Application of material-mesh algebraic collapsing acceleration technique in method of characteristics–based neutron transport code

Nuclear Science and Techniques - New-generation synchrotron light sources are being designed and operated worldwide to provide brighter radiation by reducing the beam emittance to X-ray diffraction...     

Design of a mobile neutron radiography installation based on a compact sealed tube neutron generator

A series of optimum conditions are taken into account in the construction of neutron radiography(NR) installation based on a sealed tube neutron generator capable of gnerating 10^10 n/s with 14MeV.The characteristics of NNU screens,a kind of self-made ^6LiF.ZnS(Ag)scintillation intensifying screen are presented.Finally,some neutron radiographies taken by this NR installation and NNU screens are given.     

Theoretical investigation on the steady-state natural circulation characteristics of a new type of pressurized water reactor

1 Introduction With respect to the inherent safety of nuclear re- actors, application of passive systems/components including natural circulation phenomena as the main mechanism is intended to simplify the safety-related systems and to improve their reliability, to reduce the effect of human errors and equipment failures, and to provide more time to enable the operators to prevent or mitigate serious accidents. Natural circulation is the main mode of heat removal for removing decay heat from t…     

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.     

Influence of granulation of the sample on the thermal neutron Σa measurement

The theoretical approach to the influence of granulation of samples on the measured thermal neutron absorption cross-section has been verified in an experiment on samples containing irregular grains. The neutron absorption heterogeneity effect is defined as the ratio G of the absorption cross-section of the grained sample to the cross-section of the corresponding homogenised medium. The parameter G=1 when the heterogeneity of a material does not influence the thermal neutron transport, otherwise G<1. The theoretical limit, for the “sufficiently small” grains, G→1, has been experimentally confirmed on samples of pure silicon. For the complex media: diabase grains (size from 6.3 to 12.8 mm) embedded in aqueous solutions of boric acid (1.3–2.5% weight concentration), the G parameter achieves values between 0.9 and 0.8. The observed effect can be result in an underestimation of the absorption cross-sections measured on samples insufficiently crumbled.     

Dosimetry method for β radiation based on investigations of the electron spectra in the fields of β emitters

A method has been developed for -ray dosimetry based on the investigation of the effective electron spectra in the fields of emitters. The spectra was investigated with the help of a scintillation spectrometer. It was shown, that the value of the dose , where N is the number of particles penetrating an infinitesimal volume around the point being considered; is the value of the ionization loss averaged over the spectrum. It was established that the quantity is determined by the maximum energy of the spectrum of the isotope and may be considered to be independent of the depth of the medium and of the source diameter. Curves of depth doses for S³⁵, Tl²⁰⁴, Y⁹¹, and Ce¹⁴⁴ + Pr¹⁴⁴ are given and criteria for selecting isotopes to provide optimal conditions of irradiation are established.     

Improved method for measuring the γ-ray absorbed dose rate in models of iron shielding of a thermonuclear reactor

An improved method of measuring the absorbed γ-ray dose rate usingCaSO ₄ andSrSO ₄ type thermoluminescent detectors in models of iron shielding of a thermonuclear reactor is described. The reactionT(d, n)⁴ He served as a neutron source. The method obtained makes it possible to determine the absorbed γ-ray dose rate in shielding without using computed information and relying only on experimental data on the rates of nuclear reactions in threshold detectors. 7 figures, 1 table, 9 references. Moscow Engineering-Physics Institute. Translated from Atomnaya énergiya, Vol. 86, No. 3, pp. 219–225, March, 1999.     

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.     

Analytic solutions of the multigroup space-time reactor kinetics equations—I: 1-D multiregion slab and spherical geometry

The development of analytical and numerical solutions to the reactor kinetics equations is reviewed. Analytic solutions of the multigroup space-time reactor kinetics equations are developed for bare and reflected slabs and spherical reactors for zero flux, zero current and extrapolated endpoint boundary conditions. The material properties of the reactors are assumed constant in space and time, but spatially-dependent source terms and initial conditions are investigated. The system of partial differential equations is reduced to a set of linear ordinary differential equations by the Laplace transform method. These equations are solved by matrix Green's functions yielding a general matrix solution for the neutron flux and precursor concentration in the Laplace transform space. The detailed pole structure of the Laplace transform matrix solutions is investigated. The temporally- and spatially-dependent solutions are determined from the inverse Laplace transform using the Cauchy residue theorem, the theorem of Frobenius, a knowledge of the detailed pole structure and matrix operators.     

