On the low-frequency spatial dependence of the neutron response and noise field in LWRs

By employing a 1-D homogeneous reactor model in conjunction with a simple-thermohydraulics BWR feedback model proposed by others, it is shown that contrary to the zero-power case which predicts point-kinetics behaviour at very low frequencies (below 0.1 Hz), when strong feedback effects are present, there will be significant space-dependent effects even at low frequencies and that the importance of these effects will be proportional to the reactor power and the coefficients of reactivity.By using realistic data corresponding to a commercial BWR, the importance of the higher harmonics in the low-frequency region is assessed, and the detector response as well as the coherence function are evaluated for different void reactivity coefficients. Our numerical results are in agreement with experimental measurements in commercial BWRs and show that in the frequency region where feedback effects are dominant, the point model is not valid, the ‘global’ field of view of the detectors is drastically reduced and, for spatially-distributed and radially-uncorrelated noise sources, the coherence function between two detectors located at different radial positions decreases dramatically.     

On the space cross-correlation of noise sources in boiling water reactors

In this paper, an attempt has been made to investigate the space cross-correlation of boiling noise in boiling water reactors by assuming the slip ratio to be unity and power profile to be constant along the core height of the reactor. Two cases have been considered: One, no flow fluctuations (ΔV = 0) caused by boiling noise and two, finite flow fluctuations (ΔV ≠ 0) caused by the boiling noise. It has been found that finite range space cross-correlation of noise sources exists only for ΔV ≠ 0 case and not for ΔV = 0 case. Auto power spectral density of steam content fluctuations, Δα have a break frequency which is directly related with the flow velocity and attenuation coefficient, μ of the cross-correlation of noise sources in BWRs. Normalized root mean square value of Δα is more sensitive to μ in the upper half of the core for μ ≤ 10. For $\text{μ ? 20}$, it is more sensitive to μ in the lower half of the core.     

On the problem of monitoring the neutron parameters of the fast energy amplifier

The conceptual Fast Energy Amplifier, proposed by Rubbia et al. consists of a combination of a U-233/Th-232 fuelled fast-neutron subcritical facility with a proton accelerator. An intense beam of 1 GeV protons is injected into liquid lead at the core centre and drives the reactor by producing spallation neutrons. The burst of spallation neutrons produced by a single proton alters the basic neutron statistics which are well known for thermal neutrons in conventional nuclear reactors. A short assessment of standard neutron noise analysis methods is made with respect to monitoring neutron parameter data.     

Constitutive laws for the neutron density current

In this technical note, a fractional wave equation for the average neutron motion in nuclear reactor is considered. This representation covers the full spectrum of the average neutron transport behavior, i.e., Fickian and non-Fickian effects. The fractional diffusion model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional exponent that can be manipulated to obtain the best representation of the neutron transport phenomena. The detrended fluctuation analysis (DFA) method is presented in this paper to estimate the fractional exponent.     

Error estimators and adaptivity for the neutron diffusion problem

From an Object-Oriented analysis, a new nodal method was developed for the solution of the neutron diffusion equation, consisting of the minimization and equidistribution of a total error estimator E_T by the evolution of a dynamical gradient system of the form dΦ/dτ = −ΔE_T(Φ(τ)) on the manifold given by Φ = constant. The analysis discriminates a class of functions and a class of operators; in the class of functions, bases of polynomials of increasing number of terms were defined, and some procedures related to the class were implemented, such as rotations, differentiations, and two inner products. The new method was applied to the solution of the static one-speed diffusion equation on regular polygons and on a 2-D heterogeneous hexagonal domain. The results showed that the minimization of errors by the gradient system exhibits a monotone iterative behavior, controlling the distance between the approximate and the exact solution, not merely the distance between the previous and present step solutions. Adaptivity criteria appear naturally from the error observation, suggesting how and where it is necessary to improve the solution. Finally, it is discussed how the method (and the Object-Orientation frame) allows the relievement of users from uncertainties and the conservation of the accuracy without the user intervention.     

Three-group three-dimensional analysis of the random neutron field in bare homogeneous reactors and the concepts of local and global neutron noise

A three-group theory of neutron noise is developed and it is shown that the neutron-noise field in homogeneous multiplying media can be separated into a component with a long attenuation length (global component) and two local components whose attenuation lengths in water-moderated reactors are very small and of the order of the diffusion length of thermal neutrons in the medium.The theory is subsequently applied to the investigation of the neutron noise induced by axially propagating stochastic fluctuations of the moderator density in a simple 1-D BWR model and the evaluated neutron cross-spectra and phases are compared to the corresponding ones obtained by employing the two-group model with two-group data derived by condensing the three-group data in the reactor spectrum. In this respect, it is shown that the results obtained by using the three- and the two-group models are almost identical.     

The energy dependence of neutron damage in Cu and Nb

Primary recoil spectra and specific damage energies have been computed for neutron interactions in Cu and Nb at neutron energies up to 32 MeV. The calculations are based on theoretical neutron cross sections and are in good agreement with recent radiation damage experiments using high energy neutrons from the Be(d,n) reaction. The results are particularly relevant to the understanding of radiation effects from high energy deuteron-breakup neutron sources.     

