Space and energy dependent theoretical formula for the third order neutron correlation technique

We have studied measurement techniques of subcriticality by using the neutron correlation techniques. Among various techniques, we have paid attention to the third order neutron correlation technique, which was proposed by Furuhashi originally and utilizes the third order fluctuations of neutron counts. By using this technique, we can obtain the absolute value of subcriticality with the aid of factorial moments of fission neutron ν and external source neutron q, without prior knowledge of the prompt neutron decay constant at a reference state. However, in order to apply the third order neutron correlation technique to actual experiments, we must consider the spatial and neutron energy effects in this technique. For this purpose, we derived more generalized theoretical formulas of the third order neutron correlation technique that took account of the spatial and neutron energy effects by virtue of the α-eigenfunction expansion. Making use of the newly derived formulas, we propose the practical formulas and the experimental procedures based on the fundamental mode approximation.     

Subcriticality Measurement by Neutron Source Multiplication Method with a Fundamental Mode Extraction

A new neutron multiplication method has been proposed for an accurate measurement of subcriticality. The proposed method consists of two correction processes for (1) extraction of the fundamental mode from measuring data of a neutron detector that contains higher modes as well as the fundamental mode feeding from an external neutron source and (2) spatial corrections for perturbations induced by a reactivity addition in the distributions of the fundamental mode and a neutron importance field. Feasibility of the proposed method has been verified from a numerical study, although under some limitations such that the neutron multiplying system to be analyzed is small-sized and a reactivity change takes place homogeneously in a fuel loaded region. With extraction of the fundamental mode and the spatial corrections, the subcriticality can be estimated accurately even with measuring data highly contaminated with higher modes due to a detector position near to an external point neutron source. For a future application to measurement of control rod bank worth of a nuclear power plant from measuring data during a reactor physical testing, some useful guidelines have been obtained.     

脉冲中子源法测量铅基零功率反应堆Venus-Ⅱ次临界度

本文利用脉冲中子源法测量了铅基零功率反应堆Venus-Ⅱ在4种燃料棒装载情况下的次临界度,简要介绍了脉冲中子源法测量次临界度的原理、测量系统及实验结果等,通过面积比法分析了各探测器的计数率时间谱,确定了系统次临界度。测量结果表明,当系统有效增殖因数在0.94附近时,不同位置处的探测器测量结果之间呈明显差异。基于MCNP理论模拟计算,分别用空间修正因子和普适的微扰法对面积比测量结果进行必要修正,消除了空间效应对实验结果的影响。在系统有效增殖因数约0.94时,经修正的面积比法能精确给出系统的次临界度。本实验研究为ADS嬗变系统的次临界度精确测量提供了一种有效方法。     

The spectral Green’s function linear-nodal method for one-speed X, Y-geometry discrete ordinates deep penetration problems

A new spectral nodal method is developed for the solution of one-speed discrete ordinates (S_N) problems with isotropic scattering in X, Y geometry. In this method, the spectral Green’s function (SGF) scheme, originally developed for solving S_N problems in slab-geometry with no spatial truncation error, is generalized to solve the one-dimensional transverse-integrated S_N linear-nodal equations with linear polynomial approximation for the transverse leakage terms. The resulting SGF-linear-nodal (SGF-LN) equations are solved with the full-node inversion (FNI) iterative scheme, which uses the best available estimates for the node-entering quantities to evaluate the node angular quantities in all the exiting directions as the equations are swept across the system. We give numerical results that illustrate the accuracy of the SGF-LN method for coarse-mesh calculations.     

涂硼电离室组合快中子探测器研制及其响应函数

研制了涂硼电离室组合快中子探测器。用外径分别为55、80、130、220、285 mm的5个高密度聚乙烯圆柱体作为快中子的慢化体包裹40 mm×200 mm的涂硼电离室,组合成一种可测量从热中子到十几MeV快中子的圆柱型Bonner探测器。借助Geant4蒙特卡罗方法模拟计算,给出了这种结构Bonner探测器探测系统的响应函数。将圆柱型Bonner探测器放置在标准中子源辐射场中进行了实验测量。在实际辐射场中,高密度聚乙烯圆柱体外径为220 mm时,圆柱型Bonner探测器的灵敏度达8.702×10^-15 A•cm²•s。同时对实验测量值与理论模拟结果进行了比较分析。结果表明,模拟结果与实验值在数据读取误差范围内吻合。     

