The study of a neutron spectrum unfolding method based on particle swarm optimization combined with maximum likelihood expectation maximization

The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In order to solve the problem of the maximum likelihood expectation maximization(MLEM) algorithm which is easy to suffer the pitfalls of local optima and the particle swarm optimization(PSO) algorithm which is easy to get unreasonable flight direction and step length of particles, which leads to the invalid iteration and affect efficiency and accuracy, an improved PSO-MLEM algorithm, combined of PSO and MLEM algorithm, is proposed for neutron spectrum unfolding. The dynamic acceleration factor is used to balance the ability of global and local search, and improves the convergence speed and accuracy of the algorithm. Firstly, the Monte Carlo method was used to simulated the BSS to obtain the response function and count rates of BSS. In the simulation of count rate, four reference spectra from the IAEA Technical Report Series No. 403 were used as input parameters of the Monte Carlo method. The PSO-MLEM algorithm was used to unfold the neutron spectrum of the simulated data and was verified by the difference of the unfolded spectrum to the reference spectrum. Finally, the 252Cf neutron source was measured by BSS, and the PSO-MLEM algorithm was used to unfold the experimental neutron spectrum.Compared with maximum entropy deconvolution(MAXED), PSO and MLEM algorithm, the PSO-MLEM algorithm has fewer parameters and automatically adjusts the dynamic acceleration factor to solve the problem of local optima. The convergence speed of the PSO-MLEM algorithm is 1.4 times and 3.1 times that of the MLEM and PSO algorithms. Compared with PSO, MLEM and MAXED, the correlation coefficients of PSO-MLEM algorithm are increased by 33.1%, 33.5% and 1.9%, and the relative mean errors are decreased by 98.2%, 97.8% and 67.4%.

High-resolution neutronics model for ^(238)Pu production in high-flux reactors

We proposed and compared three methods(filter burnup,single energy burnup,and burnup extremum analysis)to build a high-resolution neutronics model for 238Pu production in high-flux reactors.The filter burnup and single energy burnup methods have no theoretical approximation and can achieve a spectrum resolution of up to~1 eV,thereby constructing the importance curve and yield curve of the full energy range.The burnup extreme analysis method combines the importance and yield curves to consider the influence of irradiation time on production efficiency,thereby constructing extreme curves.The three curves,which quantify the transmutation rate of the nuclei in each energy region,are of physical significance because they have similar distributions.A high-resolution neutronics model for ^(238)Pu production was established based on these three curves,and its universality and feasibility were proven.The neutronics model can guide the neutron spectrum optimization and improve the yield of ^(238)Pu by up to 18.81%.The neutronics model revealed the law of nuclei transmutation in all energy regions with high spectrum resolution,thus providing theoretical support for high-flux reactor design and irradiation production of ^(238)Pu.

Research on perturbation of neutron fluence rate in a closed thermal neutron field due to medium materials

The neutron radiation field has vital applications in areas such as biomedicine,geology,radiation safety,and many others for neutron detection and neutron metrology.Correcting neutron fluence rate perturbation accurately is an important yet challenging problem.This study proposes a correction method that analyzes three physical processes.This method,which transforms the detection process from point detection to area detection,is based on a novel physical model and has been validated through theoretical analyses,experiments,and simulations.According to the average differences between the calculated and experimental results,the new method(1.67%)demonstrated better accuracy than the traditional simulation(2.17%).In a closed thermal neutron radiation field,the detector or strong neutron absorption material significantly perturbs the neutron fluence rate,whereas its impact on the energy spectrum shape and neutron directionality is relatively minor.Furthermore,based on the calculation results of the perturbation rate formula for medium materials with different compositions and sizes,the larger the volume and capture cross section of the medium,the higher the perturbation rate generated in the closed radiation field.

Analysis of prompt fission neutron spectrum and multiplicity for ^(237)Np(n, f) in the frame of multi-modal Los Alamos model

The improved version of Los Alamos model with the multi-modal fission approach is used to analyse the prompt fission neutron spectrum and multiplicity for the neutron-induced fission of 237Np. The spectra of neutrons emitted from fragments for the three most dominant fission modes （standard Ⅰ, standard Ⅱ and superlong） are calculated separately and the total spectrum is synthesized. The multi-modal parameters contained in the spectrum model are determined on the basis of experimental data of fission fragment mass distributions. The calculated total prompt fission neutron spectrum and multiplicity are better agreement with the experimental data than those obtained from the conventional treatment of the Los Alamos model.

Geant4 simulation of multi-sphere spectrometer response function and the detection of 241Am–Be neutron spectrum

This paper is aimed at detecting the neutron spectrum of^(241)Am–Be, a widely used neutron source, with the SP9 ~3He proportional counter, which is a multi-sphere spectrometer system of eight thermal neutron detectors embedded in eight polyethylene(PE) spheres of varying diameters. The transport processes of a neutron in the multi-sphere spectrometer are simulated using the Geant4 code. Two sets of response functions of the PE spheres are obtained for calculating the^(241)Am–Be neutron spectrum.Response Function 1 utilizes the thermal neutron scattering model G4 Neutron HPThermal Scattering for neutron energies of ≤4 eV, and Response Function 2 has no thermal treatment. Neutron spectra of an^(241)Am–Be neutron source are measured and compared to those calculated by using the response functions. The results show that response function with thermal treatment is more accurate and closer to the real spectrum.

Measurement of the Energy Spectrum of the Neutrons inside the Neutron Flux Trap Assembled in the Center of the Reactor Core IPEN/MB-01

This paper presents the neutron energy spectrum in the central position of a neutron flux trap assembled in the core center of the research nuclear reactor IPEN/MB-01, obtained by an unfolding method. To this end, we have used several different types of activation foils （Au, Sc, Ti, Ni, and plates） which have been irradiated in the central position of the reactor core （setting number 203） at a reactor power level （64.57±2.91 watts）. The activation foils were counted by solid-state detector HPGe （high pure germanium detector） （gamma spectrometry）. The experimental data of nuclear reaction rates （saturated activity per target nucleus） and a neutron spectrum estimated by a reactor physics computer code are the main input data to get the most suitable neutron spectrum in the irradiation position obtained through SANDBP （spectrum analysis neutron detection code-version Budapest University） code： a neutron spectra unfolding code that uses an iterative adjustment method. the integral neutron flux, （2.41 ± 0.01） × 10^9 n·cm^-2·s^-1 for the thermal The adjustment resulted in （3.85 ± 0.14） × 10^9 n·cm^-2·s^-1 for neutron flux, （1.09 ±0.02） × 10^9n·cm^-2·s^-1 for intermediate neutron flux and （3.41 ± 0.02） × 10^8 n·cm^-2·s^-1 for the fast neutrons flux. These results can be used to verify and validate the nuclear reactor codes and its associated nuclear data libraries, besides, show how much effective it can be that the use of a neutron flux trap in the nuclear reactor core to increase the thermal neutron flux without increase the operation reactor power level. The thermal neutral flux increased 4.04 ± 0.21 times compared with the standard configuration of the reactor core.

Simulation of the Traweling Wave Burning Regime on Epithermal Neutrons

New results of two computer experiments on modeling of superthermal neutron-nuclear combustion of natural uranium for two different flux densities of external neutron source and duration of half a year each are presented. The simulation results demonstrate the dependence of the autowave combustion modes on the parameters of the external source.

Comparison of neutron energy spectrum unfolding methods and evaluation of rationality criteria

The neutron energy spectrum was measured using a Bonner sphere spectrometer at six locations inside the containment vessel of a nuclear reactor at the Qinshan nuclear power plant. The structures of the neutron spectra obtained by the maximum entropy, iteration, and genetic algorithm methods were consistent with one another and could be interpreted as the spectral superposition of different energy regions. The characteristic parameters of the neutron spectrum, including the fluence rate,average energy, and neutron ambient dose equivalent rate H^(*)(10), were in good agreement among the three methods. In addition, an LB6411 neutron ambient dose equivalent meter was employed to obtain the H^(*)(10) directly for comparison.These findings indicate that neutron spectrum unfolding methods can be used to overcome the problems associated with the response functions of dosimeters to provide more accurate H^(*)(10) values. In this study, the following three evaluation criteria were systematically addressed to ensure the accuracy of the unfolded spectra: count rates of the inverse solutions,neutron spectrum structures, and comparison of key parameters.

Calculation of the reactor neutron time of flight spectrum by convolution technique

It is a very complex and time-consuming process to simulate the nuclear reactor neutron spectrum from the reactor core to the export channel by applying a Monte Carlo program. This paper presents a new method to calculate the neutron spectrum by using the convolution technique which considers the channel transportation as a linear system and the transportation scattering as the response function. It also applies Monte Carlo Neutron and Photon Transport Code （MCNP） to simulate the response function numerically. With the application of convolution technique to calculate the spectrum distribution from the core to the channel, the process is then much more convenient only with the simple numerical integral numeration. This saves computer time and reduces some trouble in re-writing of the MCNP program.

