摘要:

AbstractThe equations and boundary conditions that constitute theP1approximation to the space-time-energy transport equation and its adjoint can be obtained from a variational expression that admits trial functions discontinuous in space and energy. This expression can then be used to derive all the standard forms of the few-group diffusion equations—equations using flux averaged constants, over-lapping group equations, parallel group equations—as well as many more hitherto unexamined. Such a procedure is carried out in the present paper. All the standard few-group results, as well as formally exact few-group equations and multigroup equations, are shown to be special cases of a single general form derived from the variational expression. Internal boundary conditions are obtained automatically, and it is shown that in some cases discontinuities in fluxes and currents ought to be imposed across internal boundaries.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17615

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

AbstractThe nonabsorbing thermal-neutron Milne problem is solved for isotropic scattering in the laboratory system. The scattering kernel has been approximated by a two-term degenerate sum and the resulting equations are solved by analytic continuation, together with Wiener-Hopf factorization.The solution so obtained is not explicit in the sense of quadratures, but is in the form of a nonsingular Fredholm equation, which is ideally suited to solution by iteration once certain generalized energy-dependentH-functions have been tabulated.The energy transfer properties of the approximate kernel are discussed, and their effect on the structure of the total flux evaluated. In general, the complete solution consists of an asymptotic part, together with a rethermalization term, which is connected intimately with the energy exchange process, and the integral transient which depends markedly on the variation of the total cross section with energy. It is shown that, when the cross section is constant, the rethermalization term becomes zero and the solution reverts to the one-velocity one, multiplied by a Maxwellian.Certain properties of the energy-dependentH-functions are discussed in the Appendix.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17616

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

AbstractThe elastic scattering of low-energy neutrons by the nuclei of a monatomic gas, which have an isotropic Maxwellian velocity distribution, is examined in detail within the framework of classical physics. A unified mathematical treatment, which fully preserves the three-dimensional aspects of the scattering process, is employed to study the dynamics of the neutron-nuclear elastic collision. A new form of the scattering probability function in velocity space is derived under the assumption of isotropic scattering in the center-of-mass system.Unique single-integral expressions, which are valid for any analytical or numerical representations ofσs(vr) andσa(vr), the microscopic scattering and absorption cross section as functions of the relative neutron-nuclear speed, are developed for the velocity scattering kernel, its spherical-harmonics weighted moments, and the total scattering and absorption probabilities. These formulations are tested by explicitly evaluating them in closed form for certain analytical cross-section representations and comparing these solutions with known results.The utility of the collision kernels for new solutions of the transport equation under conditions of variable scattering cross section is discussed.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17617

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

AbstractAn iterative unfolding method has been applied to several types of neutron environment to obtain neutron-flux spectra. The mathematical procedure involves selection of an initial spectral approximation and its subsequent perturbation to obtain a best-fit simultaneous solution for a system of ten or more activation integral equations. The present analytical studies support earlier results that integral neutron flux may be obtained from foil data with accuracies to within±10 to 30% at any point over the energy range from 4×10−7to 18 MeV, if the activation cross-section data and measured activation rates are accurate to±10%.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17618

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

AbstractThe problem of obtaining continuity conditions for aPNapproximation is approached from a variational point of view. A functional is defined that admits piecewise discontinuous trial functions and has the transport equation and flux continuity conditions as its Euler equations. A reduced functional, formed by adopting a truncated spherical-harmonics expansion as a trial function, has as its Euler equations thePNequations and approximate flux-continuity conditions. These variational continuity conditions, which involve full-range angular integrals, are seen to be the same as those of Rumyantsev. Marshak continuity conditions, which involve half-range angular integrals obtained by Marshak matching, are shown to be equivalent to Rumyantsev’s continuity conditions. Continuity conditions for a heterogeneousPNapproximation are obtained by extending the notion of Marshak matching are shown to the case where aPN,approximation is employed in an adjacent region.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17619

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

AbstractAn investigation was conducted to estimate the error when a flat-flux approximation is used to compute the resonance integral for a simple absorber element embedded in a neutron source.An integral equation describing the collision rate as a function of energy, position, and angle is constructed and subsequently specialized to the case of energy and spatial dependence. This equation is further simplified by expanding the spatial dependence in a series of Legendre polynomials. In this form, the effects of slowing down and flux depression may be accounted for to any degree of accuracy desired. The resulting integral equation for the energy dependence is thus solved numerically, considering the slowing down and the infinite-mass model as separate cases.From the solution obtained by the above method, the error ascribable to the flat-flux approximation is obtained. In addition to this, the error introduced in the resonance integral in assuming no slowing down in the absorber is deduced.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17620

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

AbstractA method is described for predicting the neutron multiplication factors of geometrically complicated configurations of unreflected unmoderated enriched-uranium metal from the results of two delayed-critical experiments in simple geometry. The method requires two constants characteristic of the metal. These are the total collision cross section (∑t) and the number of neutrons produced per collision (ν∑f/∑t), which are obtained from the two experiments by using S12transport-theory calculations with isotropic scattering. These constants, together with the assumption of isotropic scattering, are then used in 05R Monte Carlo neutron-transport calculations to predict the multiplication factors. The method has been tested by predicting the multiplication factors of 21 different delayed-critical assemblies with a wide variety of geometries to within a standard deviation of 1.5%.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17621

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

AbstractThe effect of air channels on the diffusion length of thermal neutrons in light water was measured and calculated. The comparison between experimental results, Monte Carlo calculations, and values derived using Behrens and Benoist formulae show a good agreement for the longitudinal diffusion length. In the transverse case, Benoist’s method agrees with Monte Carlo results better than Behrens’values.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17622

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

AbstractThe age of fission neutrons was measured to the indium resonance energy for light water and three metal-to-water volume ratios (1/4, 1/2, 2/3) in aluminum-water mixtures. A large plane highly enriched235U fission plate provided the source of neutrons. Aluminum plates (0.127×122×122 cm) oriented parallel to the source plane were used for the metal.Indium foil activities were taken in planes parallel to the source and integrated over these planes to obtain the equivalent activities that would result from an infinite source. From these data, the ages for the four cases were:M/W= 0, (26.24±0.33 cm2);M/W= 1/4, (32.28±0.50 cm2);M/W= 1/2, (39.96±0.50 cm2);M/W= 2/3, (44.88±0.59 cm2). To investigate heterogeneous effects, the plates were lumped to simulate 0.635-cm-thick plates and the measurements repeated for the 2/3 metal-to-water ratio. The measured age was 44.50±0.49 cm2, indicating no lumping effect in this measurement.The data for the pure water measurement were also analyzed by applying geometric corrections for the finite size of the source plate. This resulted in a measured age of 27.82±0.66 cm2, which agrees with previous measurements utilizing this method of data analysis.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17623

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

AbstractThe logic of the time-optimal solution to the xenon shutdown problem for a point reactor model has been successfully applied to an actual reactor system. Spatial integration of the flux-square weighted xenon concentration was used. The predetermined power variation with time successfully held the xenon boundary and created a final shutdown (target) trajectory whose maximum was within three percent of the specified boundary based on the total reactivity variation of the program. Although digital computer calculation, occasionally using trial-and-error techniques, was necessary to predict the power-time shutdown program, the computer requirements were not excessive. Approximately 7 h of additional reactor operation was utilized to prevent a 16 h period during which xenon buildup would have prevented reactor operation.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17624

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor