Deterministic modeling of higher angular moments of resonant neutron scattering

An exact scattering kernel formulation for anisotropic scattering up to angular order 10 has been developed and implemented into a deterministic code. The effects of accounting for lattice dynamics on the modeling of neutron scattering in ²³⁵U, ²³⁸U, ²³⁸Pu, and other nuclides have been demonstrated. The new formulation essentially reproduces other investigators previous results for isotropic scattering and quantifies the departures from the isotropic values when higher angular orders are accounted for. The correct accounting for the lattice effects influences the estimated values for the probability of neutron absorption and scattering, which in turn affect the estimation of core reactivity and burnup characteristics. It is shown that, when using the exact scattering kernel formulation, the probability for upscattering significantly increases with increasing temperatures. For example, upscattering for ²³⁸U from below the 20.67 eV resonance increases from 5.57% at 300 K to 30.41% at 1000 K, respectively. Thus, it is shown that the exact scattering kernel is strongly sensitive to temperature, a fact of major importance for High Temperature Reactor fuels. The slowing down process is important in thermal reactors because it results in the neutrons entering the thermal energy range in which the majority of fission events occur. Correctly modeling the slowing down and hence slowing down source into the thermal energy range and consequently allowing the correct modeling of the thermal energy neutron fluxes (or the correct thermal range portion of the spectrum) is paramount to the correct prediction of criticality and safety features such as the Doppler effect. These artifacts are important for all thermal spectrum reactors. In High Temperature Reactors such as the NGNP or the Deep Burn HTR these effects are even more important.     

Improvement of the resonance scattering treatment in MCNP in view of HTR calculations

The importance of an advanced neutron scattering treatment for heavy nuclei with strong energy dependent cross-sections such as the pronounced resonances of ²³⁸U has been discussed in various publications where the full double differential scattering kernel was derived. In this study the double differential kernel is confirmed by a purely stochastic approach. We evaluate the impact of this improved resonance kernel on High Temperature Reactors (HTR) using the Monte Carlo Code MCNPX. A comparison between the standard MCNPX scattering kernel and the new one is introduced. For the analyzed HTR-10 unit cells the new kernel leads to a decrease in criticality of 170–600 pcm depending on TRISO packing factor and fuel temperature and to an increase in magnitude of the Doppler reactivity coefficient by about 10%. The ²³⁹Pu inventory increases by up to 2.5% at the end of cycle.     

Resonance Scattering Near the Thermal Region

In this paper the effect on the neutron flux, in a homogeneous mixture of moderator and fuel, of scattering from low energy resonances in the fuel is considered. Particular attention is given to resonances for which slowing down theory is inappropriate. The kernel for a monatomic gaseous resonance scatterer is derived and compared with the ‘slowing down’ kernel commonly used. The effects of the two kernels on the flux near the resonance for the particular case of ²⁴⁰Pu and a light moderator are also compared.     

Application of Multiband Method to Pin Cell Calculations

Abstract

In order to accurately calculate effective neutron cross sections in the resonance energy region, the multiband method has been applied to cell calculations. Cell calculations for UO² and MOX fuels of light water reactors have been performed and the results were compared with those of a continuous energy Monte Carlo code VIM and the conventional self-shielding method using the Dancoff factor.

The k∞values calculated by the multiband method agreed with those of the VIM calculations within 0.20% Δk for the UO² fuel cell and within 0.30% Δk for the MOX fuel cell, respectively, whereas the Dancoff factor method yielded about l.l%Δk errors for the two cells. The element- wise contribution to this error was investigated, and it was found that the effective microscopic cross sections, particularly those for the giant resonances of ²³⁸U, calculated by the multiband method were in good agreement with those of VIM. It was also found that interference effect between ²³⁸U and ²³⁵U resonances in the UO² fuel and that between ²³⁸U and ²³⁹Pu resonances in the MOX fuel made about 0.20%Δk contributions to k∞ in both fuel cells.     

Effect of Resonance Scattering of Sodium on Resonance Absorption of U-238

The interference effects of the resonance scattering of Na on the resonance absorption of ²³⁸U were investigated. The results for self-shielding factor obtained from exact treatment were compared with those from the usual conventional method, as well as with results based on the assumption that φ(u)σ_t=const. (φ(u): flux, σ_t: total cross section).

