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The count-loss effect often produces serious problems for the neutron correlation methods that employ a single neutron counting system, since this effect deteriorates the information extracted from subcritical reactor systems. On the other hand, it has been considered that the neutron correlation methods that employ two sets of neutron counting systems, e.g., the covariance-to-mean and the cross-correlation methods, are inherently robust against the count-loss effect in determining the prompt neutron decay constant. The present study investigated this virtue of the latter methods on the basis of a rigorous theoretical approach for treating the count-loss process. The investigation clarified that they indeed show the robustness against the count-loss effect except for extremely high counting rate cases. In the present study, new and alternative formulae of these methods with an explicit correction of the count-loss effect were hence proposed for such extreme cases.

In the previous study, the theoretical formulae of two time-domain reactor noise techniques, i.e., the auto-covariance and the variance-to-mean function techniques, were derived (Kitamura et al., 2018). These two techniques analyse the temporal fluctuation in continuous neutron detector current signals arising from ionization chambers such as the fission chamber. They are hence inherently insensitive to the count-loss effect that sometimes brings serious difficulties to the conventional time-domain techniques that analyse the number of detector pulse signals. With regard to these two techniques, the experimental conditions under which they successfully measure the subcriticality through determination of the prompt neutron decay constant were clarified. However, for mathematical simplicity and the sake of insight, the previous study was performed on the basis of a theoretical model neglecting delayed neutrons. The formulae of these two techniques are hence re-derived by taking delayed neutrons into consideration. Using the formulae thus derived, the delayed neutron effect in these two techniques is discussed.

The conventional time-domain reactor noise techniques analyse the number of neutron detector pulse signals, so that they sometimes encounter serious difficulties owing to the count-loss effect due to the dead time of detector systems. To avoid all the difficulties coming from the count-loss effect, a novel time-domain technique was recently proposed (Pal and Pazsit, 2015). This technique analyses the auto-covariance function of continuous current signals arising from ionization chambers such as the fission chamber, so that it is inherently insensitive to the count-loss effect. In the present study, a different time-domain technique that analyses the integral values of current signals is proposed. With regard to these two techniques, the experimental conditions under which they successfully measure the subcriticality through determination of the prompt neutron decay constant are clarified.

The rotation method is a novel method for detecting nuclear materials using a neutron source such as californium. In this method, while a neutron source is rotated rapidly nearby a measurement object, neutron measurement is carried out by synchronizing the rotation motion. If the object contains a nuclear material, as the rotation speed increases, the larger deformation of time distribution of neutron counts is observed, which in turn resulted to the detection of the nuclear material. In addition to its features of low cost and portability, this method is capable of detecting uranium that emits very few spontaneous fission neutrons. This study presents the fundamental principle of this method and its effectiveness for detecting nuclear materials through the experimental verifications.

The Telescope Array (TA) experiment is designed to detect air showers induced by ultra high energy cosmic rays. The TA ground Surface particle Detector (TASD) observed several short-time bursts of air shower like events. These bursts are not likely due to chance coincidence between single shower events. The expectation of chance coincidence is less than 10 − 4 for five-year's observation. We checked the correlation between these bursts of events and lightning data, and found evidence for correlations in timing and position. Some features of the burst events are similar to those of a normal cosmic ray air shower, and some are not. On this paper, we report the observed bursts of air shower like events and their correlation with lightning.

Recently, a modified Feynman-alpha technique for the subcritical system driven by periodically triggered neutron bursts was developed. One of the main features of this technique is utilization of a simple formula that is advantageous in evaluating the subcriticality. However, owing to the absence of the theory of this technique, this feature has not been fully investigated yet. In the present study, a theory of this technique is provided. Furthermore, the experimental conditions under which the simple formula works are discussed to apply this technique to the subcriticality monitor for the accelerator-driven system.

An inconsistency between the reactivity worth of short-sized samples measured by the critical-water-level (CWL) method and that conventionally analyzed for validating nuclear data and nuclear calcu...

