Subcritical Multiplying System Research Articles

Multiplication Factor for Subcritical Multiplying System and the Efficiency of Source Neutrons

Multiplication Factor for Subcritical Multiplying System and the Efficiency of Source Neutrons

Solution of neutron-transport multigroup equations system in subcritical systems

An iteration method has been implemented to solve a neutron transport equation in a multigroup diffusion approximation. A thermoelectric generator containing plutonium dioxide, used as a source of thermal and electric power in spacecraft, was studied. Neutron yield and multigroup diffusion approximation data was used to obtain a continuous and group distribution of neutron flux density spectra in a subcritical multiplying system. Numerical multigroup approaches were employed using BNAB-78, a system of group constants, and other available evaluated nuclear data libraries (ROSFOND, BROND, BNAB, EXFOR and ENDSF). The functions of neutron distribution in the zero iteration for the system of multigroup equations were obtained by approximating an extensive list of calculated and experimental data offered by the EXFOR and ENDSF nuclear data libraries. The required neutronic functionals were obtained by solving a neutron transport equation in a 28-group diffusion approximation. The calculated data was verified. The approach used is more efficient in terms of computational efforts (the values of the neutron flux density fractions converge in the third iteration). The implemented technique can be used in nuclear and radiation safety problems.

Stochastic Theory of the Fission Chamber Current Generated by Non-Poissonian Neutrons

The Campbell theorem, relating the variance of the current of a fission chamber (a “filtered Poisson process“) to the intensity of the detection events and to the detector pulse shape, becomes invalid when the neutrons generating the fission chamber current are not independent. Recently, a formalism was developed by the present authors, by which the variance of the detector current can be calculated for detecting neutrons in a subcritical multiplying system, where the detection events are obviously not independent. In the present paper, the previous formalism, which only accounted for prompt neutrons, is generalized to account also for delayed neutrons. A rigorous probabilistic analysis of the detector current was performed by using the same simple, but realistic detector model as in the previous work. The results of the present analysis made it possible to determine the bias of the traditional Campbelling techniques both qualitatively and quantitatively. The results show that the variance still remains proportional to the detection intensity, and is thus suitable for the monitoring of the mean flux, but the calibration factor between the variance and the detection intensity is an involved function of the detector pulse shape and the subcritical reactivity of the system, which diverges for critical systems.

Method and Means for Monitoring the Spent-Fuel Pool Subcriticality at the Smolensk NPP

Research based on the pulsed neutron experiment method (α-method) of subcriticality monitoring of the spent fuel pool at the Smolensk NPP is presented. The procedure includes stationary and nonstationary neutron-physical calculations and measurements of the main characteristics of a subcritical multiplying system, which the spent-fuel pool is. A description of the STEPAN-KhOYaT software specially developed for the computational support of the pulsed experiment is given. The subcriticality for real loads of spent-fuel pools is calculated and measured using the procedure.

Higher order mode analyses of power spectral density and Feynman-α method in accelerator driven system with periodically pulsed spallation neutron source

This paper deals with the theory of higher order modes in the Feynman Y function and the cross power spectral density (CPSD) in an accelerator-driven system (ADS) where pulsed spallation neutrons are injected at a constant frequency. A theoretical formula that considers the effect of higher order modes of the correlated and uncorrelated components in the Feynman Y function for an ADS is newly derived in this paper. Although the formula for the correlated and uncorrelated components of a CPSD was derived in a recent publication of the author of this paper, the verification has not been done yet. These formulae for the Feynman Y function and CPSD are applied to a subcritical multiplying system with a one-dimensional infinite slab geometry. The Feynman Y functions and CPSD calculated with the theoretical formulae are compared with the Monte Carlo simulations of these noise techniques. The theoretical formulae reproduce the Monte Carlo simulations very well, thereby substantiating the theoretical formulae derived in this paper. The correlated and uncorrelated components of the Feynman Y functions and CPSD are decomposed into the sum of the fundamental mode and other higher order modes. The higher order mode effect in the uncorrelated component is much more significant than in the correlated component.

Rigorous expression for the joint factoral moments of the neutron and count bivariate distribution in an infinite homogeneous multiplying system: II. Time dependent neutron source

This paper is the second of two which deal with the moments of the bivariate distribution of the neutrons and counts in a subcritical multiplying system. Following the forward Kolmogorov formalism, the expressions for the joint factorial moments of any order have been obtained for the case of an external Poissonian neutron source with time dependent mean value. The results are rigorous in the sense that no use is made of the quadratic approximation for the probability generating function of the neutrons emitted per fission. Several computations relating to a subcritical system in different steady state conditions have been performed. The results indicate that, at least in the examined cases, the relative errors between the exact moments and those obtained making use of the quadratic approximation are always rather small. Moreover a single linear relation between the error and the order of the moment has been established.

Probability profiles and moments of neutron count distribution via the Kolmogorov equations

The distribution of neutron counts in a subcritical multiplying system with an external source has been investigated in the framework of the Kolmogorov equations (KE), introducing some generalizations. The backward KE, without delayed neutrons, has been solved for the probability generating function ( pgf) in the case of many counting intervals and suitably differentiated for the determination of joint probabilities and moments. Attempts have been made to solve the backward KE taking into account the delayed neutrons and a recurrent relation has been obtained for the pgf. However, this solution is too complicated to lend itself to further manipulations. All the above calculations adopt the usual simplified fission model. Without any such assumption the backward and the forward KE with delayed neutrons have been solved for the first two moments in case of a single counting interval, thus obtaining the most general expression for the reduced variance. This formula, in the frame of the simplified fission model, reduces to a much simpler expression, which is shown to be practically equivalent to the generally used one. Finally, the backward KE with delayed neutrons and the simplified fission model assumption has been solved for the mean value, variance and covariance of neutron counts in the case of time dependent sources.