Hiroshi Nishihara

Calibration of neutron detectors for time-of-flight experiments by making use of a borated graphite standard neutron spectrum pile☆

Abstract In order to obtain a standard field of neutron spectrum in the keV region, a borated graphite pile was designed and used. Theoretical calculations revealed that the 90° (μ=0) angular lethargy spectrum of neutrons at about 22.5 cm from the center, where an isotropic photoneutron source was placed, had an essentially flat shape and little dependence on several factors. By the linac time-of-flight method with this pile, energy dependent neutron detection efficiencies of a 6Li glass scintillation counter bank and a 10Ba-vaseline plug NaI(Tl) counter were determined. As a subsidiary measurement, the spatial neutron distribution was measured by making use of the 58Ni(n,p)58Co and 197Au(n,γ)198Au reactions. It was found that neutrons distributed nearly isotropically around the photoneutron source, which verified the adequacy of the one-dimensional calculation for predicting the neutron spectrum in this pile. Radial attenuations of the reaction rates agreed with the predicted. By making use of these calibrated neutron detectors the neutron spectrum in an aluminum assembly was measured by the time-of-flight method. The values obtained with these two detectors agreed with each other and also with the theoretically predicted value.

Solutions of diffusion equations by Fourier expansions

Abstract One- and two-dimensional diffusion equations in slab geometry are solved by a method of Fourier expansion. In this method, at first, equations for the fluxes on the boundaries and their normal derivatives are derived. Applying boundary conditions, these equations are solved and all boundary values are determined. Then using these boundary values, the Fourier coefficients of the flux in the region are calculated. Different from the eigenfunction expansion method, the function series used for the expansion is independent of the boundary conditions. Therefore multi-regional problems are also solved by this method. The results of the numerical calculations are given and compared with the results by the usual finite difference method.

Numerical Solution to Critical Problem of Finite Cylindrical Reactors by Variational Method

Making use of the variational method, an expression is derived for the upper and lower bounds of the largest eigenvalue of the one-velocity transport equation, in terms of the Rayleigh quotient. It is found that the error contained in the eigenvalue thus obtained increases or decreases in keeping with the error inherent in the trial function used for expressing the neutron flux distribution. The first approximation for the eigenvalue and the extrapolation distances of finite cylindrical reactors are determined by using the asymptotic flux shape as trial function. The second and third approximations for the eigenvalue are derived by supplementing the asymptotic function with additional orthogonal terms. It is proposed to combine the eigenvalue determined by the variational method with the second approximation of the flux obtained by applying the integral transport operator to the asymptotic flux. Evidence is presented to prove the convergence of an iterative procedure devised for successively applying the ...

Solution of One-Dimensional Group-Diffusion Equation by Laplace Transformation

A group-diffusion equation for multiregion in one dimension is solved by applying the Laplace transformation and an analytical continuation. Applying the Laplace transformation, a group-diffusion equation is transformed into a system of linear algebraic equations. They are formulated with the use of the transfer matrix adopted in the method by Lie-series. Solutions are given in three different forms, analytical, Taylors series, and in a form used in the source iteration method.

Measurement and Calculation of Neutron Diffusion Parameters in Water

Neutron diffusion parameters in water at a room temperature of 10°C have been measured by the pulsed neutron method for the range of geometrical buckling from 0.093 to 1.36 cm-2. The results are 205±4 μ60 for the neutron mean life time due to absorption, 34,120±610 cm2·sec-1 for the diffusion coefficient and 3,350±560 cm4·sec-1 for the diffusion cooling coefficient. The decay constant has been calculated as a function of buckling for the Nelkin and the Rad-kowsky scattering models of water on the assumption of linear anisotropic scattering. The calculated diffusion coefficients, 36,290 cm2·sec-1 for the Nelkin model and 37.610 cm2·sec-1 for the Radkowsky model, are somewhat higher than the experimental result. It is shown that the calculated diffusion coefficient approaches the experimental value if we use μ-(E), the mean value of cosine of scattering angle, obtained from the Beysters experiment instead of that for the Nelkin model.

On the Burn-Up Characteristics of Large Pu-U Fast Reactors

Breeding ratio, effective multiplication factor k eff sodium-void reactivity effect of Pu-U fast reactors having a 3,000 l core volume are investigated as functions of burn-up. Following results are obtained. 1. Initial breeding ratio does not fail to be a measure for roughly estimating breeding character. 2. By charging Pu fuel in the internal blanket situated inside core region, Keff of the system remains almost constant along with burn-up. 3. The variation of sodium-void reactivity due to fuel burn-up of the above system does not seem to be serious.

Application of iron-filtered neutrons to radiography of a copper step within a large iron block and to computer tomography of metallic cylinders

Abstract A time-of-flight technique and iron-filtered neutrons were applied to neutron radiography and to computer tomography. By making use of iron-filtered neutrons, the existence of 1 mm thick copper within an iron block of 20 cm thickness could be clearly distinguished. To investigate the possibility of neutron computer tomography using iron-filtered neutrons, two cylindrical metallic samples made of CuFePb and CuFeAl were used. From the reconstructed image of the samples, we could clearly see the internal structures.

Numerical Solutions of Discrete-Ordinate Neutron Transport Equations Equivalent to PL Approximation in X-Y Geometry

A numerical method for solving the steady-state one-velocity neutron transport equation in x-y geometry is presented. It is based on the concept of combining the spherical harmonics theory with the discrete-ordinate method. The validity of the method is illustrated by several numerical computations using the TWOTRAN-PLXY code, formulated by modifying the ordinary discrete-ordinate code TWOTRAN-(x, y). Through numerical studies, it is shown that the present method is effective for obtaining solutions of high accuracy, as well as for eliminating the ray effects present in the ordinary discrete-ordinate method. As for the techniques for accelerating the convergence of the iterative solutions, it is proved that the Chebyshev device works well for the present method, while whole-system rebalancing is found to be less effective.

Ein niedereingangsimpedanzvorverstärker für halbleiterdetektoren

Abstract A new low input-impedance preamplifier for semiconductor detectors has been developed. The input-impedance is 92 Ω to match with the characteristic impedance of the coaxial cable RG-62U. This preamplifier supplies both a fast current-pulse with a rise-time of 8.1 ns (current-amplifier) and a charge-pulse with a decay-time of 3 μS (charge-amplifier). The charge-pulse is obtained by integrating a fast current-pulse and by extending the pulse decay-time with a built-in pulse stretcher. The gain of the current- or the charge-amplifier is equivalent to 11 kΩ or 0.195 pF respectively. The amplitude of the outputpulse is almost independent on the distance (cable length) between the detector and the preamplifier. The rms noise amplitude is 26 nA for the current-amplifier and 22.6 × 10 −17 C for the charge-amplifier.

An Analysis of Signal Pulse from Semiconductor Junction Detectors

An elementary method of wave form analysis for semiconductor detectors under certain working conditions is derived from a simple model of pulse formation. Agreement of the calculation with the corresponding experimental results is satisfactory. The experiments were carried out on an M-8811-A-50 detector (TOSHIBA, 2,500 Ω cm, p-type Si). The load resistance was in the range 100~50,000 Ω. The amplitude and the rise-time have been found to be in the ranges 1~6 mV and 3~9 ns, respectively. The energy spectrum of detector pulse for low load impedance extends up to ca. 50 Mc.