A multigroup finite-element solution of the neutron transport equation—III: Anisotropy of scattering

The extension of the theory of a multigroup finite-element method of solving the neutron transport equation, to include general anisotropy of scattering and an anisotropic spatially-dependent source, is described. The method, based on a variational principle applied to the even-parity transport equation, employs spherical harmonics for the angular basis functions. To illustrate the development in the associated computer code, three test problems, all including energy-dependent anisotropy, are solved, and the results presented in the form of tables and graphs.     

The integral form of the neutron transport equation for backward–forward scattering in bare spheres

An integral form of the transport equation for bare spheres is developed which incorporates fission plus an arbitrary proportion of isotropic, backward and forward scattering. The integral equation is solved numerically and the critical radius of the sphere is obtained. The results are compared with those from the P_N approximation as reported by Yildiz and Alcan (Yildiz, C., Alcan, E., 1995. The effect of strong anisotropic scattering on the critical sphere problem in neutron transport theory using a synthetic kernel. Annals of Nuclear Energy, 22, 671). and some interesting anomalies are found and discussed.     

Cellular neural network to the spherical harmonics approximation of neutron transport equation in x–y geometry. Part I: Modeling and verification for time-independent solution

This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P_N) to solve the time-independent neutron transport equation in x–y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.     

A method for determining the 2π-counting efficiency of betaparticle sources

This paper is concerned with the efficiency of large-area beta-particle sources. Attention is focussed on sources in which the radioactivity is distributed in a surface layer of an anodized aluminum foil. The efficiency takes into account the reflection and absorption of particles in the aluminum foil, and is defined as the ratio of the number of particles emerging from the foil to the number of particles emitted. A method of estimating the efficiency is proposed which combines measurements and transport calculations. The experimental part of the method consists of measuring the thickness of the layer of mylar which, when inserted between source and detector, cuts the counting rate in half. The theoretical part consists of calculations of beta-particle transport in a two-layer aluminum-mylar medium, which relate the efficiency of the source to the thickness of the measured half-value layer.     

Boubaker polynomials expansion scheme (BPES) solution to Boltzmann diffusion equation in the case of strongly anisotropic neutral particles forward–backward scattering

A polynomial expansion scheme is used to solve Boltzmann neutron transport equation in the case of strongly anisotropic neutral particles forward–backward scattering.     

Optimization of the steady neutron source technique for absorption cross section measurement by using an 124Sb–Be neutron source

An improved experimental approach has been developed to determine thermal neutron absorption cross sections. It uses an ¹²⁴Sb–Be neutron source which has an average neutron energy of only about 12 keV. It can be moderated in either a water tank or a paraffin filled box and can be used for aqueous or powder samples. This new design is first optimized by MCNP simulation and then benchmarked and calibrated with experiments to verify the simulations and realize the predicted improved measurement sensitivity and reproducibility. The ¹²⁴Sb–Be source device is from 1.35 to 1.71 times more sensitive than the previous method based on the use of a ²⁵²Cf source.     

Applicability of a catalytic reduction method using a palladium–copper catalyst and hydrazine for the denitration of a highly concentrated nitrate salt solution

Denitration of a highly concentrated sodium nitrate (NaNO₃) aqueous solution via a catalytic reduction method using a palladium–copper catalyst supported on carbon powder (Pd–Cu/C) and hydrazine (N₂H₄) was investigated. It was demonstrated that nitrate ion (NO₃ ^?) in a 5 mol L^?1 NaNO₃ solution was completely reduced through an intermediate nitrite ion (NO₂ ^?) to nitrogen compounds such as nitrogen, nitrous oxide, and ammonia. By comparing the reaction rates of NO₃ ^? and NO₂ ^? obtained using catalysts with various Pd–Cu compositions and different reductants (hydrogen (H₂) or N₂H₄), it was determined that the catalyst with a molar ratio of Pd:Cu = 1:0.66 provides the maximum reaction rates for NO₃ ^? and NO₂ ^? using N₂H₄, and that not only the reactions of NO₃ ^? and NO₂ ^? but also that of N₂H₄ were affected by the Pd–Cu composition.     

A method for improving the depth selectivity of conversion-electron Mössbauer spectroscopy

The possibility of improving the depth selectivity of conversion-electron Mössbauer spectroscopy by mathematical processing of the initial experimental results is demonstrated. The method constructs Mössbauer spectra for electrons from a thin layer of matter localized at an arbitrarily chosen depth of a specimen by a linear combination of the initial Mössbauer spectra. It is shown that the method allows to a higher depth resolution to be obtained than by conventional instrumentational method.     