In the accelerator-driven system (ADS), the effective delayed neutron fraction (βeff) is a requisite for converting the subcriticality from dollar units to pcm units. To evaluate the accurate βeff value in ADS, measurement of βeff complements its calculation methodology and the nuclear data on delayed neutrons. Subcriticality measurements are carried out by the pulsed neutron source method in the Kyoto University Critical Assembly, and the neutron noise analyses are conducted by the Rossi-α method with the pulsed shape of the spallation neutron source. The value of βeff is deduced with the combined use of measured subcriticality in dollar units and correction parameters by MCNP6.1 together with JENDL-4.0 and JENDL/HE-2007. A comparison between the calculated and the measured βeff represents the acceptable accuracy within the subcriticality range of around keff = 0.93 in the ADS operations. Here, the applicability of the measurement methodology based on the Rossi-α method is demonstrated by varying...

TARA (Telescope Array Radar) is a cosmic ray radar detection experiment colocated with Telescope Array, the conventional surface scintillation detector (SD) and fluorescence telescope detector (FD) near Delta, Utah, U.S.A. The TARA detector combines a 40 kW, 54.1 MHz VHF transmitter and high-gain transmitting antenna which broadcasts the radar carrier over the SD array and within the FD field of view, towards a 250 MS/s DAQ receiver. TARA has been collecting data since 2013 with the primary goal of observing the radar signatures of extensive air showers (EAS). Simulations indicate that echoes are expected to be short in duration (~10 microseconds) and exhibit rapidly changing frequency, with rates on the order of 1 MHz/microsecond. The EAS radar cross-section (RCS) is currently unknown although it is the subject of over 70 years of speculation. A novel signal search technique is described in which the expected radar echo of a particular air shower is used as a matched filter template and compared to waveforms obtained by triggering the radar DAQ using the Telescope Array fluorescence detector. No evidence for the scattering of radio frequency radiation by EAS is obtained to date. We report the first quantitative RCS upper limits using EAS that triggered the Telescope Array Fluorescence Detector., Comment: 21 pages, 30 figures

Cosmic rays in the energy range $10^{18.0}$ - $10^{18.5}$ eV are thought to have a light, probably protonic, composition. To study their origin one can search for anisotropy in their arrival directions. Extragalactic cosmic rays should be isotropic, but galactic cosmic rays of this type should be seen mostly along the galactic plane, and there should be a shortage of events coming from directions near the galactic anticenter. This is due to the fact that, under the influence of the galactic magnetic field, the transition from ballistic to diffusive behavior is well advanced, and this qualitative picture persists over the whole energy range. Guided by models of the galactic magnetic field that indicate that the enhancement along the galactic plane should have a standard deviation of about 20$^\circ$ in galactic latitude, and the deficit in the galactic anticenter direction should have a standard deviation of about 50$^\circ$ in galactic longitude, we use the data of the Telescope Array surface detector in $10^{18.0}$ to $10^{18.5}$ eV energy range to search for these effects. The data are isotropic. Neither an enhancement along the galactic plane nor a deficit in the galactic anticenter direction is found. Using these data we place an upper limit on the fraction of EeV cosmic rays of galactic origin at 1.3% at 95% confidence level.

We present an upper limit on the flux of ultra-high-energy down-going neutrinos for $E > 10^{18}\ \mbox{eV}$ derived with the nine years of data collected by the Telescope Array surface detector (05-11-2008 -- 05-10-2017). The method is based on the multivariate analysis technique, so-called Boosted Decision Trees (BDT). Proton-neutrino classifier is built upon 16 observables related to both the properties of the shower front and the lateral distribution function., 10 pages, 4 figures, accepted to JETP

Detection of hidden special nuclear materials (SNMs) used for nuclear explosives such as 235 U is important issue for nuclear security to counter terrorist threats. The interrogation systems used in a port and an airport has been developing in the world, and the active neutron-based interrogation system is the one of the candidates for this purpose. We are developing an active neutron-based interrogation system combined with radiation detectors and a D-D neutron source usable in seaports and airports. The D-D neutron source shown in Figs. 1 and 2 is a compact and light-weight portable discharge-type fusion neutron source called IECF (Inertial Electrostatic Confinement Fusion) device [1] . It provides 2.45 MeV mono-energetic neutrons whose production rate is more than 5x10 7 n/s in CW mode without using radioisotope such as tritium. An mportant advantage of IEC comes from the use of "gas target" and this enables stable high-power operation of IEC devices to produce copious amount of D-D neutrons in a compact system. We adopted new Threshold Energy Neutron Analysis (TENA) method and neutron and gamma-ray noise analysis method based on the variance-to-mean value method in the present interrogation system.