Measurement of large negative reactivity of an accelerator-driven system in the Kyoto University Critical Assembly

Large negative reactivity of a subcritical system driven by a pulsed 14 MeV neutron source has been measured in the Kyoto University Critical Assembly. The subcriticality of the accelerator-driven system (ADS) ranged in effective multiplication factor roughly from 0.98 to 0.92, which corresponded to an operational range of an actual ADS proposed by Japan Atomic Energy Agency. As the measurement technique, pulsed neutron method, power spectral analysis for pulsed neutron source, accelerator-beam trip method were employed. From neutron count decay data obtained by the pulsed neutron experiment, not only the prompt-neutron decay constant of fundamental mode but also a higher spatial mode could be derived. The subcriticality was also determined from the fundamental decay constant. The measured cross-power spectral density consisted of a familiar correlated reactor-noise component and many uncorrelated delta-function-like peaks at the integral multiple of pulse repetition frequency. The fundamental prompt-neutron decay constant, i.e., the subcriticality determined from the latter uncorrelated peaks was consistent with that obtained by the above pulsed neutron experiment. However, the magnitude of the former correlated component was reduced with an increase in the subcriticality and eventually this component became almost white at deeply subcritical state ranging in the multiplication factor under 0.95. Consequently, the determination of the decay constant from the correlated component was impossible under such a subcritical state. As data analysis method for the beam trip experiment, both the conventional integral count method and the least-squares inverse kinetics method (LSIKM) were employed. The LSIKM analysis led to the consistent subcriticality with that obtained by the pulsed neutron experiment, while the integral count method significantly underestimated the subcriticality. This underestimation originated from a residual background count, which was maintained after the beam trip. The LSIKM was mostly not influenced by such a slight count rate.     

Generalization of the eigenvalue problem of the one-speed neutron transport equation in two-region

Previous calculations on the eigenvalue spectrum of the one-speed transport equation for two-region slabs and spheres are generalized. The criticality problem is investigated in c₁ c₂, where −∞ ≤ c₁ ≤ ∞ and −∞ ≤ c₂ ≤ ∞ are the criticality factors in the respective regions. The eigenvalue spectrum consists of non-intersecting, continuous lines on the (c₁, c₂) plane. The structure of the c-map (the aggregate of such eigenvalue curves) is investigated. It is shown that at some discrete, finite values of c₁ > 1, c₂ diverges to −∞, and Φ₂ vanishes (and vice versa for c₁ and Φ₁ at certain c₂ values). Oscillating properties and completeness of the eigenfunction sets along different lines c₂ = ξc₁ on the c-map are discussed, and some theorems about completeness are proven rigorously for different values of ξ. Finally, some time eigenvalues are calculated and compared with the c-eigenvalues.     

14 MeV快中子照相准直屏蔽系统的设计与优化

基于强流氘氚中子源科学装置HINEG设计了一套快中子照相准直屏蔽系统。采用中子输运设计与安全评价软件系统SuperMC和ENDF/B-Ⅶ.0数据库计算了准直中子束的中子能谱及注量率、γ射线能谱及注量率、直射中子注量率与γ射线注量率比值（φ_d/φ_γ）、直射与散射中子注量率比值（φ_d/φ_s）、准直束中子注量率的不均匀度等特性参数,并采用MCNP5程序进行了对比验证。研究了准直屏蔽系统的内衬材料、尺寸等对特性参数的影响规律,并通过优化获取了最优设计方案。计算结果显示,在同等计算条件下,SuperMC计算结果与MCNP计算结果相对偏差小于1%,准直屏蔽系统的φ_d/φ_γ为50.1,φ_d/φ_s为5.7,在Φ30 cm视野范围内的中子注量率为4.80×10⁷ cm^-2•s^-1,其中直射中子注量率为4.09×10⁷ cm^-2•s^-1,中子注量率不均匀度为5.8%,满足快中子照相对准直束特性参数的要求。     

An empirical formula for L line X-ray production cross-section of elements from Ag to U for protons below 3.5 MeV