A comparison of the Covariance Matrix Adaptation Evolution Strategy and the Levenberg–Marquardt method for solving multidimensional inverse transport problems

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES), a powerful optimization algorithm that mimics the process of evolution in nature, is applied to the inverse transport problems of interface location identification, source composition identification, and material mass density identification (both separately and combined) in cylindrical radioactive source/shield systems. The energies of discrete gamma-ray lines emitted by the source are assumed to be known, while the uncollided line fluxes are assumed to be measured at points external to the system. CMA-ES is compared to the Levenberg–Marquardt method, a standard gradient-based optimization algorithm, on numerical test cases using both simulated data that is perfectly consistent with the optimization process and with realistic data simulated by Monte Carlo. Numerical results indicate that the Levenberg–Marquardt method is more adept at problems with few unknowns (i.e. ?3), but as the number of unknowns increases, CMA-ES becomes the superior strategy. Results also indicate that a parallel version of CMA-ES would be more robust than, and have competitive run times with, the Levenberg–Marquardt method for many inverse transport problems.     

Enhancement of neutron irradiation uniformity for the CFBR-Ⅱ fast burst reactor with a biaxial rotational technique

A biaxial rotational technique is proposed to improve the neutron irradiation uniformity for a large sample,and the theoretical method is established to predict and design the main parameters. The technique used a device to rotate the target sample around two perpendicular axes simultaneously. Numerical calculations found that the lowest common multiple of the two angular speeds should be large enough to improve the uniformity,and the minimal experimental time should be no less than 600 s. For a three-dimensional sample with a size of 20 cm × 12 cm × 14 cm, the maximal non-uniform neutron irradiation factor of the sample is mainly determined by the distance between the center of the sample and of the point neutron source. It was computed to be less than 10% when the distance was no less than 34 cm. Experiments were carried out on the CFBR-II reactor and the experimental results were in good accordance with the theoretical analysis. As a result, the theoretical conclusions given above are reasonable and of reference value for the design of future irradiation experiments.     

Measurement of thermal neutron cross-section and resonance integral for the Yb(n,γ)Yb reaction by the cadmium ratio method

The thermal-neutron cross-section and the resonance integral for the ¹⁷⁴Yb(n,γ)¹⁷⁵Yb reaction were measured by the activation method using a ⁵⁵Mn monitor as single comparator. Analytical grade MnO₂ and Yb₂O₃ powder samples with and without a cylindrical 1 mm Cd shield box were irradiated in an isotropic neutron field obtained from three ²⁴¹Am-Be neutron sources. The gamma-ray spectra from the activated samples were measured with a calibrated n-type high-purity Ge detector. The experimental results were corrected for the correction factors calculated for thermal and epithermal neutron self-shielding effects, epithermal neutron spectrum shape and gamma-ray self attenuation. Thus, the thermal neutron cross-section for the ¹⁷⁴Yb(n,γ)¹⁷⁵Yb reaction is found to be 126.5 ± 6.6 b, relative to that of the ⁵⁵Mn monitor. The resonance integral value for the ¹⁷⁴Yb(n,γ)¹⁷⁵Yb reaction is found to be 59.6 ± 8.5 b, at cadmium cut-off energy of a 0.55 eV. Using the measured cadmium ratios of ⁵⁵Mn and ¹⁷⁴Yb, the result for resonance integral of the ¹⁷⁴Yb(n,γ)¹⁷⁵Yb reaction has also been obtained relative to the reference value of the ⁵⁵Mn monitor. The present results for the ¹⁷⁴Yb(n,γ)¹⁷⁵Yb reaction agree well only with the recent experimental ones obtained by Kafala et al. [1] and De Corte and Simonits [2] within uncertainty limits. However, the previously reported experimental data for the thermal neutron cross-section for this reaction are distributed between 24 and 141 b, and similarly the experimental values for the resonance integral value also show a large scatter in the range of 30-69 b.     

The optimal number of thermal diffusion columns for deuterium recovery from H–D gas mixture in the countercurrent-flow Frazier scheme with the total sum of column heights fixed

The effect of the column number on deuterium recovery from H–D gas mixture in the countercurrent-flow Frazier scheme of thermal diffusion columns with the total sum of column heights fixed, has been investigated. The equations for predicting the optimal number of columns and the corresponding maximum separation have been derived. Considerable improvement in deuterium recovery is obtainable if the multi-column device with the optimal number of columns is employed, instead of using the single-column device with the same total sum of column heights, especially for the cases of higher volume flow-rate operation and larger total sum of column heights. Furthermore, countercurrent-flow operation is much better than forward-flow operation.     

