Prompt-neutron Decay Constant Research Articles

Application of dynamic mode decomposition to Rossi-α method in a critical state using file-by-file moving block bootstrap method

ABSTRACT Prompt neutron decay constant in a critical state is useful information to validate the numerically predicted ratio of the point kinetics parameters , where and are the effective delayed neutron fraction and prompt neutron lifetime, respectively. To directly measure in a target critical system, this study proposes the application of the dynamic mode decomposition (DMD) to the reactor noise analysis based on the Rossi- method. The DMD-based Rossi- method enables us to robustly estimate the fundamental mode component of from the Rossi- histograms measured using multiple neutron detectors. Furthermore, the file-by-file moving block bootstrap method is newly proposed for the statistical uncertainty quantification of to prevent huge memory usage when the neutron count rate is high and/or the total measurement time is long. A critical experiment has been conducted at Kyoto University Critical Assembly to demonstrate the proposed method. As a result, the proposed method can uniquely determine the value of which the statistical uncertainty is smallest. By utilizing this experimental result of , numerical results of ratio using the continuous energy Monte Carlo code MCNP6.2 with recent nuclear data libraries, which are processed by the nuclear data processing code FRENDY, are validated.

Consideration of delayed neutron effect on Rossi-α analysis for a subcritical thermal reactor

ABSTRACT An improved Rossi-α formula is derived to consider a delayed-neutron contribution to a conditional counting probability defined in the Rossi-α technique. The improved formula has an additional constant term and another additional term proportional to time interval τ to the original formula. For an university training and research reactor of Kindai University, the Rossi-α analyses based on the original and the improved formulae are carried out to examine the applicability of these formulae to the subcritical thermal reactor. The original formula results in an inconsistent prompt-neutron decay constant with that determined from a previous Feynman-α analysis considering delayed neutrons. This difficulty of the original formula originates from the neglect of delayed neutrons. Applying the improved formula leads to a consistent prompt-neutron decay constant. The additional constant term of the improved formula should be considered to determine accurately the decay constant, while the additional proportional term is much too small to consider. The additional constant term obtained from the present analysis is consistent with that from the previous Feynman-α analysis.

Applicability of several Feynman-α formulae to a subcritical thermal reactor

ABSTRACT For an university training and research reactor of Kindai University, the Feynman-α analyses based on several formulae are carried out to examine the applicability of these formulae to the subcritical thermal reactor system. The original formula, in which the effect of delayed neutrons is neglected, results in a prompt-neutron decay constant sensitive to an upper limit of the gate time range of the analysis and consequently has difficulty in determining the decay constant. This difficulty originates from the neglect of delayed neutrons. An improved formula, where a term proportional to the gate time is added to the original formula, gives a desirable decay constant insensitive to the upper limit and the insensitive decay constant well agrees with that obtained from the Rossi-α analysis. The application of a difference filtering technique also leads to a successful result similar to the above improved formula. An alternative index Z to the traditional index Y of the original formula has been sometimes employed as an indication of the non-Poisson nature of the counting statistics. The Z is defined as dividing the Y by the mean number of neutron counts accumulated in the gate time. The formula for the Z never results in a reasonable decay constant even though the effect of delayed neutrons is considered. This study suggests that the improved formula considering delayed neutrons for the Y and the formula for the difference filtering technique should be employed to determine the prompt-neutron decay constant of thermal reactors.

EXPERIMENTAL STUDY ON NEUTRON CORRELATION ANALYSIS FOR A SUBCRITICAL SYSTEM DRIVEN BY A PULSED SPALLATION NEUTRON SOURCE IN KUCA

The Feynman-α and the Rossi-α methods have been frequently employed to determine the subcriticality of subcritical reactor systems driven by Poisson source such as Am-Be neutron source. In actual accelerator-driven systems (ADS), a spallation device will be applied as an intense neutron source. This device will be probably operated in a pulse mode and it is impossible to apply a conventional analysis method to determine the subcriticality in any ADS. In previous theoretical studies, some advanced formulae of neutron correlation analysis for spallation neutron source have been presented. However, the experimental study has been hardly reported to date. The major objectives of this study are to examine experimentally an applicability of these complicated formulae to a subcritical reactor system driven by an actual pulsed spallation neutron source and to determine the prompt-neutron decay constant α of the system. To achieve these goals, we constructed an ADS core at the Kyoto University Critical Assembly (KUCA). The core was composed of highly-enriched uranium fuel assemblies surrounded by many polyethylene reflector assemblies. We carried out a series of the Feynman-α and the Rossi-α analyses for the system driven by pulsed spallation source. As a result, the prompt-neutron decay constants were experimentally obtained by using a fitting formula. The prompt-neutron decay constants determined by Feynman-α and Rossi-α analyses agrees with each other within a statistical error range of least-squares fitting.

