Neutron Diffusion Length Research Articles

A new porosity evaluation parameter based on neutron porosity logging

The neutron porosity logging is one of the main methods for measuring the formation porosity. However, for the formation with complex mineral compositions and fluid properties, it is difficult to calculate the formation porosity accurately by the neutron porosity logging. In this paper, the relationship between the neutron slowing-down length and the neutron diffusion length and the formation hydrogen index is studied. Based on the thermal-neutron flux formula, a new parameter, apparent formation hydrogen index, is constructed by the neutron counting ratio and the formation density and the capture cross section. The apparent formation hydrogen index is close to the formation hydrogen index and is not affected by the excavation effect. The response characteristic of the apparent formation hydrogen index is more consistent with the volume physical model. The porosity calculated by the new parameter is closer to the formation porosity, especially in the gas-bearing formation.

VALIDATION OF THERMAL SCATTERING LAWS FOR LIGHT WATER AT ELEVATED TEMPERATURES WITH DIFFUSION EXPERIMENTS

Light water is the most important neutron moderator in many reactor applications. Thermal neutron scattering kernels for H bound in H2O are represented by ENDF-format thermal scattering laws (TSLs) evaluated at discrete temperatures T. Nuclear data evaluations are conventionally validated utilizing a combination of critical benchmarks and experimental cross section data. Existing public critical benchmarks may be inadequate for testing water TSLs over the full range of T of interest in reactor applications, and experimental thermal scattering cross section data for water is sparse at elevated T. In this work, MC21 is used to simulate the decay of the equilibrium thermal neutron flux in light-water spheres of several radii. The fundamental-mode time eigenvalue α is calculated at 22 °C and 227 °C (at saturation pressure) for each sphere using three different H-H2O TSLs. Fitting α to a polynomial function of geometric buckling allows calculation of the thermal neutron diffusion length L. Extrapolation lengths are treated as a function of the transport mean free path and geometry. Experimental L data from 25 publications at 49 temperatures (from 10 °C to 295 °C), computed by several different time-dependent and space-dependent decay methods, is used to develop an empirical fit of L vs. T. The MC21-calculated L for the TSLs tested are within ±1% of the predicted values at 22 °C and 227 °C. This validation approach, which may be repeated at arbitrary T, constitutes an integral benchmark specific to and characterizing the detailed physics of the thermal scattering kernel applied.

Constraining density fluctuations with big bang nucleosynthesis in the era of precision cosmology

We reexamine big bang nucleosynthesis with large-scale baryon density inhomogeneities when the length scale of the density fluctuations exceeds the neutron diffusion length ($\sim 10^7-10^8$ cm at BBN), and the amplitude of the fluctuations is sufficiently small to prevent gravitational collapse. In this limit, the final light element abundances can be determined by simply mixing the abundances from regions with different baryon/photon ratios without interactions. We examine gaussian, lognormal, and gamma distributions for the baryon/photon ratio, $\eta $. We find that the deuterium and lithium-7 abundances increase with the RMS fluctuation in $\eta $, while the effect on helium-4 is much smaller. We show that these increases in the deuterium and lithium-7 abundances are a consequence of Jensen's inequality, and we derive analytic approximations for these abundances in the limit of small RMS fluctuations. Observational upper limits on the primordial deuterium abundance constrain the RMS fluctuation in $\eta $ to be less than $17\%$ of the mean value of $\eta $. This provides us with a new limit on the graininess of the early universe.

Leakage correction in group-constant generation for pebble-bed HTGRs

Neutronics design of commercial reactors currently utilizes a procedure linking lattice physics and core physics calculations together, where broad-group constants are generated by fine-group lattice calculations and are then used by downstream whole-core diffusion calculations. Among this procedure, the leakage effect in group-constant generation contributes a non-negligible source of errors. In pebble-bed high temperature gas-cooled reactors (HTGRs), this effect becomes even important because the neutron diffusion length is relatively large compared with the size of pebble lattice. Traditional neutronics analysis codes for pebble-bed HTGRs need repeatedly re-call lattice calculations with the leakage information obtained from core diffusion calculations. In this paper, existing methods for leakage correction are reviewed, and a new method is proposed to correct broad-group constants by using buckled fine-group spectrum. The new method eliminates the need of online coupling between lattice physics and core physics calculations, and thus makes it possible to use the tabular group-constant library as is done in light water reactors (LWRs). Numerical tests show that the proposed method are promising for leakage correction in pebble-bed HTGR analyses.

