Neutron Density Fluctuations Research Articles

Giant Dipole Multi-Resonances Excited by High-Frequency Laser Pulses

The worldwide advent of new laser facilities makes possible the investigation of the nuclear response to a very strong electromagnetic field. In this paper, we inquire on the excitation of one of the most conspicuous collective excitations, the giant dipole resonance, within the hydrodynamical model for a proton-neutron fluid mixture placed in a Skyrme mean-field and interacting with an external ultra-strong electromagnetic field. The variables of this approach are: proton and neutron displacement (velocity) fields, density fluctuations, and fluctuations of the electric field due to the coupling of the laser electromagnetic field to the dynamical distortions of the baryonic system (electro-magneto-hydrodynamical effect). We point out the occurrence of a multiresonance structure of the absorption cross-section.

Light-nuclei production and search for the QCD critical point

We discuss the potential of light-nuclei measurements in heavy-ion collisions at intermediate energies for the search of the hypothetical QCD critical end-point. A previous proposal based on neutron density fluctuations has brought appealing experimental evidences of a maximum in the ratio of the number of tritons times protons, divided over deuterons square, mathcal{O}_{tpd}. However these results are difficult to reconcile with the state-of-the-art statistical thermal model predictions. Based on the idea that the QCD critical point can lead to a substantial attraction among nucleons, we propose new light-nuclei multiplicity ratios involving ^4He in which the maximum would be more noticeable. We argue that the experimental extraction is feasible by presenting these ratios formed from actual measurements of total and differential yields at low and high collision energies from FOPI and ALICE experiments, respectively. We also illustrate the possible behavior of these ratios at intermediate energies applying a semiclassical method based on flucton paths using the preliminary NA49 and STAR data for mathcal{O}_{tpd} as input.

Light nuclei production in Au + Au collisions at [formula omitted] = 7.7 - 80 GeV from UrQMD model

Light nuclei production in relativistic 197Au + 197Au collisions from 7.7 to 80 GeV is investigated within the Ultra-relativistic-Quantum-Molecular-Dynamics model (UrQMD) with a naive coalescence approach. The results of the production of light nuclei at midrapidity can essentially match up the experimental data and a slight enhancement of combined ratio of NpNt/Nd2 where Np,Nd and Nt represent respectively the yields of proton, deuteron and triton, which is sensitive to the neutron density fluctuations, occurs around 20 GeV. However, this enhanced NpNt/Nd2 ratio should not be over-understood considering that the present UrQMD model is a cascade version without equation of state (EoS), i.e. there is an absence of critical end point mechanism. Furthermore, within different rapidity regions, the kinetic temperatures of different light nuclei are extracted by the Blast-wave model analysis and ratios among different light nuclei are also discussed.

Light nuclei production in Au+Au collisions at [formula omitted] = 5–200 GeV from JAM model

Light nuclei production is sensitive to the baryon density fluctuations and can be used to probe the QCD phase transition in relativistic heavy-ion collisions. In this work, we studied the production of proton, deuteron, triton in central Au+Au collisions at sNN = 5, 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV from a transport model (JAM). Based on the coalescence production of light nuclei, we calculated the energy dependence of rapidity density dN/dy and particle ratios (d/p, t/p, and t/d). More importantly, the yield ratio Nt×Np/Nd2, which is sensitive to the neutron density fluctuations, shows a flat energy dependence and cannot describe the non-monotonic trend observed by the STAR experiment. Based on the nucleon coalescence, this work can provide constraint and reference to search for the QCD critical point and/or first order phase transition with light nuclei production in future heavy-ion collision experiments.

Probing QCD critical fluctuations from intermittency analysis in relativistic heavy-ion collisions

It is shown that intermittency, a self-similar correlation with respect to the size of the phase space volume, is sensitive to critical density fluctuations of baryon numbers in a system belonging to the three-dimensional (3D) Ising universality class. The relation between intermittency index and relative baryon density fluctuation is obtained. We thus suggest that measuring the intermittency in relativistic heavy-ion collisions could be used as a good probe of density fluctuations associated with the QCD critical phenomena. From recent preliminary results on neutron density fluctuations in central Au + Au collisions at sNN=7.7,11.5,19.6,27,39,62.4 and 200 GeV at RHIC/STAR, the collision energy dependence of intermittency index is extracted and shows a non-monotonic behavior with a peak at around 20 - 27 GeV, indicating that the strength of intermittency becomes the largest in this energy region. The transport UrQMD model without implementing critical physics cannot describe the observed behavior.