REACTOR NOISE ANALYSIS FOR A GRAPHITE-MODERATED AND -REFLECTED CORE IN KUCA

In graphite-reflected thermal reactors, even a detector placed far from fuel region may detect a certain degree of the correlation amplitude. This is because mean free path of neutrons in graphite is longer than that in water or polyethylene. The objective of this study is experimentally to confirm a high flexibility of neutron detector placement in graphite reflector for reactor noise analysis. The present reactor noise analysis was carried out in a graphite-moderated and -reflected thermal core in Kyoto University Critical Assembly (KUCA). BF3 proportional neutron counters (1” dia.) were placed in graphite reflector region, where the counters were separated by about 35cm and 30cm -thick graphite from the core, respectively. At a critical state and subcritical states, time-sequence signal data from these counters were acquired and analyzed by a fast Fourier transform (FFT) analyzer, to obtain power spectral density in frequency domain. The auto-power spectral density obtained from the counters far from the core contained a significant degree of correlated component. A least-squares fit of a familiar formula to the auto-power spectral density data was made to determine the prompt-neutron decay constant. The decay constant was 63.3±14.5 [1/s] in critical state. The decay constant determined from the cross-power spectral density and coherence function data between the two counters also had a consistent value. It is confirmed that reactor noise analysis is possible using a detector placed at about 35cm far from the core, as we expected.

Power spectral analysis for a subcritical reactor system driven by a pulsed spallation neutron source in Kyoto University Critical Assembly

ABSTRACT For a subcritical reactor system driven by a periodically pulsed spallation neutron source in Kyoto University Critical Assembly, a series of power spectral analysis on frequency domain is carried out to determine the prompt-neutron decay constant and quantitatively to confirm a non-Poisson characteristics of the neutron source. Not only the cross-power but also the auto-power spectral density has a considerable correlated noise component even at a deeply subcritical state, where no correlated component could be observed under a pulsed DT(14MeV) neutron source. The non-Poisson character of the spallation source must enhance the correlation amplitude of these power spectral densities. Moreover, the Degweker’s factor (m 2-m 1 2)/m 1 2 of 0.082 ± 0.021, which is a quantitative indication of the non-Poisson character, is determined from the present analysis and is consistent with that obtained by a previous Rossi-α analysis for the same subcritical system driven by the spallation source. The non-zero value of the factor convinces us again that the present source has a different statistical distribution from the Poisson. The prompt-neutron decay constant obtained from the present analysis well agreed with that done from the above previous Rossi-α analysis.

Feynman-α and Rossi-α analyses for a subcritical reactor system driven by a pulsed spallation neutron source in Kyoto University Critical Assembly

ABSTRACT For a subcritical reactor system driven by a periodically pulsed spallation neutron source in Kyoto University Critical Assembly (KUCA), the Feynman-α and the Rossi-α neutron correlation analyses were carried out to determine the prompt-neutron decay constant and quantitatively to confirm a non-Poisson characteristics of the neutron source. In these correlation analyses, a non-negligible contribution of delayed neutrons and a non-Poisson character of the source were considered, and each pulse was assumed to be a delta function. When a neutron counter was placed closely to the reactor core, the prompt-neutron decay constant determined from the present Feynman-α analysis well agreed with that done from a previous analysis for the same subcritical system driven by an inherent neutron source. However, the decay constant determined from the present Rossi-α analysis was in poor agreement with that done from the above previous analysis. This disagreement originated from an inevitable excitation of a higher mode. In the Rossi-α counting probability distribution, the excitation deformed a sharp cusp arising from the delta function to a smooth convex shape. When the data around the convex top were masked for least-squares fitting of the present Rossi-α formula, the disagreement could be successfully resolved. Compared with the previous Feynman-α and Rossi-α analyses under the Poisson inherent source, the non-Poisson spallation source definitely enhanced the respective prompt-neutron correlation amplitudes. The enhancement rate increased with an increase in subcriticality. Moreover, the Degweker’s factor (m 2-m 1 2)/m 1 2 of 0.067 ± 0.011, which indicated a non-Poisson character of the present spallation source, could be determined from the present correlation analysis and the non-zero value of the factor convinced us that the present source had a different statistical distribution from the Poisson.

