Contribution Of Delayed Neutrons Research Articles

A Feynman-α analysis ranging over time constants of delayed neutrons based on time-sequence counting data consecutively acquired for a very long time

ABSTRACT Time-sequence counting data of a neutron counter were acquired for 17 consecutive days at shutdown state of UTR-KINKI reactor and then a Feynman-α analysis over a very wide gate width range was carried out to give light on a delayed-neutron contribution of all precursors, where statistical error of the correlation amplitude Y was estimated using the bootstrap method. A first plateau of the Y could be observed in a gate width range of several hundred milliseconds. With an enlargement of gate width beyond a time constant of prompt neutrons, the Y monotonically increased above the first plateau of prompt neutrons. Enlarging gate width beyond 100 s, the Y seemed to approach a second plateau of delayed neutrons. The second plateau originated from the delayed neutrons released from the longest-life 87Br. In the gate width range beyond 100 s, however, the statistical error increased sharply. The increasing error indicates a statistical limit resulting from the present measurement time. A value Y p of the first plateau of prompt neutrons was determined from another Feynman- analysis confined to a short gate width range and the Y was divided by the plateau’s value Y p to eliminate an unknown detection efficiency. The Y-to-Y p ratio was calculated using several sets of delayed-neutron group parameters for thermal fission of 235U nuclide, to validate these sets by comparing with the measured ratio to which all precursors contributed. The ratios calculated using Keepin’s 6-group and Spriggs’ 8-group parameters agreed very well with the measured ratio in a gate width range up to 100 s and consequently these parameters could be validated. However, the ratios calculated using the other sets were in a very poor agreement with the measured ratio in the gate width range.

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.

New variants of Bennett variance method with correlation indices for reducing delayed-neutron contribution

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.

Monte Carlo and deterministic calculation of the Bell and Glasstone spatial correction factor

Abstract The Bell and Glasstone correction factor is used in subcritical assembly pulsed neutron source experiments to correct the spatial dependency of the measured reactivity on the detector position. The correction factor is defined as the ratio between the reactivity obtained by computer codes in criticality mode and that obtained by computer codes in source mode. In the area method, the reactivity (in dollar units) of a subcritical assembly is given by the ratio between the prompt and the delayed areas; these areas are obtained by integrating the detector reaction rate over the pulse period. This work illustrates different methods to calculate the Bell and Glasstone spatial correction factor using both Monte Carlo (MCNPX) and deterministic (PARTISN) computer codes. The different calculation methods include: (1) the one-simulation dynamic method (which has been applied by MCNPX computer simulations); (2) the two-simulation static method (which has been applied by both MCNPX and PARTISN computer simulations); (3) the one-simulation static method (which has been applied by MCNPX computer simulations). In the one-simulation dynamic method: (1) the external neutron source is time dependent; (2) the detector reaction rate is obtained from a single pulse and it is superimposed until the delayed neutron contribution reaches the asymptotic value; (3) the prompt area is obtained as the difference between the total and delayed areas. In the two-simulation static method: (1) the external neutron source is time independent; (2) the total and prompt areas are obtained by two separate computer simulations (one with and the other without delayed neutrons); (3) the delayed area is obtained as the difference between the total and prompt areas. In the one-simulation static method, first introduced in this study, the prompt and delayed areas are tallied in the same MCNPX simulation, which halves the computing time and reduces the statistical error relative to the two-simulation static method.

Pulse superimposition calculational methodology for estimating the subcriticality level of nuclear fuel assemblies

One of the most reliable experimental methods for measuring the subcriticality level of a nuclear fuel assembly is the Sjöstrand method applied to the reaction rate generated from a pulsed neutron source. This study developed a new analytical methodology simulating the Sjöstrand method, which allows comparing the experimental and analytical reaction rates and the obtained subcriticality levels. In this methodology, the reaction rate is calculated due to a single neutron pulse using MCNP/MCNPX computer code or any other neutron transport code that explicitly simulates the delayed fission neutrons. The calculation simulates a single neutron pulse over a long time period until the delayed neutron contribution to the reaction rate is vanished. The obtained reaction rate is then superimposed to itself, with respect to the time, to simulate the repeated pulse operation until the asymptotic level of the reaction rate, set by the delayed neutrons, is achieved. The superimposition of the pulse to itself was calculated by a simple C computer program. A parallel version of the C program is used due to the large amount of data being processed, e.g. by the Message Passing Interface (MPI). The analytical results of this new calculation methodology have shown an excellent agreement with the experimental data available from the YALINA-Booster facility of Belarus. This methodology can be used to calculate Bell and Glasstone spatial correction factor.

Reduction of Delayed-Neutron Contribution to Variance-to-Mean Ratio by Application of Difference Filter Technique

The difference-filtering correlation analysis was applied to time-sequence neutron count data measured in a slightly subcritical assembly, where the Feynman-α analysis suffered from large contribution of delayed neutron to the variance-to-mean ratio of counts. The prompt-neutron decay constant inferred from the present filtering analysis agreed very closely with that by pulsed neutron experiment, and no dependence on the gate-time range specified could be observed. The 1st-order filtering was sufficient for the reduction of the delayed-neutron contribution. While the conventional method requires a choice of analysis formula appropriate to a gate-time range, the present method is applicable to a wide variety of gate-time ranges.

Reduction of Delayed-Neutron Contribution to Variance-to-Mean Ratio by Application of Difference Filter Technique.

The difference-filtering correlation analysis was applied to time-sequence neutron count data measured in a slightly subcritical assembly, where the Feynman-α analysis suffered from large contribution of delayed neutron to the variance-to-mean ratio of counts. The prompt-neutron decay constant inferred from the present filtering analysis agreed very closely with that by pulsed neutron experiment, and no dependence on the gate-time range specified could be observed. The 1st-order filtering was sufficient for the reduction of the delayed-neutron contribution. While the conventional method requires a choice of analysis formula appropriate to a gate-time range, the present method is applicable to a wide variety of gate-time ranges.

Measurement of the delayed neutron fraction and correction of small angle scattering data from a pulsed spallation source

The fraction of delayed neutrons in a moderated beam from the enriched uranium, pulsed spallation source at the intense pulsed neutron source at Argonne National Laboratory has been measured and found to be 0.0283 for 450-MeV protons. Delayed neutrons produce a sample-dependent background in time-of-flight instruments. Because of the distribution of neutron wavelengths in the prompt pulse, the significance of the delayed neutron contribution to the observed scattering profile is strongly dependent on the wavelength and therefore on the magnitude of the momentum transfer. This effect is demonstrated, and a general correction procedure in current use for small angle neutron scattering data is described.

A mechanical analog in nonlinear nuclear reactor stability analysis

A sufficient condition for the asymptotic stability of nuclear reactors in terms of the equilibrium power level and arbitrary feedback parameters is obtained through the use of a mechanical analog. The stability criterion (related to the amplitude of oscillations of the autonomous system and shown to contain no delayed neutron contribution) differs in this respect from previous work and provides further insight into the role of delayed neutrons in nonlinear system stability. >