00/01345 Neutron density fluctuations due to randomly distributed sources in finite media

00/01345 Neutron density fluctuations due to randomly distributed sources in finite media

Neutron density fluctuations due to randomly distributed sources in finite media

We formulate a theory which describes the effect on the neutron flux of sources in the form of lumps randomly distributed in a finite medium. One-speed diffusion theory is used, but the method can readily be extended to energy-dependent transport theory. The mean flux, the covariance and a new statistical indicator, the mean flux difference between regions, are calculated for an infinite and semi-infinite medium. Numerical results are obtained using Markov and Gaussian models for the random geometry of the lumps. We conclude that the statistical anisotropy of the medium can play a significant role and that, even though we may be considering what is ostensibly a one-dimensional problem in the x-direction, it is necessary to incorporate the medium properties in the other two directions via the correlation lengths λ y and λ z . We also note that there can be marked differences in the average fluxes in the various source regions which can deviate considerably from the conventional average flux. These results may have practical implications in the design of radioactive waste drums in which sources of neutrons (or gamma rays) are encased randomly in a background matrix. Conventional averaging may lead to a significant underestimate of the surface flux and current. The theory neglects the associated random material properties but should be a good approximation if the volume fraction of the source material is small. In the Appendix, we develop a random geometry model for the source lumps and derive the associated covariance function.

Response function of hot asymmetric nuclear matter

An approximated expression for the response function of hot asymmetric nuclear matter to small external perturbations was calculated. A general expression for the four channels (scalar, isovector, spin and spin-isovector) was obtained and the results for the isovector channel are presented in this letter. Two possible prescriptions for the neutron and proton density fluctuations are considered leading to different results. In the case of a realistic Skyrme-type force, SGII, for an asymmetry coefficient corresponding to that of the lead nucleus, a damped zero sound was found at zero temperature for small momentum transfer in the case of the first (second) prescription. For a higher asymmetry coefficient the mode becomes either more or less collective, depending on the ansatz for the density fluctuations. Although both prescriptions yield strength functions which satisfy the energy-weighted sum rule sufficiently well, it is argued that the prescription leading to a more collective mode as the asymmetry increases has a sounder physical meaning. As temperature increases collectivity weakens making the zero sound disappear whenever it occurs.

Analysis of non-stationary fluctuations in a nuclear power reactor with temperature feedback

We analyse the behaviour of the neutron density and temperature fluctuations of a non-linear power reactor model during the transient regime. The equations for both fluctuations are derived by applying the system-size expansion method to the master equation which models the system. The behaviour of the fluctuations, assuming a temperature feedback effect, is analysed.

Neutron Density Fluctuations in Point Reactor Systems with Dichotomic Reactivity Noise

The exactly solvable stochastic point reactor model systems are analyzed through the stochastic Liouville equation. Three kinds of model systems are treated: (1) linear system without delayed neutrons, (2) linear system with one-group of delayed neutrons, and (3) nonlinear system with direct power feedback. The exact expressions for the fluctuations of neutron density, such as the moments, autocorrelation function and power spectral density, are derived in the case where the colored reactivity noise is described by the dichotomic, or two state, Markov process with arbitrary correlation time and intensity, and the effects of the finite correlation time and intensity of the noise on the neutron density fluctuations are investigated. The influence of presence of delayed neutrons and the effect of nonlinearity of system on the neutron density fluctuations are also elucidated. When the reactivity correlation time is very short, the correlation time has almost no effect on the power spectral density, and the re...

Neutron density fluctuations in point reactor systems with dichotomic reactivity noise.