The Feynman-alpha method has been frequently employed to measure the subcriticality of a neutron multiplying system through determination of the prompt neutron decay constant. This method, however, often encounters a difficulty with unstable multiplying systems where the neutron population is temporally varying and drifting owing to perturbations due to removal or replacement of fuels and absorbers. In the unstable multiplying systems, the delayed-neutron contribution is remarkably enhanced and makes it difficult to extract the prompt neutron decay constant from the prompt-neutron contribution. The linear difference filter methods that are variants of the Bennett variance one were hence developed to mitigate this kind of difficulty by reducing the delayed-neutron contribution. In the present study, further new variants are proposed. It is shown that the present methods with correlation indices consisting of more than three successive gates can reduce the delayed-neutron contribution more effectively than the conventional ones.

The Simmons-King and the Sjostrand (or the area-ratio) methods have been widely applied in measurement of the subcriticality of reactor systems driven by the pulsed neutron source and operated in the stationary state. In the present study, a theory-based investigation is conducted to examine the time-response of these two methods after perturbations in various parameters. As a result, the prompt neutron decay constant determined by the Simmons-King method shows a good trackability to the subcriticality. In the Sjostrand method, calibration-free determination of the subcriticality is achieved, although it needs a long delay due to an asymptotic behaviour. Furthermore, it is found that the latter method can quickly detect the perturbation in neutron yield of the pulsed neutron source. Therefore, it is expected that a strong on-line monitoring tool for the subcritical reactor system driven by the pulsed neutron source can be developed by combining these two methods.

The Pierre Auger Collaboration (Auger) recently reported a correlation between the arrival directions of cosmic rays with energies above 39 EeV and the flux pattern of 23 nearby starburst galaxies (SBGs). In this Letter, we tested the same hypothesis using cosmic rays detected by the Telescope Array experiment (TA) in the 9-year period from May 2008 to May 2017. Unlike the Auger analysis, we did not optimize the parameter values but kept them fixed to the best-fit values found by Auger, namely 9.7% for the anisotropic fraction of cosmic rays assumed to originate from the SBGs in the list and 12.9{\deg} for the angular scale of the correlations. The energy threshold we adopted is 43 EeV, corresponding to 39 EeV in Auger when taking into account the energy-scale difference between two experiments. We find that the TA data is compatible with isotropy to within 1.1{\sigma} and with the Auger result to within 1.4{\sigma}, meaning that it is not capable to discriminate between these two hypotheses., Comment: More accurate title, fixed an inconsistency in the declination range used, with a few figures slightly changing as a result, other minor revisions

One of the uncertainties in interpretation of ultra-high energy cosmic ray (UHECR) data comes from the hadronic interaction models used for air shower Monte Carlo (MC) simulations. The number of muons observed at the ground from UHECR-induced air showers is expected to depend upon the hadronic interaction model. One may therefore test the hadronic interaction models by comparing the measured number of muons with the MC prediction. In this paper, we present the results of studies of muon densities in UHE extensive air showers obtained by analyzing the signal of surface detector stations which should have high $\it{muon \, purity}$. The muon purity of a station will depend on both the inclination of the shower and the relative position of the station. In 7 years' data from the Telescope Array experiment, we find that the number of particles observed for signals with an expected muon purity of $\sim$65% at a lateral distance of 2000 m from the shower core is $1.72 \pm 0.10{\rm (stat.)} \pm 0.37 {\rm (syst.)}$ times larger than the MC prediction value using the QGSJET II-03 model for proton-induced showers. A similar effect is also seen in comparisons with other hadronic models such as QGSJET II-04, which shows a $1.67 \pm 0.10 \pm 0.36$ excess. We also studied the dependence of these excesses on lateral distances and found a slower decrease of the lateral distribution of muons in the data as compared to the MC, causing larger discrepancy at larger lateral distances.

