Neutron Importance Function Research Articles

The effect of the importance function resolution on the accuracy of calculating the functionals of the neutron kinetics in water critical assemblies by Monte Carlo method

The paper considers a computational study of the importance function effect on the accuracy of calculating the effective fraction of delayed neutrons, βeff, and generation time of instantaneous neutrons using the MCU Monte Carlo code based on the example of three criticality experiments from the ICSBEP handbook. In the MCU code, the importance function has a piecewise constant form: the computational model is broken down into a finite number of registration objects, and the neutron importance is calculated in each. The obtained importance values are used then to calculate the kinetic functionals due to which the calculation accuracy for the latter depends on the resolution. Three types of the importance function spatial partition (axial, radial, combined) have been studied. The numerical simulation results have shown that the axial component of the neutron importance function in all experiments has practically no effect on the calculation accuracy for βeff and Λ: the difference between the obtained values is less than 1%. The radial component has a notable effect (of up to 15.9%) on the Λ calculation accuracy while having almost no effect on the βeff estimate. Using combined partition, as compared with radial partition, improves the calculation accuracy insignificantly (< 1%).

PCA Benchmark Analysis with ADVANTG3.0.1. and MCNP6.1.1b Codes

The Pool Critical Assembly Pressure Vessel (PCA) benchmark is a well known benchmark in the reactor shielding community which is described in the Shielding Integral Benchmark Archive and Database (SINBAD). It is based on the experiments performed at the PCA facility in the Oak Ridge National Laboratory (ORNL) and it can be used for the qualification of the pressure vessel fluence calculational methodology. The measured quantities to be compared against the calculated values are the equivalent fission fluxes at several experimental access tubes (A1 to A8) in front, behind, and inside the pressure-vessel wall simulator. This benchmark is particularly suitable to test the capabilities of the shielding calculational methodology and cross-section libraries to predict invessel flux gradients because only a few approximations are necessary in the overall analysis. This benchmark was analyzed using a modern hybrid stochastic-deterministic shielding methodology with ADVANTG3.0.1 and MCNP6.1.1b codes. ADVANTG3.0.1 is an automated tool for generating variance reduction (VR) parameters for Monte Carlo (MC) calculations with MCNP5v1.60 code (and higher versions). It is based on the multigroup, discrete ordinates solver Denovo, used for approximating the forward-adjoint transport fluxes to construct VR parameters for the final MC simulation. The VR parameters in form of the weight windows and the source biasing cards can be directly used with unmodified MCNP input. The underlining CADIS methodology in Denovo code was initially developed for biasing local MC results, such as point detector or a limited region detector. The FW-CADIS extension was developed for biasing MC results globally over a mesh tallies or multiple point/region detectors. Both CADIS and FW-CADIS are based on the concept of the neutron importance function, which is a solution of the adjoint Boltzmann transport equation. The equivalent fission fluxes calculated with MCNP are based on several highenergy threshold reactions from international dosimetry libraries IRDF-2002 and IRDFF-2014, distributed by the IAEA Nuclear Data Section. The obtained results show a good agreement with referenced PCA measurements. Visualization of the deterministic solution in 3D was done using the VisIt code from the Lawrence Livermore National Laboratory (LLNL).

Design of an ultra-compact imaging chamber and radiation beamstop for a neutron radiography system employing particle transport

A new neutron radiography facility for the University of Utah TRIGA Reactor (UUTR) is computationally designed to support a multi-purpose irradiation and imaging chamber with a terminal beamstop. Previous efforts from a 3-D MCNP6 UUTR neutron beamport simulation reveals an available neutron flux of 2.5 × 107 ± 1.4 × 105n/cm2/s with an associated dose rate of 5.0 × 105 ± 2.8 × 103 mrem/hr at the end of the beamline system. The shielding required to attenuate the neutron beam and other secondary radiation from reaching the surrounding environment during radiography experiments has been assessed and implemented into MCNP6 Monte Carlo and PENTRAN SN transport code models to assess shield performance and directly compare response solutions between the two methods. In addition, the neutron importance function obtained from adjoint-SN transport is utilized to optimize calculation efficiency in a weight window accelerated PENTRAN-CADIS-MCNP6 model of the irradiation chamber beamstop. Good agreement between adjoint-SN and PENTRAN-CADIS-MCNP6 dose rate calculations is achieved, yielding predicted detector responses within an 8% difference in tally regions of importance. The total neutron dose rate is estimated throughout the entirety of the beamstop prototype, where recommended dimensions and material compositions of the shielding apparatus are provided with supporting analysis.

Adjoint neutron flux calculations with Tripoli-4®: Verification and comparison to deterministic codes

The possibility of computing adjoint-weighted scores by Monte Carlo methods is a subject of active research. In this respect, a major breakthrough has been achieved thanks to the rediscovery of the so-called Iterated Fission Probability (IFP) method, which basically maps the calculation of the adjoint neutron flux into that of the neutron importance function. Based on IFP, we have recently developed the calculation of effective kinetics parameters and sensitivity coefficients to integral reactor responses in the Monte Carlo production code Tripoli-4®. In view of the next release of the code, we have added a new routine allowing for the calculation of the adjoint angular flux (and more generally adjoint-weighted sources) in eigenvalue problems, which can be useful for code-code comparisons with respect to deterministic solvers. In this work we analyse the behaviour of the adjoint angular flux as a function of space, energy and angle for a few benchmark configurations, ranging from mono-kinetic transport in one-dimensional systems to continuous-energy transport in fuel assemblies. The Monte Carlo adjoint flux profiles are contrasted to reference curves, where available, and to simulation results obtained from ERANOS and APOLLO2 deterministic codes.