In the exact treatment, the neutron spectrum used is obtained with accurate treatment of the slowing down by the elastic scattering of light and medium elements. In the φ(u)σ_t = const, assumption, the energy dependence of the Na resonance scattering cross section is taken into account as in the exact treatment, whereas only the averaged value is used in the conventional method.

Self-shielding factors and their temperature dependence were calculated for several compositions and energy regions. It was found that the conventional method is not satisfactory, while the assumption that φ (u)σ_t= const, compares well with the exact treatment.     

多普勒展宽舍弃修正对氟盐冷却球床高温堆中子学的影响分析

超热区中子的弹性散射易受靶核热运动影响,传统的蒙特卡罗程序采用常数散射截面自由气体模型来描述超热区中子的散射过程。研究表明,忽略共振弹性散射效应所引入的误差随温度的升高而增加,而氟盐冷却球床高温堆工作在高温条件下,为减小共振区弹性散射计算误差,有必要在中子学计算中使用多普勒展宽舍弃修正方法以考虑其共振弹性散射效应。本文使用修改源码后的蒙特卡罗程序MCNP5对氟盐冷却球床高温堆栅元开展中子学计算,发现经多普勒展宽舍弃修正后的²³⁸U的中子俘获率增加,无限增殖因数减小123～1182 pcm,且无限增殖因数偏差随燃料球栅元填充率及温度的升高而增大。     

Investigation of the void reactivity effect in large-size Lead Fast Reactors

An aspect of great relevance in Lead Fast Reactors (LFRs) is the actual void reactivity evaluation. The purpose of this work is double: to inquire into the physical problem, and to evaluate the impact of different approaches and numerical methods on the calculation of the critical reactor parameters involved. Thus, results concerning void effect contributors have been evaluated through a cross-checked analysis performed by means of both a deterministic and a stochastic code. The field of investigation that has been assumed consists in the reference configuration of the 600 MW_e European Lead-cooled SYstem (ELSY), under development within the 6th and 7th EURATOM Framework Programmes. Calculations have been carried out on a 1500 MW_th MOX-fuelled core, composed by wrapper-less square Fuel Assemblies (FAs) with pins on a square lattice. The ERANOS (European Reactor Analysis Optimized System) deterministic code ver. 2.1 and the MCNP Monte Carlo code ver. 4c have been employed in conjunction with the JEFF-3.1 nuclear data library to assess the void reactivity variation and its breakdown into the most relevant nuclides, using both the neutron balance equation method and perturbation theory. Results have shown a very good agreement between ERANOS and MCNP outcomes: the huge reactivity worth determined by the core active region voiding (approximately 5000 pcm) is due to the predominant contributions of even isotopes – among which ²³⁸U plays a major role, being responsible for roughly 4300 pcm – as a consequence of their fission cross-section high sensitivity to spectral hardening (threshold reactions), despite their modest contribution to the total fissions.     

On the use of S(α,β) tables for nuclides with well pronounced resonances

The use of S(α,β) tables for evaluating the secondary energy distribution is restricted in the MCNP code [Briesmeister, J.F. (Ed.), 1997. MCNP – A General Monte Carlo N-Particle Transport Code, LA-12625-M] to light isotopes only. The reason is the free gas model in NJOY, [Macfarlane, R.E., Muir, D.W., 1994. The NJOY Nuclear Data Processing System Version 91, LA-12740-M] which does not account for heavy isotopes with strongly energy dependent cross-sections. The joint scattering kernel developed by [Rothenstein, W., Dagan, R., 1998. Ann. Nucl. Energ. 25, 209–222] improved the secondary energy distribution treatment in a manner consistent with the BROADR module in NJOY. [Rothenstein, W., 2004. Ann. Nucl. Energ. 31, 9–23] enabled the generation of S(α,β) by implementing a new formalism for the modified kernel into the NJOY module THERMR.The new generated S(α,β) tables for heavy isotopes with pronounced resolved resonances were added to the MCNP library data files and the MCNP code itself, was modified accordingly. The quantitative effects of using scattering kernel tables in the vicinity of resonances were analyzed by introducing them into the Tellier et al. [Tellier, H., Costa, M., Raepsaet, C., Van der Gucht, C., 1993. 113, 20–30] benchmark problem. The absorption rate and the Doppler effect were calculated for the pronounced eight S-type resonances of ²³⁸U within the energy range 2.7–210 eV. The introduced S(α,β) tables for ²³⁸U increases the Doppler effect by 23.5% in comparison with the existing MCNP calculation method. Over the entire Resolved Resonance Region (RRR) this means an increase of 17.5%. The overall absorption rate over the entire RRR is increased by 1.4% at 1200 K and by 2.1% at 1800 K.     