The Telescope Array observatory utilizes fluorescence detectors and surface detectors to observe air showers produced by ultra high energy cosmic rays in the Earth's atmosphere. Cosmic ray events observed in this way are termed hybrid data. The depth of air shower maximum is related to the mass of the primary particle that generates the shower. This paper reports on shower maxima data collected over 8.5 years using the Black Rock Mesa and Long Ridge fluorescence detectors in conjunction with the array of surface detectors. We compare the means and standard deviations of the observed $X_{\mathrm{max}}$ distributions with Monte Carlo $X_{\mathrm{max}}$ distributions of unmixed protons, helium, nitrogen, and iron, all generated using the QGSJet~II-04 hadronic model. We also perform an unbinned maximum likelihood test of the observed data, which is subjected to variable systematic shifting of the data $X_{\mathrm{max}}$ distributions to allow us to test the full distributions, and compare them to the Monte Carlo to see which elements are not compatible with the observed data. For all energy bins, QGSJet~II-04 protons are found to be compatible with Telescope Array hybrid data at the 95% confidence level after some systematic $X_{\mathrm{max}}$ shifting of the data. Three other QGSJet~II-04 elements are found to be compatible using the same test procedure in an energy range limited to the highest energies where data statistics are sparse., Comment: 39 pages, 18 figures, 5 tables, published in The Astrophysical Journal. This is a peer-reviewed, un-copyedited version of an article published in The Astrophysical Journal. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.3847/1538-4357/aabad7

An intermediate-scale energy spectrum anisotropy has been found in the arrival directions of ultra-high energy cosmic rays of energies above $10^{19.2}$ eV in the northern hemisphere, using 7 years of data from the Telescope Array surface detector. A relative energy distribution test is done comparing events inside oversampled spherical caps of equal exposure, to those outside, using the Poisson likelihood ratio. The center of maximum significance is at $9^h$$16^m$, $45^{\circ}$. and has a deficit of events with energies $10^{19.2}$$\leq$$E$$

We present the results of the search for ultra-high-energy photons with nine years of data from the Telescope Array surface detector. A multivariate classifier is built upon 16 reconstructed parameters of the extensive air shower. These parameters are related to the curvature and the width of the shower front, the steepness of the lateral distribution function, and the timing parameters of the waveforms sensitive to the shower muon content. A total number of two photon candidates found in the search is fully compatible with the expected background. The $95\%\,$CL limits on the diffuse flux of the photons with energies greater than $10^{18.0}$, $10^{18.5}$, $10^{19.0}$, $10^{19.5}$ and $10^{20.0}$ eV are set at the level of $0.067$, $0.012$, $0.0036$, $0.0013$, $0.0013~\mbox{km}^{-2}\mbox{yr}^{-1}\mbox{sr}^{-1}$ correspondingly., Comment: 7 pages, 2 figures

The results on ultra-high-energy cosmic rays (UHECR) mass composition obtained with the Telescope Array surface detector are presented. The analysis employs the boosted decision tree (BDT) multivariate analysis built upon 14 observables related to both the properties of the shower front and the lateral distribution function. The multivariate classifier is trained with Monte-Carlo sets of events induced by the primary protons and iron. An average atomic mass of UHECR is presented for energies $10^{18.0}-10^{20.0}\ \mbox{eV}$. The average atomic mass of primary particles shows no significant energy dependence and corresponds to $\langle \ln A \rangle = 2.0 \pm 0.1 (stat.) \pm 0.44 (syst.)$. The result is compared to the mass composition obtained by the Telescope Array with $\mbox{X}_{\mbox{max}}$ technique along with the results of other experiments. Possible systematic errors of the method are discussed., Comment: 11 pages, 9 figures

New benchmark models with respect to criticality data are established on the basis of seven uranium-fueled assemblies constructed in the ninth experimental series at the fast critical assembly (FCA...

We report on the search for steady point-like sources of neutral particles around 10$^{18}$ eV between 2008 May and 2013 May with the scintillator surface detector of the Telescope Array experiment. We found overall no significant point-like excess above 0.5 EeV in the northern sky. Subsequently, we also searched for coincidence with the Fermi bright Galactic sources. No significant coincidence was found within the statistical uncertainty. Hence, we set an upper limit on the neutron flux that corresponds to an averaged flux of 0.07 km$^{-2}$ yr$^{-1}$ for $E>1$ EeV in the northern sky at the 95% confidence level. This is the most stringent flux upper limit in a northern sky survey assuming point-like sources. The upper limit at the 95% confidence level on the neutron flux from Cygnus X-3 is also set to 0.2 km$^{-2}$ yr$^{-1}$ for $E>0.5$ EeV. This is an order of magnitude lower than previous flux measurements., 27 pages, 10 figures, 3 tables, accepted for publication in the Astrophysical Journal

We measure the spectrum of cosmic rays with energies greater than 10 18.2 eV with the fluorescence detectors (FDs) and the surface detectors (SDs) of the Telescope Array Experiment using the data taken in our first 2.3-year observation from May 27, 2008 to September 7, 2010. A hybrid air shower reconstruction technique is employed to improve accuracies in determination of arrival directions and primary energies of cosmic rays using both FD and SD data. The energy spectrum presented here is in agreement with our previously published spectra and the HiRes results.