An improved Feynman-α analysis with a moving–bunching technique

ABSTRACTThe bunching technique has been widely utilized in Feynman-α neutron correlation analysis to synthesize neutron counts within longer gate widths by bunching time-sequence neutron counts stored in multichannel scaler channels. An alternative technique referred to as “moving–bunching technique” was proposed to reduce a statistical scatter of variance-to-mean ratio of neutron counts. The conventional bunching technique has no overlap of adjacent bunches, while the present technique makes adjacent bunches overlap as long as possible similarly to the moving average technique. A Feynman-α experiment was performed in the UTR-KINKI, to confirm the advantage of the proposed bunching technique. When a neutron detector was placed far from the core, a Feynman-α analysis with the conventional bunching technique led to a scattered variance-to-mean ratio from which the prompt-neutron decay constant was never determinable. However, another analysis with the proposed technique remarkably reduced the above scatter and enabled the determination of the decay constant. For a neutron detector close to the core, the proposed technique also reduced statistical error of the decay constant.

Determination of prompt-neutron decay constant from phase shift between beam current and neutron detection signals for an accelerator-driven system in the Kyoto University Critical Assembly

A unique power spectral analysis for a subcritical reactor system driven by a pulsed 14 MeV neutron source was carried out at the Kyoto University Critical Assembly (KUCA). In this analysis, a complex cross-power spectral density between time-sequence signal data from an accelerator beam ammeter and a neutron detector was measured to determine the prompt-neutron decay constant of an accelerator-driven system (ADS) from the phase data of the spectral density. Assuming the one-point kinetics model, in theory, the decay constant can be arithmetically derived from the phase at the integral multiples of the pulse repetition frequency. However, the actual derivation from the phase at a pulse repetition frequency of 20 Hz considerably underestimated the prompt-neutron decay constant, compared with that obtained by a previous pulsed neutron experiment, and the derived decay constant apparently decreased with an increase in the multiple of the pulsed repetition frequency. Considering a lag time in detector response, the above underestimation and the above apparent decrease were solved to obtain the consistent decay constant. While both previous power spectral analysis and Feynman-α analysis for pulsed neutron source require non-linear least-squares fits of the respective complicated formulae, the present analysis makes the fitting unnecessary except at regular calibration of the lag time. This feature is advantageous for a robust online monitoring of subcritical reactivity of an actual ADS.

Measurement of large negative reactivity of an accelerator-driven system in the Kyoto University Critical Assembly

Large negative reactivity of a subcritical system driven by a pulsed 14 MeV neutron source has been measured in the Kyoto University Critical Assembly. The subcriticality of the accelerator-driven system (ADS) ranged in effective multiplication factor roughly from 0.98 to 0.92, which corresponded to an operational range of an actual ADS proposed by Japan Atomic Energy Agency. As the measurement technique, pulsed neutron method, power spectral analysis for pulsed neutron source, accelerator-beam trip method were employed. From neutron count decay data obtained by the pulsed neutron experiment, not only the prompt-neutron decay constant of fundamental mode but also a higher spatial mode could be derived. The subcriticality was also determined from the fundamental decay constant. The measured cross-power spectral density consisted of a familiar correlated reactor-noise component and many uncorrelated delta-function-like peaks at the integral multiple of pulse repetition frequency. The fundamental prompt-neutron decay constant, i.e., the subcriticality determined from the latter uncorrelated peaks was consistent with that obtained by the above pulsed neutron experiment. However, the magnitude of the former correlated component was reduced with an increase in the subcriticality and eventually this component became almost white at deeply subcritical state ranging in the multiplication factor under 0.95. Consequently, the determination of the decay constant from the correlated component was impossible under such a subcritical state. As data analysis method for the beam trip experiment, both the conventional integral count method and the least-squares inverse kinetics method (LSIKM) were employed. The LSIKM analysis led to the consistent subcriticality with that obtained by the pulsed neutron experiment, while the integral count method significantly underestimated the subcriticality. This underestimation originated from a residual background count, which was maintained after the beam trip. The LSIKM was mostly not influenced by such a slight count rate.