The exactly solvable stochastic point reactor model systems are analyzed through the stochastic Liouville equation. Three kinds of model systems are treated: (1) linear system without delayed neutrons, (2) linear system with one-group of delayed neutrons, and (3) nonlinear system with direct power feedback. The exact expressions for the fluctuations of neutron density, such as the moments, autocorrelation function and power spectral density, are derived in the case where the colored reactivity noise is described by the dichotomic, or two state, Markov process with arbitrary correlation time and intensity, and the effects of the finite correlation time and intensity of the noise on the neutron density fluctuations are investigated. The influence of presence of delayed neutrons and the effect of nonlinearity of system on the neutron density fluctuations are also elucidated. When the reactivity correlation time is very short, the correlation time has almost no effect on the power spectral density, and the relative fluctuation of neutron density in the stationary state is not affected very much by the presence of delayed neutrons and also by the nonlinearity of system. On the other hand, if the reactivity correlation time is very long, the effect of the reactivity noise on the power spectral density appears at very low frequency, and the presence of delayed neutrons has an effect of reducing the neutron density fluctuations.

A non-linear problem in neutronic fluctuations

The behaviour of the fluctuations in a multiplying medium has been studied using a simple birth and death process. The investigation differs from the classical approach to this problem in that it includes the effects of burnup, i.e. removal, of the absorbing particles. Thus we consider a mixture of two species one of which feeds upon the other. However, species ‘1’ is renewable by births, whereas species ‘2’ is not. We associate species ‘1’ with neutrons and species ‘2’ with the fissile isotope. A probability-balance equation is formed and the associated equation for the probability generating function is derived. From this equation we obtain values for the mean and variance by a cumulant expansion technique. Results show that the burnup effect leads to non-linear equations for the moments and that these in turn show a significant deviation from the conventional linear solutions for high supercriticality. The variance of the neutron density fluctuations is shown to tend to a constant value as time increases. The rate at which this occurs might be detectable experimentally and provides further evidence of the non-physical nature of the unboundedness of the classical linear variance with time.

Stochastic Analysis of Nonlinear Point Reactor Systems with Colored Multiplicative Noise

This paper presents a master equation formulation of the fluctuations of neutron density in a nonlinear power reactor model system perturbed by colored multiplicative noise using the Van Kampen's master equation. The reactivity and power reactivity feedback coefficient are assumed to be stationary stochastic processes with short but finite correlation times. Some statistical characteristics of the neutron density fluctuations, such as moment equations, stationary distribution and stationary moments, are derived and compared with the results calculated for the system with Gaussian white parametric noise. It is shown that in the limit of Gaussian white noise our results converge to those obtained by using the Stratonovich calculus. Some remarks on the divergence between the Stratonovich calculus and the Ito calculus are also given.

Stochastic analysis of nonlinear point reactor systems with colored multiplicative noise.

This paper presents a master equation formulation of the fluctuations of neutron density in a nonlinear power reactor model system perturbed by colored multiplicative noise using the Van Kampen's master equation. The reactivity and power reactivity feedback coefficient are assumed to be stationary stochastic processes with short but finite correlation times. Some statistical characteristics of the neutron density fluctuations, such as moment equations, stationary distribution and stationary moments, are derived and compared with the results calculated for the system with Gaussian white parametric noise. It is shown that in the limit of Gaussian white noise our results converge to those obtained by using the Stratonovich calculus. Some remarks on the divergence between the Stratonovich calculus and the Ito calculus are also given.

Exact Statistical Analysis of Nonlinear Dynamic Power Reactor Models by the Fokker-Planck Method. Part II: Reactor with On-Off Control

The paper deals with the exact stochastic analysis of the low-frequency neutron density fluctuations in an on-off controlled nuclear power reactor without delayed neutrons and perturbed by Gaussian white reactivity noise. The stochastic process, being Markovian, is completely characterized by its first-order probability density function (pdf) and the transition pdf. The first-order pdf is the normalized solution to the time-independent Fokker--Planck equation (FPE). Using this pdf, a general expression for the moments is obtained. The conditions for stochastic stability in probability, in the mean, and in the mean-square are derived. The time-dependent FPE is solved using the Laplace transform technique, which results in four distinct expressions for the transition pdf, according to the relative magnitude of initial and final reactor power with respect to the regulator level. After Laplace inversion, a physical interpretation of the controller's effect on the stochastic process becomes possible. Finally, making use of the obtained pdf's, the spectral density of the reactor power fluctuations is calculated.