CTOF measurements and Monte Carlo analyses of neutron spectra for the backward direction from an iron target irradiated with 400–1200 MeV protons

A calorimetric-time-of-flight (CTOF) technique was used for real-time, high-precision measurement of the neutron spectrum at an angle of 175° from the initial proton beam direction, which hits a face plane of a cylindrical iron target of 20 cm in diameter and 25 cm thick. A comparison was performed between the neutron spectra predicted by the MARS and the MCNPX codes and that measured for 400, 600, 800, 1000 and 1200 MeV protons.     

Method for calculating the current–voltage characteristics of thermionic electricity-generating channels with complex geometry

A method for performing numerical calculations of the thermo-electro-physical characteristics of an electricity generating channel with a complex geometry using the experimental databases developed at the Leipunskii Institute for Physics and Power Engineering is described. The current–voltage characteristic of the electricity-generating channel is calculated in order to predict the electro-thermo-physical characteristics of new-generation space-craft thermionic nuclear power facilities. An analytical relation for determining the current–voltage characteristic of an electricity-generating element on the basis of the average temperature of the electrodes is derived; this relation can be used to compare the output characteristics of advanced thermionic nuclear power facilities. An iterative algorithm for calculating the parameters of the electricity-generating elements and the entire channel by the grid method is developed.     

A function to provide neutron spectrum produced from the 9Be + p reaction with protons of energy below 12 MeV

A function to give the total neutron production cross section, angular distribution, and energy spectrum via the ⁹Be + p reaction has been created by fitting experimental data to characterize compact neutron sources with thick Be targets bombarded by protons with energy below 12 MeV. To examine the suitability of the function, calculations of the angle-dependent neutron energy spectra produced in thick Be targets with 4- and 12-MeV protons using the function were compared with corresponding experiments and calculations using the nuclear data libraries of ENDF/B-VII.0 and JENDL4.0/HE. The function was in better agreement with the experiments than the calculations using the libraries except for at backward angles. The ¹¹⁵In(n,n’)^115mIn reaction rates calculated using GEANT4 with source neutrons given by both the function and ENDF/B-VII.0 were compared with that measured at the RIKEN Accelerator-Driven Compact Neutron Source to evaluate the neutron spectrum above 1 MeV. The function slightly overestimated the measurement by 14% and the calculation with ENDF/B-VII.0 underestimated by 35%. It was concluded that the function can be applied in compact neutron source designs.     

Rossi-α and Feynmann Y functions for non-Poissonian pulsed sources of neutrons in the stochastic pulsing method: Application to subcriticality monitoring in ADS and comparison with the results of Poissonian pulsed neutron sources

In this paper, analytical expressions for the Rossi-α and the Feynmann Y functions are deduced for the case of Poissonian and non-Poissonian neutron sources when the stochastic pulsing method is used. These analytical expressions are used to fit the experimental data and to obtain the prompt neutron time constant. Also we perform in this paper a comparison of the results obtained for the Rossi-α and Feynmann Y functions with Poissonian and non-Poissonian neutron sources, and we study how much change the shape of these functions when the fission probability decreases and the capture probability increases due to the depletion with time of the fuel, and the increase of the fission products. Some comparisons with experimental data and with the results of other authors have been performed. Another important question analyzed in this paper and that it is interesting from an academic point of view is that the average number of detected counts induced by one single neutron injected in the system at an arbitrary time t′, should obey in point kinetics theory an adjoint equation in the time domain. Also the cross-factorial moment of the number of counts induced by one neutron in two counting intervals should obey also an adjoint equation in the time domain with a source term that depends on the first moments. These results are a consequence of more general results that have been obtained using stochastic transport theory for the one particle probability generating function or Kernel generating function.     

Investigation of the characteristics of an e, φ scintillation spectrometer with a BGO crystal for energies of 0.5–100 MeV

Conclusions The measurements have shown that a BGO crystal with a diameter of 5 cm can be used to build relatively compact, highly efficient spectrometers for electrons and quanta; the resolution is 15–5% for energies of 0.5–6 MeV and 40% for 20–100 MeV; the characteristic of the spectrometer is linear in this entire range.Translated from Atomaya Énergiya, Vol. 69, No. 4, pp. 246–248, October, 1990.