The stability of the gain of the photomultiplier (PMT) camera for the Fluorescence Detector (FD) of the Telescope Array experiment was monitored using an 241 Am loaded scintillator pulsers (YAP) and a diffused xenon flasher (TXF) for a selected set of 35 PMT-readout channels. From the monitoring of YAP pulses over four years of FD operation, we found slow monotonic drifts of PMT gains at a rate of −1.7~+1.7%/year. An average of the PMT gains over the 35 channels stayed nearly constant with a rate of change measured at −0.01±0.31(stat)±0.21(sys)%/year. No systematic decrease of the PMT gain caused by the night sky background was observed. Monitoring by the TXF also tracked the PMT gain drift of the YAP at 0.88±0.14(stat)%/year.

It was pointed out in the previous paper that the neutron decay constant determined by the pulsed neutron source method that employs the neutron detection system operated in the pulse mode is expected to be biased owing to the count-loss effect even when the intensity of pulsed neutron source is not high. To avoid this difficulty, by paying attention to the current mode that is inherently free from the count-loss process, the pulsed neutron source method with neutron detection system operated in the current mode was proposed. Using this method, not only the neutron decay constant but also the absolute value of subcriticality are obtained when a proper time constant of neutron detection system is selected.

A series of integral reactor physics experiments conducted at the Very High Temperature Reactor Critical Assembly was analyzed to assemble it into a benchmark through an extensive peer-review proce...

It is well known that the count-loss effect produces serious problems for the neutron correlation methods that employ a single neutron counting system, e.g. the variance-to-mean and the auto-correlation methods, since it deteriorates the information extracted from the subcritical reactor system. New formulae of the variance-to-mean and auto-correlation methods were hence obtained on the basis of a rigorous theoretical approach for treating the count-loss process. It is expected that the present formulae work better than conventional ones for determination of the neutron decay constant.

The count-loss effect in determination of neutron decay constant by pulsed neutron source method was investigated. It was found that overestimation of neutron decay constant due to count-loss effect is seen while underestimation appears superiorly as the intensity of pulsed neutron source is getting higher. It was further demonstrated that the well-known count-loss correction procedures are not effective for overestimation although they suppress underestimation. Therefore, the pulsed neutron source method should be modified so as to have robustness against the count-loss effect.

We present a measurement of the energy spectrum of ultra-high-energy cosmic rays performed by the Telescope Array experiment using monocular observations from its two new FADC-based fluorescence detectors. After a short description of the experiment, we describe the data analysis and event reconstruction procedures. Since the aperture of the experiment must be calculated by Monte Carlo simulation, we describe this calculation and the comparisons of simulated and real data used to verify the validity of the aperture calculation. Finally, we present the energy spectrum calculated from the merged monocular data sets of the two FADC-based detectors, and also the combination of this merged spectrum with an independent, previously published monocular spectrum measurement performed by Telescope Array’s third fluorescence detector [T. Abu-Zayyad et al., The energy spectrum of Telescope Array’s middle drum detector and the direct comparison to the high resolution fly’s eye experiment, Astroparticle Physics 39 (2012) 109-119, http://dx.doi.org/10.1016/j.astropartphys.2012.05.012 , Available from: ]. This combined spectrum corroborates the recently published Telescope Array surface detector spectrum [T. Abu-Zayyad, et al., The cosmic-ray energy spectrum observed with the surface detector of the Telescope Array experiment, ApJ 768 (2013) L1, http://dx.doi.org/10.1088/2041-8205/768/1/L1 , Available from: ] with independent systematic uncertainties.

A reflector reactivity worth was measured by replacing stainless steel with zirconium at the FCA. The experimental result of the positive reflector reactivity worth demonstrates the effectiveness of the zirconium reflector compared with the SS reflector in the fast reactor core. This paper also focuses on the validation of standard calculation methods used for fast reactors with JENDL-4.0. As a result, it is confirmed that the standard calculation methods for the reflector reactivity worth show agreement within the experimental error.

