Imre Pázsit

Methods for the determination of the in-phase and out-of-phase stability characteristics of a boiling water reactor

Measurements, taken in the Ringhals-1 boiling water reactor after revision in 1990, showed that instability occurred at high power and low core flow. Measurements in several points of the power-flow map showed that the decay ratio (DR), obtained by conventional methods, jumps from a moderate value directly to unity. This was valid for DR values calculated from both average power range monitor (APRM) and local power range monitor (LPRM) signals. Thus, the conventional DR cannot be used as a measure of the margin to instability. It was found that both global (in-phase) and regional (out-of-phase) oscillations occur, the global with low DR but large signal amplitude, and the regional with high DR but low signal amplitude. The former dominates the DR calculated from both APRMs and LPRMs, except when the instability is fully developed and impedes detection of the actual margin to instability. Methods for obtaining the stability characteristics of both modes separately from neutron noise signals were developed. The DR of the out-of-phase mode appears to be a good indicator of the margin to instability.

On the Neutron Noise Diagnostics of Pressurized Water Reactor Control Rod Vibrations II. Stochastic Vibrations

AbstractIn an earlier publication, using the theory of neutron fluctuations induced by a vibrating control rod, a complete formal solution of rod vibration diagnostics based on neutron noise measurements was given in terms of Fourier-transformed neutron detector time signals. The suggested procedure was checked in numerical simulation tests where only periodic vibrations could be considered.The procedure and its numerical testing are elaborated for stochastic two-dimensional vibrations. A simple stochastic theory of two-dimensional flow-induced vibrations is given; then the diagnostic method is formulated in the stochastic case, that is, in terms of neutron detector auto- and cross-power spectra. A previously suggested approximate rod localization technique is also formulated in the stochastic case. Applicability of the methods is then investigated in numerical simulation tests, using the proposed model of stochastic two-dimensional vibrations when generating neutron detector spectra that simulate measure...

THEORY OF NEUTRON FLUCTUATIONS IN SOURCE-DRIVEN SUBCRITICAL SYSTEMS

Abstract Neutron fluctuations are investigated in a subcritical system driven by a non-Poisson (correlated) source. Such sources arise in e.g. accelerator-driven systems (ADS) where several neutrons are born simultaneously with a certain fluctuation in the spallation process. The second moment of the neutron number and of the detector counts is calculated. In particular, the Feynman-alpha formula is derived both by a master equation technique and with a heuristic approach. It is shown that the dependence of the variance-to-mean of the counts on the time gate is the same as in the traditional case (Poisson source), but its magnitude is enhanced by the source fluctuations and multiplicity. Thus, the presence of a correlated source is beneficial for the application of the Feynman technique. Consequently, it may be possible to perform measurements with deeper subcriticalities than in the traditional case.

Linear response of the neutron field to a propagating perturbation of moderator density (two-group theory of boiling water reactor noise)

According to recent investigations the neutron noise field in a boiling water reactor can be separated into a local and a global component. These two components are discussed further via two-group diffusion theory. The expediency of the local-global concept is compared to another concept based on separating components corresponding to the two roots of the dynamic eigenvalue problem. The mathematical discussion of the neutron response to a propagating perturbation of the moderator density is given. Point reactor behavior and linear-phase behavior appear as two extremes of the neutron response. The mathematical results are illustrated numerically for the cases of a large power reactor core and a small highly enriched core.

Theoretical investigation of the neutron noise diagnostics of two-dimensional control rod vibrations in a PWR

Abstract In order to develop a method for monitoring control rod vibrations by neutron noise measurements, the noise induced by two-dimensional vibrations of control elements is investigated. The two-dimensional Greens function relating the small stochastic cross-section fluctuations to the neutron noise is determined for a rectangular slab reactor in the modified one-group theory, and subsequently, the neutron response to two-dimensional vibrating noise sources is investigated. Two possible diagnostical applications are considered: (a) the reconstruction of the mechanical trajectory of the vibrating element by neutron noise measurements, and (b) the possibility of locating the vibrating element in the core.