Neutron fluctuations induced by absorber vibrations: the QMC reactor experiment—I

The dependence of rod vibration induced, neutron density fluctuations on the static neutron gradients was investigated experimentally at the QMC research reactor. By appropriate fuel loading arrangements the rod was made to vibrate (a) within a flat flux and (b) a flux gradient. The neutron density was fluctuating with the frequency of the vibrating absorber only when the static flux gradient in the vicinity of the absorber was not zero. The double frequency effect was not observed.

Experimental Studies of Core Flow Fluctuations as Noise Source in BWR

Among various fluctuating quantities in a BWR plant the present authors dealt with core channel flow fluctuations. Using the instrumented fuel assemblies (IFA) installed in the Japan Power Demonstration Reactor II core, fluctuations of the inlet and outlet channel flow rates were observed at power operation condition. Correlation analyses of the fluctuating signals revealed the followings: (a) the flow fluctuations in any IFA channel showed almost uncorrelated cross-correlation with other IFA channel flow, (b) cross-correlation between the neutron density fluctuations and each IFA channel flow fluctuations also showed little correlation, and (c) the forced circulation pump flow showed unexpectedly weak correlation with the core channel flow. To attempt to explain the above facts, some hypotheses are introduced: (1) Each channel will be actuated by an independent weak noise source. (2) The fluctuating flow of a channel will interfere with each other, then the interferences will spread to the whole core and...

A stochastically perturbed nonlinear point reactor model

We present an exact analysis of the fluctuations of neutron density in a stochastically perturbed nonlinear point reactor model in the absence of delayed neutrons. The reactivity and feedback coefficients are assumed to have white noise Gaussian component. The time development of probability distribution is obtained from the Fokker-Planck equation. It is found that for small density of neutron population the stationary probability distribution is more sensitive to the random change in the reactivity than in the feedback coefficient, whereas for large neutron density the probability distribution is more sensitive to the random change in the feedback coefficient than in the reactivity.

Exact Statistical Analysis of Nonlinear Dynamic Nuclear-Power Reactor Models by the Fokker-Planck Method—Part I: Reactor with Direct Power Feedback

This paper presents an exact and complete statistical analysis of the neutron density fluctuations resulting from Gaussian white reactivity noise in a point reactor model with proportional power feedback, but without delayed neutrons. The analysis includes the multiplicative effect of neutron density and reactivity variations.An exact solution of the time-independent Fokker-Planck equation is found, resulting in a gamma density function for the stationary first-order probability density of the power fluctuations.The time-dependent Fokker-Planck equation is solved for the Laplace transformed function, which can be written in terms of confluent hypergeometric functions. The subsequent inversion yields the transition probability density function.The most common first- and second-order statistical characteristics, such as moments, autocovariance function, and power spectral density, are calculated and compared to the results of a linearized analysis.

Reactivity and neutron density noise excited by random rod vibration

The reactivity and neutron density noise induced by rod vibrations is studied for the following cases: (a) thin absorbing plate vibrating in a slab reactor, (b) rod vibrating in a cylindrical reactor. The following models are used for the neutron density fluctuations: (a) the point reactor model, (b) the prompt spread approximation for the space dependence at ω < β Λ and (c) the homogeneous approximation for the space dependence at ω > β Λ . It is found that when the rod-vibration PSD has a peak at ω 1, the reactivity and the neutron density PSD have peaks at ω 1 and 2 ω 1. The power of the peak at ω 1 depends on the macroscopic neutron flux gradient and that at 2 ω 1 on the flux depression gradient at the position of the rod; they also depend on the direction of the rod vibration. The results of the model are found to be consistent with experimental evidence.