When computing element concentration from proton induced X-ray emission analysis, an important parameter is the X-ray production cross-section. There have been numerous experimental and theoretical works in this field. Nonetheless, although there is a simple analytical formula to compute K X-ray cross-sections, there is no such ones for the L lines. We present here analytical formulas for the cross-section of the three main X-ray lines L, L_β and L_γ based on experimental data. So far, nearly 3000 values of cross-sections for elements from Ag to U and proton energy ranging from 0.5 to 3.5 MeV have been collected from various references. This experimental data set has been fitted for each X-ray line with an exponential function depending on the proton energy and on the element atomic number. These fitted values have then been compared to the experimental data and with theoretical values obtained by the ECPSSR theory and Coster–Kronig fluorescence yields.     

Analysis of the desorption of clusters of intact amino acid valine molecules induced by energetic monoatomic and cluster ions

The experiments on the desorption of intact valine molecules and (nM + H)⁺ clusters are analyzed and a ln(Y/S_e) − 1/S_e scaling is found where Y, and S_e are the sputtering yield and the electronic stopping power, respectively. The scaling can be derived with the assumption of a thermal activation mechanism. In the plots the desorption is a uniform process without threshold value of S_e, having different activation energies U in various charge states. The desorption of (nM + H)⁺ clusters proceeds in n steps with varying Coulomb contributions. Irradiation with C₁₀ and C₆₀ ions leads to higher Y, however, the increment is reduced with the increase of S_e.     

On-line subcriticality measurement using a pulsed spallation neutron source

To investigate the applicability of the pulsed neutron source method using a pulsed spallation neutron source for an on-line subcriticality monitoring system of an accelerator-driven system, a subcritical experiment is conducted using the Kyoto University Critical Assembly in combination with the fixed-field alternating gradient accelerator. Reactivity values obtained from different traditional techniques, the area-ratio method and the α-fitting method, are discussed with respect to the applicability to on-line subcriticality monitoring. The results show that the area-ratio method robustly and accurately monitors subcriticality in shallow subcritical states with negative reactivity of up to a few dollars; however, this method faces problems with temporal fluctuations, spatial dispersion, and sensitivity to the proton-beam current with increasing depth of subcriticality. On the other hand, it is shown that the α-fitting method alleviates such problems in deep subcritical states. Moreover, a proposed fitting technique using the maximum-likelihood estimation method based on the Poisson distribution is robust enough to be applicable to on-line subcriticality monitoring for negative reactivity levels of up to roughly nine dollars.     

Characteristics of delayed neutrons: Systematics and correlation properties

Newly found features of delayed neutron characteristics are used to evaluate total delayed neutron yields, V_d and average half-lives, T, of delayed neutron precursors from fast neutron induced fission. On this basis different sets of time dependent parameters (Y_i, T_i) and V_d values obtained using the summation method are evaluated.     

Derivation of theoretical formula for the third order neutron correlation technique by using importance function

The third order neutron correlation technique is one of the subcriticality measurement techniques. This technique was originally proposed by Furuhashi and utilizes the second and third order neutron correlation factors Y(T) and X(T), which are evaluated from the variance and third order central moment of neutron counts detected during a counting gate width T, respectively. We can obtain the absolute value of subcriticality from the Y_∞ and X_∞, which are saturation values of Y(T) and X(T) when T goes to infinity. In the previous paper, we derived the generalized theoretical formulas of Y_∞ and X_∞ that took account of both the spatial and neutron energy effects. Its derivation was based on a heuristic method in which we consider the branching process of neutron family, and we utilized the α-eigenfunction expansion technique. Then, the previous formulas are expressed by multiple sums involving both the α-eigenfunctions and their adjoint functions. In this paper, we derive the new compact expressions of Y_∞ and X_∞ by using the importance functions related to the neutron detection process. Present derivation is based on the stochastic equation of neutron transport. New expressions have two advantages. We can clarify the physical meanings of Y_∞ and X_∞. And, without α-eigenfunction expansion, we can calculate Y_∞ and X_∞ directly by calculating the importance functions which satisfy the adjoint neutron transport equations. Moreover, we prove that new expressions of Y_∞ and X_∞ are identical with the previous ones, so that we can conclude that our previous derivation based on a heuristic method is correct.     