Analysis of fuel temperature effects on reactivity of light water reactor fuel assemblies by using MVP-2 adopting an exact resonance elastic scattering model

Using the continuous-energy Monte Carlo code MVP-2 adopting a resonance elastic scattering model considering the thermal motion of a target nucleus (the exact model) for major heavy nuclides, analysis of fuel temperature effects on reactivity of mockup UO₂ and MOX fuel assemblies for light water reactors was performed, and the results were compared with those of the conventional asymptotic model. A base condition was a hot operating condition with an in-channel void fraction of 40% and fuel temperature of 520 ℃ for the BWR fuel assemblies and a hot zero-power condition with fuel temperature of 284 ℃ for the PWR fuel assemblies. The fuel temperature of a high-temperature condition was 1500 ℃ for both types of assemblies. The calculated results showed that the exact model made the neutron multiplication factors at the high-temperature condition lower by ?220 to ?440 pcm (10^?5 Δk) and the Doppler reactivity between the base- and high-temperature conditions more negative by 7% to 10% compared with those obtained by the asymptotic model. The energy-dependent reaction rates of capture and ν-fission were also analyzed to study the detail mechanism in the effect of the exact model on the assembly reactivity.     

Accuracy of Analytical Treatments for Resonance Absorption in Doppler Resonance Regions

Resonance shielding factors based on the assumption of constant collision density have been compared with those obtained by solving rigorously the slowing down equation. The results obtained by calculating numerically the flux for this assumption have been thoroughly examined for several compositions and temperatures. This detailed investigation has been based on consideration of the interaction effects between neighboring resonances in both the same and different nuclear species. The results obtained have permitted determination of the limits of accuracy obtained with conventional analytical methods. The accuracy of two typical methods of approximation based on the above basic assumption has also been investigated for important Doppler resonance regions in large fast reactor.

The study has covered the resonance regions below 21.5 keV for ²³⁸U, and below lOkeV for ²³⁵U and ²³⁹Pu. It has been found that the results obtained numerically from the assumption of constant collision density are fairly good at higher energies, but the errors become large with decreasing neutron energy and the increasing concentration of fuel. Furthermore the shielding factor and the temperature coefficient of ²³⁹Pu are affected considerably by superposition of the resonances of ²³⁸U, and the errors are thereby accentuated by a factor of more than two. And the errors resulting from the analytical methods have been found larger than those incurred by the assumption of constant collision density.     

Verification of Monte Carlo transport codes FLUKA, GEANT4 and SHIELD for radiation protection purposes at relativistic heavy ion accelerators

The crucial problem for radiation shielding design at heavy ion accelerator facilities with beam energies of several GeV/n is the source term problem. Experimental data on double differential neutron yields from thick targets irradiated with high-energy uranium nuclei are lacking. At present there are not many Monte Carlo multipurpose codes that can work with primary high-energy uranium nuclei. These codes use different physical models for simulating nucleus–nucleus reactions. Therefore, verification of the codes with available experimental data is very important for selection of the most reliable code for practical tasks. This paper presents comparisons of the FLUKA, GEANT4 and SHIELD code simulations with experimental data on neutron production at 1 GeV/n ²³⁸U beam interaction with a thick Fe target.     