The Telescope Array (TA) experiment is the largest detector to observe ultra-high-energy cosmic rays in the northern hemisphere. The fluorescence detectors at southern two stations of TA are newly constructed and have now completed seven years of steady operation. One advantage of monocular analysis of the fluorescence detectors is a lower energy threshold for cosmic rays than that of other techniques like stereoscopic observations or coincidences with the surface detector array, allowing the measurement of an energy spectrum covering three orders of magnitude in energy. Analyzing data collected during those seven years, we report the energy spectrum of cosmic rays covering a broad range of energies above 10$^{17.2}$ eV measured by the fluorescence detectors and a comparison with previously published results., Submitted to Astroparticle Physics

The benchmark specification for the sodium-void reactivity experiments is given. The detailed benchmark calcu- lations for the new integral data were performed by using a continuous-energy Monte Carlo code (MVP) with use of the evaluated nuclear data libraries JENDL-3.2, -3.3, -4.0, ENDF/B-VII.0 and JEFF-3.1. The MVP calculations were performed with 2,000,000,000 particles. The statistical uncertainties of the MVP calculations were within several percents of the measured sodium-void reactivities. The ratios of calculated to experimental (C/E) values of sodi- um-void reactivities with respect to JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1 are less than those with respect to JENDL-3.2 and -4.0. The analysis results are similar to those of sodium-void reactivities previously obtained at the BFS facility which is another fast critical assembly in Russia. The benchmark calculations demonstrate the improve- ment of the reliability of the integral data such as the new integral data obtained at the FCA and the previously obtained data in the BFS and the usefulness of the new integral data for the validation of the re-evaluated cross sec- tion of 235 U. In addition, the benchmark tests with various correction factors by a deterministic calculation system are summarized for the help to validate the re-evaluated capture cross section of 235 U.

The temporal evolution of the distribution of the number of neutrons in a time-varying multiplying system, producing only prompt neutrons, was treated recently with the master equation technique by some of the present authors. Such a treatment gives account of both the so-called zero power reactor noise and the power reactor noise simultaneously. In particular, the first two moments of the neutron number, as well as the concept of criticality for time-varying systems, were investigated and discussed. The present paper extends these investigations to the case when delayed neutrons are also taken into account. Due to the complexity of the description, only the expectation of the neutron number is calculated. The concept of criticality of a time-varying system is also generalized to systems with delayed neutrons. The temporal behaviour of the expectation of the number of neutrons and its asymptotic properties are displayed and discussed.

The validity of various simplified treatments of anisotropic scattering is investigated in typical LWR configurations that simulate PWR, BWR, and APWR. In addition to the explicit treatment of anisotropic scattering, the diagonal approximation of anisotropic scattering matrixes and the transport corrected cross section with the assumption of isotropic scattering are also tested. Calculation results indicate that the anisotropic scattering matrix of the P1 component would be explicitly treated to obtain accurate results in the present calculations. The P2 or higher order anisotropic scattering matrix could be approximated by the diagonal approximation while maintaining the calculation accuracy. In addition to the above investigation, the physical meaning of the transport corrected cross section used in a transport calculation is discussed through a simple one-group fixed-source benchmark problem with anisotropic scattering. Though the transport corrected cross section is usually used to consider the P1 sca...

The zero-power reactor noise theory in a steady neutron multiplying medium was extended recently to a medium randomly varying in time to bridge the fields of the zero-power and the power reactor noise. For a time-varying medium in which the transition probability randomly fluctuates, only the use of the probability generating function technique based on the forward master equation approach is practical. However, with the forward master equation approach, the treatment of the joint moments of the neutron number and the medium state leads to a closure problem. Recently, the capability of the moment calculation technique for such cases was extended such that the closure problem could be solved exactly. The present paper describes and demonstrates this closure-free moment calculation technique in a time-varying binary multiplying medium, in which the medium state has two possible realizations. In addition to the first two moments of the neutron number N alone (irrespective of the medium state η), the joint moments of Nn and ηm, i.e., 〈Nnηm〉, were also obtained in a compact form for n = 1, 2 and arbitrary values of m, without a closure assumption. It was found that, for even m values, the asymptotic values of Nn and ηm are uncorrelated, whereas, for odd m values, they are negatively correlated, namely, their covariance is less than zero. The first two moments of the neutron number theoretically obtained were verified by the Monte Carlo technique. A perfect agreement was found between the Monte Carlo and the theoretical solutions. The closure-free moment calculation technique demonstrated in the present paper is expected to be applicable to various other problems related to the birth-and-death process with fluctuations of the transition probability, in which a closure problem occurs.