板状Bi样品泄漏中子和γ谱实验测量与模拟计算

通过飞行时间法,测量了氘氘脉冲中子与不同厚度209Bi样品作用后61°和119°方向的泄漏中子飞行时间谱和泄漏γ能谱,样品尺寸分别为30 cm×30 cm×5 cm、30 cm×30 cm×10 cm和30 cm×30 cm×15 cm。采用BC501A液体闪烁体探测器测量0.8～3.2 MeV能区的泄漏中子飞行时间谱,钾冰晶石探测器（CLYC）测量0.2～0.8 MeV的泄漏中子飞行时间谱和泄漏γ能谱。用MCNP-4C程序对泄漏中子飞行时间谱和泄漏γ能谱进行了模拟计算,²⁰⁹Bi的评价中子核数据分别采用了CENDL-3.1库、ENDF/B-Ⅷ.0库、JENDL-4.0库以及JEFF-3.3库中的数据,模拟结果分别与实验结果进行比较分析,研究结果表明,泄漏中子谱CENDL-3.1库的模拟结果在119°方向弹性峰位置有较严重的低估现象,JENDL-4.0库在1.5 MeV附近（第二非弹能区）有一定高估,而在低能区有明显低估;泄漏γ能谱JENDL-4.0库和JEFF-3.3库的模拟结果与实验结果偏差明显,而CENDL-3.1库符合较好。     

Measurement of the cross sections for the reactions Cr(n,2n)Cr, Zn(n,2n)Zn, Y(n,2n)Y and Zr(n,2n)Zr from 13.5 to 14.8 MeV

Cross section measurements for the reactions ⁵²Cr(n,2n)⁵¹Cr, ⁶⁶Zn(n,2n)⁶⁵Zn, ⁸⁹Y(n,2n)⁸⁸Y and ⁹⁶Zr(n,2n)⁹⁵Zr were carried out in the neutron energy range 13.47–14.79 MeV applying the activation technique. Neutrons were produced via the T(d,n)⁴He reaction, making use of the variation of neutron energy with the emission angle. The neutron fluences incident on the samples were determined relative to the well-evaluated cross section for the reaction ⁹³Nb(n,2n)^92mNb.

The induced γ-ray activities of the irradiated Zn, Zr and Y₂O₃ samples and their monitor foils were measured by means of a calibrated Ge(Li) γ-ray detector at the KFI, Debrecen. At the IRK, Vienna, relative γ-ray measurements using a high-purity Ge detector were combined with integral γ-ray counting by means of a NaI(TI) well-type detector on the Cr, Zn and Zr foils of highest activity and on some Nb monitor foils; integral γ-ray counting only was applied in the case of the Y₂O₃ samples. All necessary corrections were taken into account.

The results are compared to the corresponding results of cross section measurements published in the literature. The uncertainties obtained in this work are considerably smaller in most cases than the uncertainties given by other authors.     

Effects of Ag and Au ion implantation of lithium niobate

The optical effects of implantation of lithium niobate crystals with 100 keV Ag⁺ and 8 MeV Au³⁺ ions with fluences of 1 × 10¹⁷ ions/cm² have been investigated. Metal nanoparticle formation has been studied as a function of annealing temperature, and the resulting optical extinction curves have been simulated by the Mie theory in the small particle limit. Transmission electron microscopy (TEM) has provided direct evidence for the MNP sizes allowing comparison with the calculated results. A TEM study of an X-cut sample implanted with Ag⁺ ions show that the implanted region is partially amorphised. The differences in the temperature of Au colloid development in X- and Y-cut faces of the lithium niobate crystal are attributed to restoration of crystallinity as a result of annealing.     