Calculation of the Neutron Importance Function and the Delayed Neutron Effective Fraction by the Monte Carlo Method

An algorithm for calculation of the neutron importance function and the delayed neutron effective fraction by the Monte Carlo method implemented in the KIR program is presented. The results of calculation of the delayed neutron effective fraction in some critical experiments are given in comparison with the experimental results.

The role of neutron importance in bilinear weighted cross sections for burnup evaluation

This work presents the development and implementation of bilinear weighted cross-sections for improving the accuracy of isotopic concentration calculations, considering neutron importance function in burnup evaluation. Monte Carlo based MCNIC method is used for calculation of the required neutron importance function. A module is developed for this purpose and is implemented into the IRBURN code system. Role of the neutron importance function in accuracy and precision of the burnup calculation is evaluated. An OECD/NEA experimental benchmark problems is used for this evaluation. The results are indicative of the fact that using the bilinear weighted cross-sections give a better estimation of the isotopic concentration in the burnup calculation for most isotopes.

Enhanced finite difference scheme for the neutron diffusion equation using the importance function

Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function.In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in regions with greater neutron importance, density of mesh elements is higher than that in regions with less importance. The forward calculations are then performed for both of the uniform and improved non-uniform mesh point distributions and the results (the neutron fluxes along with the corresponding eigenvalues) for the two cases are compared with each other. The results are benchmarked against the reference values (with fine meshes) for Kang and Rod Bundle BWR benchmark problems. These benchmark cases revealed that the improved non-uniform mesh point distribution is highly efficient.

Calculation of the neutron importance and weighted neutron generation time using MCNIC method in accelerator driven subcritical reactors

The difference between non-weighted neutron generation time (Λ) and the weighted one (Λ†) can be quite significant depending on the type of the system. In the present work, we will focus on developing MCNIC method for calculation of the neutron importance (Φ†) and importance weighted neutron generation time (Λ†) in accelerator driven systems (ADS). Two hypothetic bare and graphite reflected spallation source driven system have been considered as illustrative examples for this means. The results of this method have been compared with those obtained by MCNPX code. According to the results, the relative difference between Λ and Λ† is within 36% and 24,840% in bare and reflected illustrative examples respectively. The difference is quite significant in reflected systems and increases with reflector thickness. In Conclusion, this method may be used for better estimation of kinetic parameters rather than the MCNPX code because of using neutron importance function.

Calculation of kinetic parameters in an accelerator driven subcritical TRIGA reactor using MCNIC method

The effective delayed neutron fraction (βeff) and neutron reproduction time (Λ) play an important role in nuclear reactor control and safety analysis. In this work, calculation of these parameters in an Accelerator Driven Subcritical TRIGA reactor is investigated using MCNIC method. The result of this method has been compared with those obtained by MCNPX code, 1/v poisoning method and reference data. The relative difference between MCNIC method results with MCNPX code and reference data for βeff is −3.0% and 1.7%, respectively. Our results indicate that, the Λ value from MCNIC method has relative differences of −19.4% and −10.3% with MCNPX code and 1/v poisoning method calculations, respectively. These values are increased by increasing the reflector thickness. Finally, this method may be used for better estimation of kinetic parameters rather than the MCNPX code because of using neutron importance function.

Determination of the relative power density distribution in a heterogeneous reactor from the results of measurements of the reactivity effects and the neutron importance function

A method for experimental determination of the relative power density distribution in a heterogeneous reactor based on measurements of fuel reactivity effects and importance of neutrons from a californium source is proposed. The method was perfected on two critical assembly configurations at the NARCISS facility of the Kurchatov Institute, which simulated a small-size heterogeneous nuclear reactor. The neutron importance measurements were performed on subcritical and critical assemblies. It is shown that, along with traditionally used activation methods, the developed method can be applied to experimental studies of special features of the power density distribution in critical assemblies and reactors.

Calculation of neutron importance function in fissionable assemblies using Monte Carlo method

The purpose of the present work is to develop an efficient solution method for the calculation of neutron importance function in fissionable assemblies for all criticality conditions, based on Monte Carlo calculations. The neutron importance function has an important role in perturbation theory and reactor dynamic calculations. Usually this function can be determined by calculating the adjoint flux while solving the adjoint weighted transport equation based on deterministic methods. However, in complex geometries these calculations are very complicated. In this article, considering the capabilities of MCNP code in solving problems with complex geometries and its closeness to physical concepts, a comprehensive method based on the physical concept of neutron importance has been introduced for calculating the neutron importance function in sub-critical, critical and super-critical conditions. For this propose a computer program has been developed. The results of the method have been benchmarked with ANISN code calculations in 1 and 2 group modes for simple geometries. The correctness of these results has been confirmed for all three criticality conditions. Finally, the efficiency of the method for complex geometries has been shown by the calculation of neutron importance in Miniature Neutron Source Reactor (MNSR) research reactor.