In order to verify the Feynman-alpha formula with stationary multiple emission sources [Pazsit, I., Yamane, Y., 1998. Nuclear Instruments and Methods A403, 431–441], a series of experiments were performed by using three different neutron sources, i.e., an Am–Be, a 252 Cf, and a randomly triggered D–T pulsed neutron generator. As a result, it was found that the prompt neutron decay constant evaluated from the measured Y -function was hardly affected by the difference of neutron sources that have respective source multiplicities. On the other hand, it was demonstrated that the amplitude of Y -function, i.e., the correlation amplitude, depended on both the subcriticality and the neutron source multiplicity. These experimental facts agreed with the theoretical prospects that were deduced from the Feynman-alpha formula with multiple emission sources. Therefore, it was concluded that the validity of this formula was experimentally shown.

In this paper, new optimization algorithms for the in-core fuel shuffling sequence of a boiling water reactor (BWR) are proposed to reduce outage time. During the short outage of a BWR, fuel shuffling can be a critical path in the periodic overall plant inspection. Therefore, a reduction in operation time for in-core fuel shuffling is essential to improve the plant capacity factor. For BWR in-core fuel shuffling, the shuffling sequence should be selected carefully since a fuel shuffling operation may affect those following it. Furthermore, several constraints must be satisfied during the in-core fuel shuffling of a BWR; e.g., two fuel assemblies must be inserted diagonally in a cell to fix the position of a control blade in it. Therefore, it is difficult to optimize BWR in-core fuel shuffling. In order to resolve this issue, new optimization methods are proposed, and the performances of some optimization algorithms are compared. Test calculations in actual BWR plants reveal that the workload for in-core fuel shuffling can be reduced by the proposed methods. The results of this paper will contribute to increasing the plant capacity factor by reducing the outage time.

The Rossi-alpha formula for subcritical systems driven by a pulsed neutron source was derived with a solution technique that can effectively take different shape functions of the pulsed neutron source into account. The result of derivation showed that the present formula consists of the correlated and uncorrelated terms and an oscillating term whose period was identical to that of the pulsed neutron source. To investigate the validity of the pulsed Rossi-alpha formula and its applicability for the evaluation of the prompt neutron decay constant alpha from measurements, an experiment was performed at the Kyoto University Critical Assembly with a pulsed D-T neutron source. Although it seemed that fitting the present formula to the experimental curves was not practical because of an infinite-series expansion structure of the oscillating term, it was possible to extract only the correlated term, that explicitly includes the alpha value, by a simple data handling procedure. It was found that the measured alpha values agreed with those obtained by the pulsed neutron source method very well. This finding means that the pulsed Rossi-alpha method will be an attractive candidate for the monitoring method of the subcritical reactivity of future accelerator driven systems.

An effective method of calculating the pulsed Feynman-alpha formula for finite width pulses is introduced and applied in this paper. The method is suitable for calculating both the deterministic and the stochastic Feynman-alpha formulae, while also being capable of treating various pulse shapes through very similar steps and partly identical formulae. In the paper both the deterministic and the stochastic cases are treated for square and Gaussian pulses. The solutions show a very good agreement with the results of currently performed experiments by some of the authors at the Kyoto University Critical Assembly (KUCA). The formulae obtained are also used for a quantitative evaluation of the prompt neutron decay constant from a large number of experiments made at the KUCA for a wide range of parameters such as subcritical reactivity, pulse repetition frequency and pulse width. The suitability of the formulae to determine the prompt neutron decay constant a by curve fitting to the measured data was investigated. It was found that, despite the larger deviation from the traditional Feynman Y(T)-curves from the traditional ones with a constant source (i.e., larger ripples superimposed on a smooth curve), the stochastic pulsing method is superior to the deterministic one in that it yields the correct a value for all subcriticalities. The deterministic method also works fine for most cases, but its application is not so straightforward.