Neutron energy dependence of delayed neutron yields and its assessments

Incident neutron energy dependence of delayed neutron yields of uranium and plutonium isotopes is investigated. A summation calculation of decay and fission yield data is employed, and the energy dependence of the latter part is considered in a phenomenological way. Our calculation systematically reproduces the energy dependence of delayed neutron yields by introducing an energy dependence of the most probable charge and the odd–even e?ect. The calculated fission yields are assessed by comparison with JENDL/FPY-2011, delayed neutron activities, and decay heats. Although the fission yields in this work are optimized to delayed neutron yields, the calculated decay heats are in good agreement with the experimental data. Comparison of the fission yields calculated in this work and JENDL/FPY-2011 gave an important insight for the evaluation of the next Japanese evaluated nuclear data library (JENDL) .     

中子注量空间分布规律的理论模拟

分别以高斯聚变中子谱和麦克斯韦裂变中子谱为源谱,采用Monte-Carlo方法,对中子从不同的源高度到达不同轨道高度及不同角度处的中子注量进行数值计算,通过对计算结果进行曲线拟合,获得中子注量的空间分布规律。同时引入方向散射因子的概念,并通过对方向散射因子变化规律的研究来获得中子的大气散射规律。     

中子场空间分布特性研究

采用Monte-Carlo方法,以高斯聚变中子谱和麦克斯韦裂变中子谱为源谱,进行了中子在大气中输运的理论模拟,给出了不同源高度,空问不同位置处的中子注量、能谱和吸收剂量,并总结了中子场的空问分布特性。     

Two-group theory of neutron noise in Molten Salt Reactors

In a previous paper, the kinetics, dynamics and the neutron noise in a Molten Salt Reactor (MSR) was investigated in a simple homogeneous reactor model in one-group diffusion theory. In this paper those investigations are extended to two-group theory in the same reactor model. In addition, unlike in the previous paper where in the quantitative work data from a thermal LWR were used, here material data of a conceptual MSR with a thermal spectrum and thorium fuel are used, along with data from both fast and thermal LWRs. Among other things, the relative weight and the range of the local component is investigated. It is found that the strong neutronic coupling in an MSR, which was pointed out in the preceding paper, diminishes the role of the local component as compared to light water reactors. Some further new features of the noise in MSR, not directly related to the two-group approach, are also found.     

The role of the eigenvalue separation in reactor dynamics and neutron noise theory

The concept of eigenvalue separation (ES) was introduced in the past for the characterisation of the space-time kinetics of reactor transients, and the stability properties of large loosely coupled cores. However, most of the investigations reported so far concern the determination of the ES itself either from static calculations, or from measurements of the flux tilt or neutron noise cross-correlations. Conclusions on system behaviour were only drawn from the properties of the static eigenfunctions, comparing non-perturbed and perturbed systems, without explicitly solving the time- or frequency-dependent problem. In this paper, we explore the role of the ES on the neutronic response of a critical core to small stochastic perturbations (neutron noise); in particular, the spatial and frequency characteristics of the arising neutron noise as a function of the ES, as well as the spatial structure of the perturbation. It is shown that for systems with small ES and non-uniform perturbations, point kinetics will not dominate even for very low frequencies. The results lend some further insight into the origin and properties of the various types of boiling water reactor instabilities.     

Multi-group theory of neutron noise induced by vibrating boundaries

The paper extends the one-group analysis of the neutron noise induced by fluctuating boundaries [Ann. Nucl. Energy 27(2000)1385] to the general multi-group non-homogeneous model. The full solution is given through the Green's function of the static problem, the static flux, and a quantity describing the boundary movements. A multi-group absorber model is proposed to represent the perturbation, which turns out to be very useful, for instance, to derive the point reactor and adiabatic approximations of the neutron noise arising from the oscillating boundaries. Finally, an equivalent solution is given in terms of the adjoint function.     

Characterization studies of BWR-4 neutron noise analysis spectra

Neutron noise analysis measurements were made in three BWR-4 reactors under full-power conditions to determine the noise characterization spectra of the reactors with two different instrument-tube cooling configurations. Both configurations were designed to prevent flow-induced vibration of the instrument tubes and subsequent damage of fuel channel boxes caused by impacts of the tubes with the boxes. Noise spectra from these three reactors were compared with spectra previously obtained prior to changing the instrument-tube cooling configuration, and no evidence of impacting was found.     

Diagnostics of core barrel vibrations by in-core and ex-core neutron noise

Diagnostics of core-barrel vibrations has traditionally been made by use of ex-vessel neutron detector signals. We suggest that in addition to the ex-core noise, also the in-core noise, induced by core barrel vibrations, be also used. This would enhance the possibilities of diagnostics where the number of the ex-core detectors is not sufficient or their positions are disadvantageous for effective diagnostics, especially for shell-mode vibrations.

To this order, the theory of in-core noise induced by a fluctuating core boundary has been elaborated and applied to the diagnostics of beam and shell mode vibrations. The formulas were tested on some measurements taken in the Ringhals PWRs. The results confirm the validity of the model itself, and the possibilities for enhanced diagnostics were demonstrated. A more effective use of these novel possibilities requires more in-core detectors and/or better detector positioning.