Convergence acceleration of neutronic Monte Carlo calculations

Often neutrons are produced in nuclear reactors with high energies, but they are needed at low energies for uses like activation analysis and neutron capture therapy. The evaluation of the slowed down neutron amount by using the Monte Carlo method is very expensive in computation time and the variance is large for natural simulation. In order to reduce the variance and the computation time, we used two biasing techniques to accelerate the calculation convergence. We have used the adjoint flux in the considered system as an importance function in the neutron slowing down equation. In this study, we have considered a homogeneous medium that contains a mixture of U238 (absorber) and hydrogen (scatterer). By handling the adjoint slowing down equation, we have used an analytical approximation of the fine structure of the adjoint flux, as a neutron importance function in the Monte Carlo simulation, for selecting the nuclide with which neutrons interact during their slowing down without absorption. For the second method, we modified the neutron slowing down equation by multiplying it by the adjoint flux. This allowed us to select neutron energies after collision and to avoid the energies corresponding to the absorption resonance. In fact, this was accomplished by assigning an appropriate statistical weight to the neutron, since its birth. For the two methods, a correction in the statistical weight was made after each neutron collision and a Fortran program was used to perform these calculations.

Verification of more general correspondence between eigenvalue separation and coupling coefficient

By taking neutron importance function as a new base of evaluating the coupling magnitude, and by identifying the boundary of a constituent core by zeroes of the first spatial mode, a generalized relation between coupling coefficients and eigenvalue separation is derived. By this equality one can obtain a unified, consistent view in the treatment of a large single core whose two partial zones are loosely coupled, and that of a two-core system with the two physically separated.

Probabilistic Method of Discrete Ordinates in a Neutron Transport Problem

A new numerical method, the probabilistic method of discrete ordinates (PMDO) for solving multigroup transport equations in three-dimensional complex geometry, is presented. The method can be used for reactor core and shielding calculations. Integral equations are adopted for the angular flux in cells of arbitrary form. They are coupled by means of net currents defined at interfaces. The sphere of directions is arbitrarily subdivided into a number of angular diapasons. These diapasons, along with cell volume and pieces of cell surface, produce elementary phase domains, so the basic PMDO equations are the algebraic analogues of piece-wise coupled integral transport equations. They are written for neutron flux and currents integrated over corresponding phase domains. The coefficients of the equations discretely depend on the angular variable and have the meaning of probabilities of uncollided neutrons being transmitted between different phase domains. On the basis of algebraic equations separately obtained for coarse and fine domains, the global-local iterative PMDO scheme has also been developed specifically for calculations in extensive heterogeneous media. Together with the direct PMDO equations, the system of conjugate equations has been constructed for the calculation of neutron importance function related to various nonlinear functionals. Codes based on the method andmore » some numerical applications, including examples related to criticality calculations and deep penetration problems, have been briefly described.« less

Investigation of a moderated SB-Be-photoneutron source and its application to the determination of the neutron importance function

Abstract The neutron importance function in a nuclear fission reactor can be determined by means of the usual radioactive neutron sources only down to a lower energy limit of about 20 keV. The energy range can be extended to epithermal energies if a polyethylene moderated Sb-Be-photoneutron source is used. The results of experimental and theoretical investigations are given concerning the determination of the source spectrum and the source strength and regarding the pecularities of the pseudo-reactivity measurements by means of the moderated Sb-Be- source. Determining the neutron importance function in the fast substituted lattice SEG-III of the Rossendorf annular core reactor RRR the usefulness of this novel source and of the source parameters ascertained are confirmed.

Distribution of the neutron importance function in a reactor with a trap

Distribution of the neutron importance function in a reactor with a trap

Neutron importance function in heterogeneous reactors

Neutron importance function in heterogeneous reactors

Neutron Flux and Importance Distribution by Collision Method, Starting from a Generalized Source

In this paper a multigroup method in finite monodimensional geometry is presented for neutron distribution calculation from a given source distribution. This method is extended to neutron importance function calculation for a given detector distribution.Furthermore, it is shown how truncating the calculation at whatever collision, it is possible to evaluate the “residual” neutron distribution by means of usual methods in diffusion or transport theory.An application is presented related to the generalized perturbation methods and the numerical solution of problems of general interest.

Perturbation theory for the breeding ratio and for other number ratios pertaining to various reactor processes

A perturbation theory formula is derived for use in computing the changes in the frequency ratios of various processes caused by changes (perturbations) affecting any of the reactor parameters. Into this formula are inserted the differences between the values of the parameters, the neutron flux functions and the neutron importance functions with respect to the particular processes being considered. The significance of neutron importance functions is explained in detail and an algorithm is given by which they can be computed. The basis of this algorithm is the algorithm used to compute the ordinary neutron importance function with respect to the asymptotic power by the method of successive approximations.