Theory and Analysis of the Feynman-Alpha Method for Deterministically and Randomly Pulsed Neutron Sources

Abstract In future planned accelerator-driven subcritical systems, as well as in some recent related experiments, the neutron source to be used will be a pulsed accelerator. For such cases the application of the Feynman-alpha method for measuring the reactivity is not straightforward. The dependence of the Feynman Y(T) curve (variance-to-mean minus unity) on the measurement time T will show quasi-periodic ripples, corresponding to the periodicity of the source intensity. Correspondingly, the analytical solution will become much more complicated. One can perform such a pulsed Feynman-alpha measurement in two different ways: either by synchronizing the start of each measurement block with the pulses (“deterministic pulsing”) or by not synchronizing (“random pulsing”). The variance-to-mean has been derived analytically for both cases and reported briefly in previous publications. However, two different methods were used and the two cases were reported separately. In this paper we give a unified treatment and a comparative analysis of the two cases. It is found that the stochastic pulsing leads to an analytic solution that is much simpler than that for the deterministic case, and the relationship between the pulsed and continuous source is much more straightforward than in the deterministic case. However, the amplitude of the ripples, constituting a deviation of the pulsed Feynman Y curve from the smooth curve corresponding to the traditional constant source case, is much larger for the stochastic pulsing than for the deterministic one. The reasons for this are also analyzed in the paper. The results are in agreement with recent measurements, made by other groups in the European Community-supported project MUSE.

The variance-to-mean ratio in subcritical systems driven by a spallation source

Abstract In a previous work, we have derived a formula for the variance-to-mean ration, used in the Feynman-alpha method, of the neutron counts in a subcritical system driven by a correlated (multiple or non-Poisson) source (such as a spallation or a 252 Cf one). The formal derivation as made by assuming prompt neutrons only in the fission chain, and the results were extended to include delayed neutrons by intuitive arguments. To confirm this procedure and the validity of the former result, in this paper the variance-to-mean formula has been derived by using a master equation technique including one group of delayed neutrons. The result shows, in agreement with the previous work, that both the prompt and the delayed neutron terms include the effect of the correlated source in form of additive factors, multiplying the corresponding time dependent terms. It is thus also confirmed that the presence of a correlated source with large multiplicity, such as in the case of a spallation source in an accelerator driven system, is very beneficial for the application of the Feynman alpha technique because it enhances the prompt alpha component from which the prompt neutron time constant is determined. Hence, in such systems the reactivity may be monitored with larger subcriticalities than in conventional systems.

Two-group theory of noise in reflected reactors with application to vibrating absorbers

Abstract A one-dimensional semi-analytic method, based on the adjoint technique, has been developed for two-group treatment of noise in reflected reactors. The adjoint for a symmetric system is given and examined in detail. The local and global characters of noise are investigated for in-core and ex-core perturbations. Finally, the noise induced by a vibrating absorber is determined.

Analytical solution for the Feynman-Alpha formula for ADS with pulsed neutron sources

Abstract The theory of Feynman-alpha measurements is elaborated for the case of a “stochastically pulsed” subcritical system. The corresponding physical situation is when a pulsed neutron source is used, and no synchronisation between the start of the measurement time gate and the pulsing is made. This is the case in the European Community supported research project MUSE. The solution to the Feynman-alpha formula was obtained for such a case through complex function techniques in an analytical form by Laplace transform and residue calculus. The final expression is a smoothly regular function with a simple periodic modulation. It consists of a Feynman-curve corresponding to a stationary source, plus an infinite sum of periodic sine functions squared. The series converges as 1/n 6 with the summation index n, thus in practice two or three terms are sufficient for a high accuracy quantitative result. This few-term representation amounts to a compact closed form analysis solution. Such a solution is well suitable for use in the determination of the subcritical reactivity from measurements, in contrast to the case of deterministic pulsing (measurement start synchronized with pulsing), where no simple solution is available, and where no explicit relationship between the continuous and pulsed forms of the Feynman-alpha exists.

Determination of PWR control rod position by core physics and neural network methods

A method is described by which the axial position of a control rod can be determined. The method is based on the influence of a partially inserted control rod on the axial flux profile. By measuring this flux profile, the control rod position can be in principle unfolded. One problem is however that the relationship between rod position and flux profile is rather implicit and cannot be explicitly inverted. Thus, it is suggested here to use neural network techniques to unfold the rod position from the measured flux profile. For training of the network, a large number of flux profiles are needed, corresponding to various known rod positions. These data can be generated by advanced core calculational codes. In this study, the Studsvik core master system SIMULATE was used. The method was tested with good results on both fully simulated data as well as on a measurement taken at the Swedish pressurized water reactor Ringhals 4.