New findings on neutron noise propagation properties in void containing water using neutron noise transport calculations

This paper presents new findings in predicting the void fraction or void transit time of void-containing water flow using the results of multi-group neutron noise transport calculations. The neutron noise transport equation in the frequency domain is solved with a recently developed Monte Carlo method that uses complex-valued weights. In the calculations, the noise of thermal neutrons that penetrates a two-dimensional channel of void-containing water is obtained to predict the void properties. The thermal neutron noise is influenced by the slow down from the neutron noise in the higher energy range and by the transport of the thermal neutron noise. This influence becomes more notable in a lower void fraction or in a wider water channel. If the thickness of the channel is small enough, the void transit time can be accurately predicted using the CPSD between detector pairs aligned in the flow direction. In a wider channel, an anomalous void transit time would be obtained from the CPSD. The results of the multi-group calculation show that the APSD in a lower void fraction deviates from the Lorentzian form that holds in the one-energy group approximation. This deviation is caused by the higher energy neutron noise, whose frequency characteristics are different from the thermal neutron noise. Assuming that the one-energy group approximation is applicable, the relationship between the break frequency of the APSD and the neutron diffusion length or neutron age is clearly observed, which suggests that the measurement of the APSD could lead to the prediction of void properties.

Implementation of a tree algorithm in MCNP code for nuclear well logging applications

The goal of this paper is to develop some modeling capabilities that are missing in the current MCNP code. Those missing capabilities can greatly help for some certain nuclear tools designs, such as a nuclear lithology/mineralogy spectroscopy tool. The new capabilities to be developed in this paper include the following: zone tally, neutron interaction tally, gamma rays index tally and enhanced pulse-height tally. The patched MCNP code also can be used to compute neutron slowing-down length and thermal neutron diffusion length.

Problems of homogeneous irradiation of Si ingots more than 200 mm in diameter under neutron doping

The problem of homogeneous irradiation of Si ingots of large diameter (i.e., comparable with the thermal neutron diffusion length in silicon—20 cm) by thermal neutrons is considered. The effect of neutron absorption on the irradiation homogeneity is discussed. It is established for some usual cases of neutron doping that the neutron distribution in the irradiation zone affects the irradiation homogeneity. The results obtained can be useful for choosing and designing the irradiation zone for neutron doping of silicon.

Experimental study of effect of void volume fraction on neutron diffusion parameters in water

The dependence of the diffusion parameters including slowing down area, neutron diffusion length and migration length on the voided volume fraction in water has been studied experimentally. For this purpose, the PIEAS Neutron Transport Facility (PNTF) comprised of a 10 Ci Am–Be neutron source and a water filled aluminum tank with Perspex voided tubes has been designed and fabricated. A BF 3 detector was used for the neutron counting. The slowing down area was determined at the cadmium cutoff level. The diffusion parameters were determined first in the absence of voids. The experimentally measured values of the slowing down area, the diffusion length and the migration length have been found in good agreement with the corresponding values determined by other workers. By varying void volume fraction from 0% to 7.5%, the experimental measurements show a monotonic increase in the slowing down area from 58.71±2.6 to 71.28±3.2 cm 2, in the diffusion length from 2.95±0.13 to 3.11±0.13 cm and in the migration length from 8.21±0.165 to 8.99±0.169 cm. Our measurements show that the diffusion parameters exhibit a quadratic dependence on the void volume fraction.

Primordial Magnetic Fields, Anomalous Matter-Antimatter Fluctuations, and Big Bang Nucleosynthesis

We show that the presence of primordial stochastic (hypercharge) magnetic fields before the electroweak (EW) phase transition induces isocurvature fluctuations (baryon number inhomogeneities). Depending on the details of the magnetic field spectrum and on the particle physics parameters (such as the strength of the EW phase transition and electron Yukawa couplings) these fluctuations may survive until the Big Bang nucleosynthesis (BBN). Their lenghtscale may exceed the neutron diffusion length at that time, while their magnitude can be so large that sizable antimatter domains are present. This provides the possibility of a new type of initial conditions for non-homogeneous BBN or, from a more conservative point of view, stringent bounds on primordial magnetic fields.

Delayed neutron effectiveness in a fluidized bed fission reactor

In a fluidized bed of fuel particles suspended by gas a considerable spatial redistribution of delayed neutron precursors occurs due to mixing processes. On the basis of a simple reactor model the reactivity effect of precursor redistribution is analyzed. This analysis is performed for both the limit case of ideal mixing and the general case of finite precursor diffusion length. It is shown that k-infinity and the ratio between precursor diffusion length and neutron diffusion length are the relevant parameters determining the reactivity effect and the effectiveness of the delayed neutrons.