Low energy nitrogen ion doping into GaAs using combined ion-beam and molecular-beam epitaxy method

Low energy nitrogen (N) ions were irradiated during the epitaxial growth of GaAs using combined ion beam and molecular beam epitaxy (CIBMBE) method as a function of N⁺ ion acceleration energy (E_a) and N⁺ ion beam current density (I_N). E_a was varied from 70 to 170 eV I_N from 900 pA/cm² to 75 nA/cm². GaAs growth rate was fixed to 1 μm/h. In 2 K photoluminescence (PL) spectra of the samples with I_N = 3 nA/cm² and E_a = 70–100 eV, two sharp emissions at 1.508 eV (X₁) and 1.495 eV (X₂), which have been attributed to the emissions of excitons bound to isolated N atoms, and another one at 1.443 eV (X₅) were observed. These results show that nitrogen (N) atom in GaAs becomes optically active as an isoelectronic impurity at least in as-grown condition. For N⁺ ion-irradiated samples with rather high I_N, e.g., with I_N = 75 nA/cm² and E_a = 100 eV, a broad emission together with multiple sharp ones were observed after furnace annealing at 750°C which were ascribed to emissions of excitons bound to nitrogen-nitrogen (N---N) pairs.     

单球中子谱仪的能量响应模拟及解谱方法研究

本文阐述了单球中子谱仪的原理,介绍了基于单慢化球和19对⁶Li-⁷Li闪烁体探测器构成的单球中子谱仪的结构及解谱方法,使用蒙特卡罗中子输运程序模拟了单球中子谱仪的中子响应函数。计算结果表明,该谱仪具有较好的空间对称性,能根据谱仪中各探测器的计数对源的大致方位进行判断;模拟了单球谱仪在²⁴¹Am-Be源照射下各探测器的计数,使用Unfolding with Maxed and Gravel (UMG)解谱程序在不同解谱算法以及初始谱的情况下对模拟数据进行解谱计算,在使用最大熵散发以及与源项相同的预置谱的情况下,解谱结果最为准确,验证了响应函数的准确性。     

Measurement of the subcriticality of power-stressed reactors with an analog reactimeter

Conclusions A technique has been developed for measuring the effects of reactivity in a subcritical reactor with an analog reactimeter. It is based on the compensation of the current applied to the reactimeter input from the neutron detector. The compensation of current produced by neutrons of the subcritical multiplying assembly formalizes the algorithm for reactivity calculation, making it an adequate model of a reactor with a source and making it possible to determine the subcriticality without prior entry into the critical state. In this case the measurements are made in the presence of neutron sources characteristic of power-stressed reactors. The regular devices of the control and safety system could be used to produce unsteady variation of the neutron flux.All of this permits the proposed method to be extended to zero-power reactors and to power-stressed reactors. Once the subcriticality has been measured an analog of the neutron source is introduced into the reactimeter. This instrument measures the effects of reactivity in the subcritical state without the reactor being previously put into the critical state, monitors the entry of the reactor into the critical state by checking the reactivity, and makes all the measurements usually made with analog reactimeters. If the intensity of the source does not change during measurements (5–10 min) when chambers sensitive to rays (e.g., KNK-56 chambers) are used as neutron-flux detectors, then the accuracy of -ray compensation does not affect the results of the measurements.Translated from Atomnaya Énergiya, Vol. 45, No. 5, pp. 375–376, November, 1978.     

Determination of Large Negative Reactivity by Integral Versions of Various Experimental Methods

The large negative reactivity is measured in Semi-Homogeneous Experimental facility (SHE). Experimental methods are Sjöstrand's pulsed neutron, source multiplication and rod drop methods beside revised King-Simmons' pulsed neutron methods. Neutron detectors are placed at various points in the core region for multi-points measurement.

Usual one-point reactor model analysis resulted in the reactivity values, strongly dependent on the detector position with the increase of subcriticality. In addition, disagreements between the used experimental methods are also pointed out.

In order to overcome these difficulties due to the spatial higher harmonics and the kinetic distortion in the neutron flux distribution, an integral version analysis is applied, in which use is made of multi-points reactor model. In the analysis, space integration of the neutron counts obtained throughout the core region is made with weights of the adjoint function of fast neutrons, calculated using the two- or three-dimensional diffusion code. The negative reactivity values determined by the integral version analysis agreed well with each other within the uncertainty of ～5% in the reactivity range down to ～50 dollars.

It is concluded that all the experimental methods are adequate for precise determination of the large negative reactivity of reactor provided that the integral version analysis is utilized or that correction is made for the change of the neutron generation time using precise calculation.