included in determining the uncertainties and biases normally associated with the calculated neutron multiplication. Fission product cross-sections can be important in criticality safety analyses for irradiated nuclear fuel. Fission product cross-section measurements and evaluations over broad energy ranges have not been emphasized to the extent that actinide cross-sections have. Therefore, the adequacy of fission product cross-sections used in the assessment should be considered and justified by the safety analyst. 

These methods have been tested by neutronics calculations for a group of simple spherical assemblies consisting of a central core of Pu and reflected by 93.2% U, U(nat), W, and BeO. Independent calculations for these evaluated assemblies have been made at tee Los Alamos Scientific Laboratory and AWRE, Aldermaston. The results and conclusions of this study are presented. 

The spherical critical mass of 93% " ll enriched uranium metal which has teen used as a benchmark problem for verification of calculational methods is based on foe delayed critical mass measurements made on Godiva corrected to standard conditions. A near Spherical mass of U(93.2), recently surplused from an ei erimental program examining fast reactor behavior with an accelerator booster, was re-machined to a spherical radius of 3.466 in. Tte device is to be used in a study of neutron kinetic parameters. The data obtained for the delayed critical configuratian confirm the reevaluated critical parameters recently reported by Man-sen and Paxton. ... 

In like manner, toe program with U(5) rods of several dianmters has been extmided, beyond toe arrays made critical with water and with dilute boron solution as moderator and. reflector, to arrays critical in dilute (about 300 g U/llter) aqueous iiraiqrl fluoride solution, to submerged arrays irdOected by lead on four sides, and to submerged arrays reflected by depleted uranium on one side. Some of these lattices also contained a solid neutron absorber, either stainless steel, Boral, or cadmium. The latter experiments have applicability to shipping casks for reactor foel elements for which validated calculational methods are needed. 

The analytical tool used in this investigation is the Los Alamos Pajarito Dynamics Code (PAD). This code employs the coupled neutronic-hydrodynamics method in one dimension, with the neutronics provided by DTF-IV transport calculations. Without prior normalization, the PAD code has reproduced the fission energy releases of various reactor transient experiments to within a factor of 2 (Ref. 2). Furthermore, identifying the kinetic energy calculated by the PAD code With explosive energy, experimental results for this tatter quantity have also been reproduced with about the same accuracy. ... 

The theory/ejq)eriment comparison is presented in Fig. 1 at the three experimental concentrations. The calculational method consistently predicts neutron reproduction factors less than unity for e q>erimentally critical systems. Based on this comparison, this calculational method may be used for nuclear safety evalua-... 

The solid angle model relates the neutron multiplication factor of a uniform array of units to the multiplication factor of the units and the total solid angle subtended at a unit by all other units of the array. The solid angle method in application is an empirical procedure. The use of such is permitted by the American National Standard for Nuclear Criticality Safety, N16.1-1975, provided the procedure has been validated. The American National Standard N16.9-197S outlines the requirements for establishing the validity and area(s) of applicability of such a calculational method. This standard on solid angle will permit use of the solid angle technique in compliance with the requirements of N16. l and N 16.9. ... 

The good agreement between the calculated and measured parameters validates this calculationat method for unreflected, low-enriched, fuel-solution systems with a central Cf neutron source. Further comparisons between measurement and calculations for a variety of solution systems are required before acceptance of this calculational method for these types of experiments. 

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