The influence of cavities on the critical mass of a “basin-type” reactor

It is shown that the influence of cavities, formed in the reactor active zone after the removal of regulating and emergency rods, on the critical mass of a basin-type reactor cannot always be neglected. For example, after the removal of four special assemblies representing a combination of regulating rods and heat-producing elements, the reactor critical mass can increase by 20–30%, depending on the position of the rods and the size of the cavities in the active zone.The evaluation of the influence of the cavities was made with the help of the two-group method, for a reactor consisting of a number of zones. The first zone was taken to be the central cavity, which behaves as a reflector, the second taken to be the active zone. The external reflector was considered to be the third zone.It was found that the change in the distribution of the thermal neutron flux, caused by the presence of the central cavity, extends to a distance of 8 cm from the center of a cavity of radius 3.2 cm. Therefore, if the regulating rods in a basin-type reactor are separated by a distance of 15–20 cm, as is the case in practice, then it can be expected that the influence of one cavity on another will be small and that reasonably good results can be obtained if the effects produced by the individual cavities are simply added.The author expresses his gratitude to Dr. K.S. Syngve and Mes. Udgaonkar and Kotari for discussion and advice during the work, and, also, for permission to use results of their calculations.     

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.     

Dynamic scenario quantification for level 2 PRA of sodium-cooled fast reactor based on continuous Markov chain and Monte Carlo method coupled with meta-model of thermal–hydraulic analysis

In probabilistic risk assessment (PRA), an event tree (ET) methodology is widely used to quantify accident scenarios which result in core damage and fission products release. However, the current approach using the ET methodology is not applicable to evaluate dynamic characteristics of accident progression, when the accident progression is time-dependent and headings in the ET have inter-dependency between events. Thus, a dynamic approach of accident scenario quantification is necessary to evaluate more realistic PRA.

This research addressed this need by developing a dynamic scenario quantification method for the level 2 PRA by coupling of Continuous Markov chain and Monte Carlo (CMMC) method and a plant thermal–hydraulic analysis code for a sodium-cooled fast reactor (SFR).

The CMMC method is applied to protected loss of heat sink (PLOHS) accident of the SFR to analyze dynamic scenario quantifications. The coupling method requires heavy computational cost and it makes difficult to quantify the whole accident scenarios by comparing the results from existing plant state analysis codes. Thus, a meta-analysis coupling method is proposed to obtain dynamic scenario quantifications with reasonable computational cost. Also, a categorizing method is used to depict analytical results in a transparent manner.     

Study of a self-regulated nuclear burn wave regime in a fast reactor based on a thorium–uranium cycle

The possibility of a wave of slow nuclear burning in a fast reactor in thorium–uranium fuel cycle is investigated. The calculations were performed using a model based on the solution of a nonstationary nonlinear diffusion equation for a cylindrical homogeneous reactor using the concept of a radial geometric factor (buckling) and the effective multigroup approximation taking account of the nuclear kinetics of the precursors of delay neutrons and burnup and production of the main nuclides of the thorium–uranium fuel cycle. The calculations showed that the generation and propagation of a wave of nuclear burning traveling with velocity approximately 2 cm/yr are possible in a thorium–uranium medium. However, the addition of even small quantities of a construction material and coolant to the composition of the reactor makes it impossible to obtain the burn wave regime. A self-maintained nuclear burn regime is also established in this case and exists for a long time (∼5 yr), but the system does not transition into a regime with a nuclear burn wave propagating along the axis of the reactor.     

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.     

Fission vacuum chambers and secondary-emission detectors as effective tools for measuring the characteristics of <Emphasis Type=Italic>γ</Emphasis> and neutron radiation from intense sources

The results of measurements of the flux of fast neutrons in the density range 2·10⁸–2·10¹⁹ sec^–1·cm^–2 and γ-ray dose rate in the range 2·10^–3–1·10⁹ Gy/sec in different operating regimes of pulsed nuclear reactors and accelerators are presented. The parameters of the delayed photon radiation are presented.     

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.     

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.     

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.     

Calculation of response matrix of CaSO4:Dy based neutron dosimeter using Monte Carlo code FLUKA and measurement of 241Am–Be spectra

Response matrix for CaSO₄:Dy based neutron dosimeter was generated using Monte Carlo code FLUKA in the energy range thermal to 20 MeV for a set of eight Bonner spheres of diameter 3–12″ including the bare one. Response of the neutron dosimeter was measured for the above set of spheres for ²⁴¹Am–Be neutron source covered with 2 mm lead. An analytical expression for the response function was devised as a function of sphere mass. Using Frascati Unfolding Iteration Tool (FRUIT) unfolding code, the neutron spectrum of ²⁴¹Am–Be was unfolded and compared with standard IAEA spectrum for the same.