SNUPAR-a nuclear parameter code for nuclear geophysics applications

A computer code, SNUPAR, has been developed to calculate nuclear measurement parameters for mixtures of elements found in nuclear geophysics applications. Parameters calculated are the neutron slowing-down length, the thermal neutron diffusion length, the thermal neutron capture cross-section, the formation density, the electron density index, the volumetric photoelectric absorption coefficient, and the effective atomic number. The code has been extensively benchmarked with published laboratory measurements and with results from the Monte Carlo Neutron Photon code. Special algorithms have been developed to handle variations in salinity of formation water. The first application has been the successful development of a modified migration-length model to describe the thermal neutron response to Schlumberger's compensated neutron log. Some examples of applications of the SNUPAR code for determining reservoir gas saturation, carbon-dioxide saturation in an enhanced oil recovery project, and the effects of mineral mixtures on neutron log response are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effect of235U Concentration on Fast Neutron Space and Time Eigenvalues and Eigenfunctions in Uranium

The results of a detailed study of a fast neutron diffusion length and pulsed problem in depleted and enriched subcritical uranium assemblies (0.2 to 4% /sup 235/U) are reported. The multigroup space- and time-dependent equations are solved using the eigenfunction expansion method. The effect of /sup 235/U concentration on space (diffusion length problem) and time (pulsed problem) eigenvalues and eigenfunctions, particularly on the ''discrete'' eigenvalue and eigenfunction, is discussed. The approach to equilibrium (both in space and in time) of fast neutrons changes with changing /sup 235/U concentration.

Calculations of the Spectra of Fast Neutrons in Iron Spheres Using the Vitamin-C File

Steady-state space-dependent fast neutron angular and scalar spectra and total flux in various iron spheres have been calculated using the one-dimensional discrete ordinate transport code ANISN and Vitamin-C nuclear data file. The results have been used to study the question of establishment of equilibrium and of an associated fast neutron diffusion length in iron. We find that true equilibrium conditions are not established even inside a 3-m-radius iron sphere. However, from the study of spatial decay of total flux, one can obtain the value of the fast neutron diffusion length in iron, which in the present case is found to be 24.4 cm.

On the possibility of nucleosynthesis in any matter-antimatter symmetric cosmology

In any matter-antimatter symmetric cosmology the primeval nucleosynthesis imposes a typical size of a region of matter (antimatter) much larger than the diffusion length of neutrons. Observational results on the abundances of cosmic deuterium and helium are used to evaluate how large it has to be.

A study of neutron diffusion lengths in heterogeneous, non-multiplying plate assemblies

A study of the diffusion length of neutrons in an infinite lattice of alternate slabs of two different materials in the direction parallel to the slabs has been carried out on the basis of integral transport theory. In the one-velocity approximation we obtain, numerically, curves for aluminium water lattices from which one can observe the possibility of the existence or non-existence of a discrete decay constant ν for a given configuration. In the energy dependent case, two of the configurations studied by Palmedo and Conant have been chosen, and it has been shown that neither of them possesses a discrete decay constant, which is consistent with their experimental findings. The asymptotic spectra in the aluminium and water regions for certain configurations have also been discussed. Calculations are also made for the lead-water systems studied experimentally by Mukhin et al. and satisfactory agreement obtained.

The Experimental Determination of the Thermal Neutron Diffusion Length in Graphite

The experimental determination of the thermal neutron diffusion length in gra- phite was carried out by measuring the distribution of neutron fiux along the x, y, and z axis. The neutron flux distribution have been measured with a BF,3 counter using a Ra - Be neutron source. For the calculation of the results the least sguares method was chosen in order to obtain the most probable value of the diffusîon length. The value of the diffusion length was found to be L = 58 i 2 cm for the Diffusi- on Stack and L — 53,46 cm (average) for the Exponential Stack.

Rethermalization of neutrons in graphitebismuth systems

Using plane geometry, with first block of media of finite thickness and the second block extending to infinity, we calculated the steady state neutron spectra at different space points in fourteen different systems of graphite-bismuth which involved medium discontinuity at 500°K, 300°K and 100°K for six cases, temperature discontinuity in bismuth for four cases and medium and temperature discontinuties together at the same time for four cases. The space variation of effective neutron temperature has been studied from the calculated spectra. Starting from an equilibrium distribution in the first medium (of finite thickness) we find that the equilibrium is disturbed as the interface is approached and in the second medium it is only at some distance from the interface that equilibrium is again re-established. Diffusion length of neutrons in graphite and bismuth at 500°K, 300°K and 100°K have also been reported.

A Note on the Existence of a Minimum Value for the Neutron Diffusion Length

A minimum in the value of the neutron diffusion length is shown to exist as variations in the anisotropy change the ratio of forward scattered neutrons to backward scattered neutrons.

Disappearance of Neutron Diffusion Length of Beryllium and Graphite according to Temperature

Disappearance of Neutron Diffusion Length of Beryllium and Graphite according to Temperature

Disappearance of Neutron Diffusion Length of Beryllium and Graphite according to Temperature

Disappearance of Neutron Diffusion Length of Beryllium and Graphite according to Temperature