Power spectral analysis for a thermal subcritical reactor system driven by a pulsed 14 MeV neutron source

A series of power spectral analyses for a thermal subcritical reactor system driven by a pulsed 14 MeV neutron source was carried out at Kyoto University Critical Assembly (KUCA), to determine the prompt-neutron decay constant of the accelerator-driven system (ADS). The cross-power spectral density between time-sequence signal data of two neutron detectors was composed of a familiar continuous reactor noise component and many delta-function-like peaks at the integral multiple of pulse repetition frequency. The prompt-neutron decay constant inferred from the reactor noise component of the cross-power spectral density was consistent with that obtained by a pulsed neutron experiment. However, the reactor noise component of the auto-power spectral density of each detector was hidden by a white chamber noise in the higher-frequency range and this feature resulted in a considerable underestimation of the decay constant. For several runs with a low pulse-repetition frequency, furthermore, we attempted to infer the decay constant from point data of the delta-function-like peaks. The analysis for a run under a slightly subcritical state resulted in the consistent decay constant; however, those for other runs under significantly subcritical states underestimated the decay constant. Considering the contribution of a spatially higher mode to the point data, the above underestimation was solved to obtain the consistent decay constant. While the Feynman-α formula for a pulsed neutron source is too complicated to be fitted directly to variance-to-mean ratio data, the present analysis on frequency domain is much simpler and the conventional formula based on the first-order reactor transfer function is available for fitting to power spectral density data.

Calculation of the effective delayed-neutron fraction and prompt-neutron lifetime in IBR-2M

The main parameters of IBR-2M are presented: the effective delayed-neutron fraction βeff and the promptneutron lifetime τ, calculated using the DORT two-dimensional multigroup neutron-transport compute code and the SCALE4 code with a system of multigroup nuclear constants. For a regular IBR-2M regime βeff = 0.00216 ± 0.00007, τ = (6.5 ± 0.5)·10–8 sec, the delay-neutron value γ = 0.980, the prompt-neutron decay constant in the critical state α = 3.5·104 sec–1. The calculations showed that the effective delayed-neutron fraction for IBR-2M is identical, within the error limits, to the measured value for IBR-2, the prompt-neutron lifetime is approximately 5% longer (βeff = 0.00216, τ = (6.2 ± 0.2)·10–8 sec). It is shown that βeff and τ increase somewhat as the IBR-2 core size increases in the radial direction.

Feynman-α Analysis for a Thermal Subcritical Reactor System Driven by an Unstable 14MeV Neutron Source

In a series of Feynman-α correlation measurements for a thermal Accelerator-Driven System (ADS) with 14MeV neutrons at the Kyoto University Critical Assembly (KUCA), an unstable accelerator condition such as a drift of beam current has been frequently observed. Neutron source instability caused by such unavoidable beam-current instability resulted in a divergent variance-to-mean ratio and, consequently, the correlation analysis failed. Nevertheless, we attempted to apply a difference-filtering technique to the correlation analysis to reduce the influence of the above instability. The present attempt resulted in consistent prompt-neutron decay constants with those obtained in a previous pulsed neutron experiment. The application of the filtering is expected to enhance the robustness of Feynman-α analysis against various instabilities of accelerator operation in actual ADS.

Feynman-α Analysis for a Thermal Subcritical Reactor System Driven by an Unstable 14 MeV Neutron Source

In a series of Feynman-α correlation measurements for a thermal Accelerator-Driven System (ADS) with 14MeV neutrons at the Kyoto University Critical Assembly (KUCA), an unstable accelerator condition such as a drift of beam current has been frequently observed. Neutron source instability caused by such unavoidable beam-current instability resulted in a divergent variance-to-mean ratio and, consequently, the correlation analysis failed. Nevertheless, we attempted to apply a difference-filtering technique to the correlation analysis to reduce the influence of the above instability. The present attempt resulted in consistent prompt-neutron decay constants with those obtained in a previous pulsed neutron experiment. The application of the filtering is expected to enhance the robustness of Feynman-α analysis against various instabilities of accelerator operation in actual ADS.

Determination of Lambda-Mode Eigenvalue Separation of a Thermal Accelerator-Driven System from Pulsed Neutron Experiment

Basic research on the Accelerator-Driven System (ADS) with thermal neutron spectrum has been promoted by the Kyoto University Research Reactor Institute. At the Kyoto University Critical Assembly (KUCA), various experiments on thermal ADS with a pulsed spallation source are planned. In such an ADS, neutron flux distribution may be sensitive to the injection of neutrons, and the high sensitivity results in various spatial effects. In this study, a pulsed neutron experiment with 14MeV neutrons was carried out in a thermal ADS of KUCA, to determine the λ-mode eigenvalue separation, which is a quantitative indication of spatial effects. An original data-processing technique was applied to infer prompt-neutron decay constants of fundamental and higher modes from neutron count decay data, and then the eigenvalue separation around 13%Δk/k was obtained from these decay constants.