Extended Bonner sphere spectrometer for dynamic neutron spectrum on HL-2A

The extended Bonner sphere spectrometer （EBSS） at the HL-2A tokamak for the neutron spectrum is described. This device was developed on the basis of previous Bonner sphere spectrometry （BSS）, aiming to obtain a more accurate neutron spectrum in the HL-2A tokamak hall. The previous BSS contained eight Bonner spheres （BS）. This EBSS contains 13 3He-filled detectors embedded in polyethylene spheres （PS）, pre-amplifiers, and a parallel processing data acquisition system （DAQ）. A response matrix is simulated in Geant4 taking the effect of the environment into account.

Using activation method to measure neutron spectrum in an irradiation chamber of a research reactor

Neutron spectrum should be measured before test samples are irradiated.Neutron spectrum in an irradiation chamber of a research reactor was measured by using activation method when the reactor is in normal operation under 2 MW.Sixteen kinds of non-fission foils(19 reaction channels) were selected,of which 10 were sensitive to thermal and intermediate energy regions,while the others were of different threshold energy and sensitive to fast energy regions.By measuring the foil radioactivity,the neutron spectrum was unfolded with the iterative methods SAND-Ⅱ and MSIT.Finally,shielding corrections of group cross-section and main factors affecting the calculation accuracy were studied and the uncertainty of solution was analyzed using the Monte Carlo method in the process of SAND-Ⅱ.

Energy spectrum measurement and dose rate estimation of natural neutrons in Tibet region

In this work, natural neutron spectra at nine sites in Tibet region were measured using a multi-sphere neutron spectrometer. The altitude-dependence of the spectra total fluence rate and ambient dose equivalent rate were analyzed. From the normalized natural neutron spectra at different altitudes, the spectrum fractions for neutrons of greater than 0.1 MeV do not differ obviously, while those of the thermal neutrons differ greatly from each other. The total fluence rate, effective dose rate and the ambient dose equivalent rate varied with the altitude according to an exponential law.

GEANT4 simulation of the characteristic gamma-ray spectrum of TNT under soil induced by DT neutrons

The characteristic gamma-ray spectrum of TNT in the soil induced by DT neutrons is measured by the PFTNA demining system. The GEANT4 toolkit is used to simulate the whole experimental procedure. The simulated spectra are compared with the experimental spectra, and they are mainly consistent. The share of the background sources such as neutrons and gamma is obtained and the contribution that the experimental apparatus to the background, such as shielding, detector sleeve and moderator, is analyzed. The effective gamma signal(from soil and TNT) is 29% of the full spectrum signal, and the background signal, more than 68%, this is mainly produced by shielding and the detector sleeve. By gradually optimizing the shielding and the cadmium sheet of the detector sleeve, the share of the effective gamma signal increases to 47%, and the background signal reduces to 18%.

Benchmarking of JEFF-3.2, FENDL-3.0 and TENDL-2014 evaluated data for tungsten with 14.8 MeV neutrons

Integral experiments on tungsten slab samples were carried out on the D-T neutron source facility at China Institute of Atomic Energy. Leakage neutron spectra from the irradiated tungsten target were measured by the time-of-flight technique. Accuracy of the nuclear data for tungsten was examined by comparing the measured neutron spectra with the leakage neutron spectra simulated using the MCNP-4C code with evaluated nuclear data of the JEFF-3.2, FENDL-3.0 and TENDL-2014 libraries. The results show that the calculations with JEFF-3.2 agree well with the measurements in the whole energy range and all angles, whereas the spectra calculated with FENDL-3.0 and TENDL-2014 have some discrepancies with the experimental data.