Uranium assay in mineral samples by means of neutron detection of uranium-238 spontaneous fission

An “in situ” method to determine uranium content in mineral samples by means of detecting neutrons from ²³⁸U spontaneous fission is presented. The method is simple, exact, reliable and passive (it does not need any external excitation source). The technique was experimentally validated, and those experiments were also modeled by a Monte Carlo neutron transport code (MCNP), to check the concordance between experimental results and simulations. Relying on this concordance, calculation ability to describe hypothetical situations was established. The influence of many factors (multiplicative medium, electronic noise, etc.) was estimated. The results obtained allow us to affirm that, with this method it is possible to determine concentrations of 0.05 wt% of uranium (detection limit).The technique has the advantage of sampling very considerable mineral volumes (≈0.2 m³).     

Feedback on neutron capture cross sections of 238Pu and 241Am from analyses of measured isotopic compositions of irradiated LWR fuels and MOX core physics experiments

The atomic fractions of ²³⁸Pu and ²⁴¹Am in MOX fuels recycled in light water reactors are 1% to 2% and not significant compared with those of major Pu isotopes. On the other hand, recent evaluated nuclear data libraries, such as JENDL-4.0 and JEFF-3.2, give noticeably different thermal and epithermal neutron capture cross sections for ²³⁸Pu and ²⁴¹Am. The thermal neutron capture cross sections of ²³⁸Pu and ²⁴¹Am in JEFF-3.2 are 31% and 9% larger than those of JENDL-4.0, respectively. This paper shows the effect of the differences in the neutron cross sections on analysis results of two different integral experiments. The first is the isotopic compositions of ²³⁸Pu on UO₂ and MOX fuels irradiated in BWR and PWR, and the second is the critical experiments of the water moderated cores fully loaded with MOX fuels. The former was analyzed by using the continuous energy Monte Carlo burnup calculation code MVP-BURN and the latter by the continuous energy Monte Carlo calculation code MVP. The comparisons between the calculated and measured results indicate that the most likely thermal and epithermal neutron capture cross sections of ²³⁸Pu and ²⁴¹Am should be around at the middle between those of JEFF-3.2 and JENDL-4.0.     

Neutron Self-Shielding Factor of Scattering-Predominant Resonance Foils

The neutron self-shielding factor of ⁵⁹Co resonance foil as an example of foils whose scattering cross section predominate over their absorption cross sections was obtained by both Monte Carlo method (analog) and the collision probability method for various thicknesses of the foil. Also, the transmission and reflection probabilities of neutrons which have various energies near the resonance energy were obtained, and the effects of multiple scattering of neutrons on the neutron self-shielding factor are discussed.

The neutron self-shielding factors obtained by the Monte Carlo method and by the collision probability method agreed well with each other in the cases Σ t ～ 4.0, in which the Monte Carlo method requires considerably longer machine time. Although for the cases of large Σ t (～4.0) the agreement is not always good because of the flat flux approximation in the collision probability method, the calculation time by Monte Carlo is conveniently short. A combination of both methods is useful in obtaining the neutron self-shielding factor of resonance foils.     

Neutronics and material attractiveness for PWR thorium systems using monte carlo techniques

Thorium (Th) oxide fuel offers a significant advantage over traditional low-enriched uranium and mixed uranium/plutonium oxide (MOX) fuel irradiated in a Light Water Reactor. The benefits of using thorium include the following: 1) unlike depleted uranium, thorium does not produce plutonium, 2) thorium is a more stable fuel material chemically than LEU and may withstand higher burnups, 3) the materials attractiveness of plutonium in Th/Pu fuel at high burnups is lower than in MOX at currently achievable burnups, and 4) thorium is three to four times more abundant than uranium. This paper quantifies the irradiation of thorium fuel in existing Light Water Reactors in terms of: 1) the percentage of plutonium destroyed, 2) reactivity safety parameters, and 3) material attractiveness of the final uranium and plutonium products. The Monte Carlo codes MCNP/X and the linkage code Monteburns were used for the calculations in this document, which is one of the first applications of full core Monte Carlo burnup calculations. Results of reactivity safety parameters are compared to deterministic solutions that are more traditionally used for full core computations.Thorium is fertile and leads to production of the fissile isotope ²³³U, but it must be mixed with enriched uranium or reactor-/weapons-grade plutonium initially to provide power until enough ²³³U builds in. One proposed fuel type, a thorium-plutonium mixture, is advantageous because it would destroy a significant fraction of existing plutonium while avoiding the creation of new plutonium. ²³³U has a lower delayed neutron fraction than ²³⁵U and acts kinetically similar to ²³⁹Pu built in from ²³⁸U. However, as with MOX fuel, some design changes may be required for our current LWR fleet to burn more than one-third a core of Th/Pu fuel and satisfy reactivity safety limits. The calculations performed in this research show that thorium/plutonium fuel can destroy up to 70% of the original plutonium per pass at 47 GWd/MTU, whereas only about 30% can be destroyed using MOX. Additionally, the materials attractiveness of the final plutonium product of irradiated plutonium/thorium fuel is significantly reduced if high burnups (∼94 GWD/MTU) of the fuel can be attained.     