Criticality of a 237Np Sphere

A series of critical-mass experiments using a 6-kg neptunium sphere was performed on the Planet vertical-assembly machine at Los Alamos National Laboratory (LANL). The purpose of the experiments was to obtain a better estimate of the critical mass of 237Np. The configurations that were studied included surrounding the neptunium sphere with highly enriched uranium (HEU) shells as well as reflecting it with iron and polyethylene. An additional experiment using a 4.5-kg α-phase plutonium sphere surrounded with HEU was performed to demonstrate how well the computer transport code and the existing cross-section data for uranium and plutonium could reproduce the experiment. For some of the configurations, the prompt-neutron decay constants at delayed critical were measured. These experiments provided an integral measurement of the cross sections for 237Np in the fast-energy and possibly in the intermediate-energy regions. The measured keff from these experiments was compared with the calculated keff from the Monte Carlo N-Particle (MCNP) transport code using ENDF/B-V and ENDF/B-VI and cross-section data evaluated by the Nuclear Theory and Applications group (T-16) at LANL. In all the neptunium experiments, the calculated keff values based on ENDF/B-VI data were ~1% lower than the experimental keff. After adjusting the cross sections for neptunium and 235U to match the bare neptunium/HEU experiment as well as Godiva keff criticality and spectra indexes, the MCNP code yielded a value of 57 ± 4 kg for the bare critical mass of 237Np.

Feynman-α correlation analysis by prompt-photon detection

Two-detector Feynman-α measurements were carried out using the UTR-KINKI reactor, a light-water-moderated and graphite-reflected reactor, by detecting high-energy, prompt gamma rays. For comparison, the conventional measurements by detecting neutrons were also performed. These measurements were carried out in the subcriticality range from 0 to $1.8. The gate-time dependence of the variance-and covariance-to-mean ratios measured by gamma-ray detection were nearly identical with those obtained using standard neutron-detection techniques. Consequently, the prompt-neutron decay constants inferred from the gamma-ray correlation data agreed with those from the neutron data. Furthermore, the correlated-to-uncorrelated amplitude ratios obtained by gamma-ray detection significantly depended on the low-energy discriminator level of the single-channel analyzer. The disriminator level was determined as optimum for obtaining a maximum value of the amplitude ratio. The maximum amplitude ratio was much larger than that obtained by neutron detection. The subcriticality dependence of the decay constant obtained by gamma-ray detection was consistent with that obtained by neutron detection and followed the linear relation based on the one-point kinetic model in the vicinity of delayed critical. These experimental results suggest that the gamma-ray correlation technique can be applied to measure reactor kinetic parameters more efficiently.

97/01955 Prompt Neutron decay constants at delayed criticality for the oak ridge research reactor with 20 and 93 wt% 235U enriched fuel

In this study, the feasibility of yttria-stabilized zirconia (YSZ) was investigated for use as a ceramic material, which can be commonly used for both electrolytic reduction and electrorefining. First, the stability of YSZ in salts for electrolytic reduction and electrorefining was examined. Then, its stability was demonstrated by a series of pyroprocessing tests, such as electrolytic reduction, LiCl distillation, electrorefining, and LiClKCl distillation, using a single stainless steel wire mesh basket containing fuel and YSZ. A single basket was used by its transportation from one test to subsequent tests without the requirements for unloading.

97/01237 Prompt neutron decay constants at delayed criticality for the oak ridge research reactor with 20 and 93 wt.% 235U enriched fuel

97/01237 Prompt neutron decay constants at delayed criticality for the oak ridge research reactor with 20 and 93 wt.% 235U enriched fuel

Prompt neutron decay constants at delayed criticality for the Oak Ridge Research Reactor with 20 and 93 wt% 235U enriched fuel

Measurements of the prompt neutron decay constant at delayed criticality with water-reflected, unirradiated low- and high-enrichment fuel loadings and a beryllium-reflected low-enrichment fuel loading were performed for the Oak Ridge Research Reactor. The prompt neutron decay constants were obtained from nonlinear least-squares filling of the frequency-dependent cross-power spectral densities measured between two detectors placed adjacent to the core. The fitting function was derived from the point neutron kinetics equations, ignoring delayed neutrons. The measurements with this water-moderated pool-type reactor determined that the prompt neutron decay constant (for the water-reflected cores) is about 15% higher for the low-enrichment fuel loading (194.9 ± 0.9 s −1) than for the high-enrichment fuel loading (169.1 ± 1.1 s −1). Measurements also showed that the prompt neutron decay constant is about 28% less for the Be-reflected low-enrichment fuel loading than for the water-reflected low-enrichment fuel loading.