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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.

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.

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.

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.

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.

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...

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

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 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.

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.

In this paper, performances of spatial homogenization methods for fuel or non-fuel cells are compared in slab geometry in order to facilitate pin-by-pin core calculations. Since the spatial homogenization methods were mainly developed for fuel assemblies, systematic study of their performance for the cell-level homogenization has not been carried out. Importance of cell-level homogenization is recently increasing since the pin-by-pin mesh core calculation in actual three-dimensional geometry, which is less approximate approach than current advanced nodal method, is getting feasible. Four homogenization methods were investigated in this paper; the flux-volume weighting, the generalized equivalence theory, the superhomogenization (SPH) method and the nonlinear iteration method. The last one, the nonlinear iteration method, was tested as the homogenization method for the first time. The calculations were carried out in simplified colorset assembly configurations of PWR, which are simulated by slab geometries, and homogenization performances were evaluated through comparison with the reference cell-heterogeneous calculations. The calculation results revealed that the generalized equivalence theory showed best performance. Though the nonlinear iteration method can significantly reduce homogenization error, its performance was not as good as that of the generalized equivalence theory. Through comparison of the results obtained by the generalized equivalence theory and the superhomogenization method, important byproduct was obtained; deficiency of the current superhomogenization method, which could be improved by incorporating the “cell-level discontinuity factor between assemblies”, was clarified.

Derivation of a variance-to-mean formula was performed to obtain the prompt neutron decay constant α of the subcritical reactor system that is driven by the periodic and pulsed neutron source. The formula was derived for an experimental technique where the Y value is measured by choosing an injection of pulsed neutrons as the origin of the counting gate. By using the derived formula, it was indicated that the α value can be easily determined. From this fact, it was concluded that the present formula was useful to measure the α value for future experiments with the accelerator driven system.

Recently, the bunching technique has been widely utilized in the Feynman-α experiment using a multi-channel scaler (MCS) to measure the prompt neutron decay constant α p . Although the bunching technique enables us to perform efficient experiments, it was pointed out that an inherent count-loss process arises due to the channel advance time Δ between adjacent MCS channels. Through derivation of a Feynman-α variance-to-mean formula containing Δ by means of the multi-gate Pal-Bell equation, Yamane and Hayashi ([Yamane, Y. & Hayashi, Y. 1995]. Annals of Nuclear Energy, 22(8), 533) indicated that this count-loss process does not play any important roles when the channel advance time is much smaller than the dwell time T. However, the Δ / T ratio often becomes large in thermal systems at deep-subcritical states or fast ones, because the dwell time should be chosen to be much smaller than reciprocals of α p values for such systems. On the other hand, since the ratio of the dead time d of neutron detectors to the dwell time becomes also large when the Δ / T ratio is not small, the count-loss process due to the dead time cannot be neglected. Therefore, Feynman-α variance-to-mean and covariance-to-mean formulae containing both Δ and d were derived by means of the compound detection probabilities. Based on the covariance-to-mean formula, a new experimental technique was developed and examined at the Kyoto University Critical Assembly. The result of the examination indicated that one can measure exact α p values when Δ / T ratios are known, even though Δ / T and d / T ratios are not small.

An acquisition system for the time series data of a pulse train was developed to perform the reactor noise experiments. Using this acquisition system, some important reactor kinetic parameters can be obtained by using various data analysis methods for the reactor noise experiments, which facilitates to achieve new experimental knowledge about characteristics of them proposed so far through direct comparison among the results of various methods. In the present study, the prompt neutron decay constant αpat two near delayed critical states of a core constructed in the Kyoto University Critical Assembly were measured by four well-known data analysis methods; the Feynman-α, the Rossi-α (Type-I and Type-II) and the frequency analysis methods. The results showed that ap values measured by the Type-I Rossi-α and the frequency analysis methods agreed with those by the Feynman-α method considering both effects of the delayed neutrons and the counting loss of neutron counter, whereas it was impossible to obtain the ...

Time-spatial neutron measurement was carried out by using a position-sensitive 3He proportional counter (PSPC) in the Kyoto University Critical Assembly. The data of the output pulses from the PSPC were acquired by a data acquisition system which was based on the LN-9000 system of Laboratory Equipment Corporation. In this system, the time and the position data of the neutron detection pulses were simultaneously accumulated by a personal computer. In the present study, the Rossi-α method, which was derived for time-domain neutron correlation analysis, was extended in order to process the measured two-dimensional data of time and space. The processed experimental results and a theoretical formula based on the one-group diffusion approximation neglecting the higher modes agreed well with each other, which indicates the present system is applicable for reactor physics experiments including reactor kinetics.

Previous measurements of the composition of Ultra-High Energy Cosmic Rays(UHECRs) made by the High Resolution Fly's Eye(HiRes) and Pierre Auger Observatory(PAO) are seemingly contradictory, but utilize different detection methods, as HiRes was a stereo detector and PAO is a hybrid detector. The five year Telescope Array(TA) Middle Drum hybrid composition measurement is similar in some, but not all, respects in methodology to PAO, and good agreement is evident between data and a light, largely protonic, composition when comparing the measurements to predictions obtained with the QGSJetII-03 and QGSJet-01c models. These models are also in agreement with previous HiRes stereo measurements, confirming the equivalence of the stereo and hybrid methods. The data is incompatible with a pure iron composition, for all models examined, over the available range of energies. The elongation rate and mean values of Xmax are in good agreement with Pierre Auger Observatory data. This analysis is presented using two methods: data cuts using simple geometrical variables and a new pattern recognition technique., Comment: 23 pages, 30 figures