Design of moderator and multiplier systems for D–T neutron source in BNCT

Boron Neutron Capture Therapy (BNCT) is an outstanding way to treat Glioblastoma Multiforme. Epithermal neutrons with energy from 1 eV to 10 keV represent the most effective range for brain tumor therapy. In this research we have focused on ³H(d, n)⁴He reaction as a neutron source using Cock Craft Walton accelerator. High neutron yield with 14.1 MeV energy can be generated via accelerating a deuteron beam with 110 keV energy.A Monte Carlo simulation code (MCNP4C) was used to design the D–T source. Pb and ²³⁸U are suggested as neutron multipliers; AlF₃ and BeO as a moderator and reflector, respectively. An Al layer is used for decreasing the ratio of fast to total neutron fluxes. Epithermal neutron flux in the suggested system is 10⁸ n/cm² s and is a suitable flux for BNCT applications. Finally the suggested configuration is compared to the most recent works and it is shown that the proposed configuration works better.     

在MCNP中考虑共振弹性散射的修正方法

蒙特卡罗方法采用自由气体模型来考虑中子与靶核的弹性碰撞中的热效应。传统的模型假设绝对零度下的弹性散射截面是常数,忽略了截面的共振效应所带来的影响。为在自由气体模型中考虑共振弹性散射效应,采用多普勒展宽舍弃修正方法,修正了连续能量蒙特卡罗程序MCNP的自由气体模型,并对Mosteller轻水堆多普勒基准题进行了分析。数值结果表明：对于轻水堆,在热态零功率的情况下,忽略共振弹性散射会高估燃料棒的无限介质增殖因数（k_∞）40～100 pcm,热态满功率下高估140～200 pcm;忽略共振弹性散射给燃料温度系数带来7%～15%正的偏差。同时分析了新的抽样方法对计算时间的影响,以及共振弹性散射效应对中子出射能量分布的影响。     

Reaction of Titanium Beryllide with Water Vapor

The Doppler reactivity effect of 238U was measured in simulated MOX fuel using the FCA facility for the purpose of obtaining data on the ²³⁸U Doppler reactivity effect in light-water-moderated MOX fuel and evaluating the prediction accuracy of the current analysis code systems and nuclear data library. Experimental data on the Doppler reactivity effect from room temperature up to 800°C were obtained for a uranium fueled core and mockup cores for MOX-fueled LWR using cylindrical natural-uranium samples. With the use of various samples with various neutron spectra, ²³⁸U Doppler reactivity effects at energies generally in the low range below 1 keV were evaluated. Analyses were performed using the current standard analysis code systems for fast and thermal reactors, with the JENDL-3.3 data library. Both analyses yielded calculated/experimental value (C/E) ratios of 0.96 to 1.06 for the MOX cores, a good agreement within the experimental error, and those in the uranium core were similar.     

Resonance absorption of neutrons in an infinite homogeneous medium

The problem of the slowing down of neutrons in an infinite homogeneous medium with strong resonance absorption and uniformly distributed neutron sources is investigated in this paper. The solution of the adjoint equation represents the probability that a neutron of energy E escapes resonance absorption during the process of slowing down to a certain asymptotic energy. The solution of the main and the adjoint problems makes it possible for us to apply a perturbation method to take into account the influence on the resonance integral of the Doppler broadening of the resonance level. The methods developed have been applied to the calculation of the collision density and the resonance integrals for the first level of U²³⁸ (E₀ = 6.7 ev) in pure uranium and in uranium oxide UO₂.