In previous works, the authors have developed an effective solution technique for calculating the pulsed Feynman- and Rossi-alpha formulae. Through derivation of these formulae, it was shown that the technique can easily handle various pulse shapes of the pulsed neutron source. Furthermore, it was also shown that both the deterministic (i.e.{} synchronizing with the pulsing of neutron source) and stochastic (non-synchronizing) Feynman-alpha formulae can be obtained with this solution technique. However, for mathematical simplicity and the sake of insight, the formal derivation was performed in a model without delayed neutrons. In this paper, to demonstrate the robustness of the technique, the pulsed Feynman- and Rossi-alpha formulae were re-derived by taking one group of delayed neutrons into account. The results show that the advantages of this technique are retained even by inclusion of the delayed neutrons. Compact explicit formulae are derived for the Feynman- and Rossi-alpha methods for various pulse shapes and pulsing methods.

In this paper, improvement of the SPH method (the improved SPH method) is proposed. The SPH method is commonly used in pin-by-pin mesh core calculations to reduce cell-homogenization error. The investigation revealed that the normalization condition of the SPH factor in the conventional SPH method is not appropriate for multi-assembly calculations in which different assembly types are adjacent. Since the conventional normalization condition does not incorporate flux discontinuity between assemblies, cell homogenization error in assembly peripheral region becomes larger. In the improved SPH method, the SPH factor is divided by an averaged “cell-level” discontinuity factor obtained in each fuel assembly. Though the SPH factor is somewhat modified from the conventional value, no additional homogenization parameters (e.g. discontinuity factor) is necessary in core calculations. Test calculations were carried out in a simplified one-dimensional slab and two-dimensional PWR colorset geometries that simulate par...

In this paper, simultaneous optimization is carried out for successive two cycles of pressurized water reactors. At first, a simplified problem of the simultaneous optimization was studied by assuming the batch-wise power sharing as independent variable, i.e., batch-wise power sharing was optimized without considering corresponding loading patterns. The optimization of the batch-wise power sharing was carried out for the conventional single cycle, the equilibrium cycle and the two successive (tandem) cycles. The analysis indicated that the tandem cycle optimization well reproduce that of the equilibrium cycle optimization, which is considered as a typical case of the true multicycle optimization. Next, simultaneous optimization of loading patterns for tandem cycles is carried out using the simulated annealing method. Since the design space of the tandem cycles optimization is much larger than that of the conventional single cycle optimization, the optimization condition (i.e., number of calculated pattern...

In this paper, thermal expansion effect on neutronics characteristics is approximately taken into account by a correction on cross sections. Dimensions of reactor core components depend on their temperatures due to the thermal expansion phenomena. However, the variation of calculation geometry requires considerable computational load for trajectory based lattice transport calculations such as the characteristics method since ray tracing must be re-executed. Therefore, if a correction on cross sections can accurately capture the effect of geometrical variation due to the thermal expansion, computation time of a lattice transport calculation that treat temperature variation can be reduced. Three different corrections on cross sections were tested in PWR fuel assembly geometry using UO2 and MOX fuels. It was found that the correction of cross sections that preserves neutron attenuation in a region almost reproduce the reference calculation that explicitly considers geometrical variation due to the thermal ex...

The coarse mesh rebalance (CMR) is a simple acceleration method that is commonly used for transport calculations though it is conditionally stable, i.e. acceleration failed under certain calculation conditions. In this paper, a new acceleration scheme, i.e. the generalized coarse mesh rebalance (GCMR) method, is proposed and applied to improve convergence property of the CMR method. Definitions of partial neutron currents used in CMR are modified in the present method and convergence property of CMR is improved by the modifications. The proposed method was applied to transport calculations in slab and light water reactor assembly geometries. The calculation results were compared with those by the CMR and the coarse mesh finite-difference (CMFD) acceleration methods, and it was revealed that the present method significantly improves the convergence property of the traditional CMR method. Since the present method can be easily applied to existing transport codes using the CMR method, it is considered as a p...

In this paper, various approximations of the exponential function are tested from the viewpoint of computational efficiency, i.e. accuracy and computation time. Since considerable part of computation time is devoted to the evaluation of the exponential function in transport calculations using the characteristics method, reduction of its computation time is important. Evaluations of the approximations are carried out on a Linux operating system using two different processors, i.e. Xeon 2.8GHz with 2MB L3 cache and Pentium-III 800 MHz with 512 KB L2 cache. In order to grasp the impact of approximation error of the exponential function on transport calculation results, some sensitivity calculations are executed using the characteristics method. The evaluation results indicate that the table lookup method with linear interpolation or second-order interpolation is computationally efficient for practical calculations.