Unfolding neutron spectra from water-pumping-injection multilayered concentric sphere neutron spectrometer using self-adaptive differential evolution algorithm

A self-adaptive differential evolution neutron spectrum unfolding algorithm(SDENUA)is established in this study to unfold the neutron spectra obtained from a water-pumping-injection multilayered concentric sphere neutron spectrometer(WMNS).Specifically,the neutron fluence bounds are estimated to accelerate the algorithm convergence,and the minimum error between the optimal solution and input neutron counts with relative uncertainties is limited to 10^(-6)to avoid unnecessary calculations.Furthermore,the crossover probability and scaling factor are self-adaptively controlled.FLUKA Monte Carlo is used to simulate the readings of the WMNS under(1)a spectrum of Cf-252 and(2)its spectrum after being moderated,(3)a spectrum used for boron neutron capture therapy,and(4)a reactor spectrum.Subsequently,the measured neutron counts are unfolded using the SDENUA.The uncertainties of the measured neutron count and the response matrix are considered in the SDENUA,which does not require complex parameter tuning or an a priori default spectrum.The results indicate that the solutions of the SDENUA agree better with the IAEA spectra than those of MAXED and GRAVEL in UMG 3.1,and the errors of the final results calculated using the SDENUA are less than 12%.The established SDENUA can be used to unfold spectra from the WMNS.

MEASUREMENT OF NEUTRON SPECTRA FROM THICK Be TARGET BOMBARDED WITH DEUTERONS

Neutron spectra of Be(d,n) reaction were measured for deuteron energies from 13.5 to 22 MeV by using a stilbene scintillator detector and flight time technique.A special calibration method of neutron detector efficiency for higher energy portion was adopted. The spectral neutron yield per unit beam charge on the Be target at 0° was determined. The fluence-averaged mean neutron energies of the neutron spectra are given as a function of the incident energy for several thresholds. The measured neutron spectra have an almost same shape at different incident deuteron energies. High energy portion (En】1.8MeV) and low energy portion (En【2.0MeV)of the neutron spectra were separately measured and they were concerned with each other by normalization. The energy range of whole neutron spectra is 0.7 MeV to 30MeV.

Neutronic analysis of deuteron-driven spallation target

Deuteron-driven spallation targets have garnered attention recently because they can provide high-energy neutrons to transmute long-lifetime fission products.In this study,the Geant4 toolkit was used to simulate the inter-action between a deuteron beam at 500 MeV and a com-posite target composed of alternating lead-bismuth eutectic(LBE)and water.The water was used because it may be employed as a target coolant.The energy spectrum,neu-tron yield,average energy,and total energy of the emitted neutrons were calculated for different thicknesses and thickness ratios between the LBE and water.For a constant target thickness,the neutron yield increases with an increasing thickness ratio of LBE to H 2 O,while the aver-age energy of the emitted neutrons decreases with an increasing in the aforementioned thickness ratio.These two aspects support the use of a pure target,either LBE or water.However,with an increasing LBE-to-H 2 O thickness ratio,the total energy of the emitted neutrons increases and then decreases.This result supports the addition of water into the LBE target.The angular distributions of the emitted neutrons show that the rear of the target is suit-able for loading nuclear waste containing minor actinides and long-lifetime fission products.

Further Analysis of Neutron Double-Differential Cross Section of n ＋ ^16O at 14.1 MeV and 18 MeV

By using a new reaction model for light nuclei, the double-differential cross section of total outgoing neutron with LUNF code for n＋^16O reactions at En=14.1 MeV and 18 MeV have been calculated and analyzed. In this paper the opened reaction channels, which have contribution to emitting the neutrons, are listed in detail. To improve the fitting results the direct inelastic scattering mechanism is involved. The calculating results agree fairly well with the experimental data at E,~ = 14.1 MeV and the deviation from calculated results and experimental data in low energy region at En= 18 MeV has been analyzed. Since the possibility of 5He has been affirmed theoretically [J.S. Zhang, Sci. Chin. G 47 （2004） 137], so 5He emission from n＋ ^16O reaction is taken into account, which plays an important role at the region of the outgoing neutron energy εn〈3 MeV in total outgoing neutron energy-angular spectrum. The calculated results indicate that the pre-equilibrium mechanism dominates the whole reaction processes, and the recoil effect in light nuclear reactions is essentially important.

Study on element detection and its correction in iron ore concentrate based on a prompt gamma-neutron activation analysis system

A prompt gamma-neutron activation analysis(PGNAA) system was developed to detect the iron content of iron ore concentrate. Because of the self-absorption effect of gamma-rays and neutrons, and the interference of chlorine in the neutron field, the linear relationship between the iron analytical coefficient and total iron content was poor, increasing the error in the quantitative analysis. To solve this problem, gamma-ray self-absorption compensation and a neutron field correction algorithm were proposed, and the experimental results have been corrected using this algorithm. The results show that the linear relationship between the iron analytical coefficient and total iron content was considerably improved after the correction. The linear correlation coefficients reached 0.99 or more.