摘要:

AbstractUsually a number of separating stages have to be connected in series to attain the desired degree of isotope separation by gaseous diffusion. Such a series-connected group of stages is called a cascade. In this paper the differential equation describing the time-dependence of a tapered cascade in which the interstage flow changes stage by stage is derived and solved under some reasonable assumptions. On the basis of these analytical results, the static and dynamic characteristics of a tapered cascade are discussed. For the same total number of stages, the cascade requiring the largest equilibrium time to reach steady-state condition is described. Also shown is that the so-called ideal cascade is not recommended from the standpoint of dynamic characteristics, although its superiority in static characteristics is familiar. It is pointed out that by a slight reduction of the cutθfrom that of the ideal cascadeθidealthe dynamic characteristics are improved to some extent, but the selection ofθgreater thanθidealresults in both static and dynamic characteristics being unfavorable. It is also shown that the equilibrium time of a tapered cascade tends to increase with the total number of stagesNin proportion toN2as in a square cascade. The top stage is not always the last to reach the steady-state condition. A simple method is proposed to predict how the equilibrium time differs in each stage of the cascade.

ISSN:0029-5639    

DOI:10.13182/NSE68-A19728

出版商:Taylor&Francis    

年代:1968

数据来源: Taylor

摘要:

AbstractCalculations are made of the radiation flux of gamma rays that have originated from a point isotropic source and have been singly scattered in the air lying beyond a plane interface. Calculations are made in the limit that the source-detector separation distance is small compared to a mean-free-path in air. These results are interpreted in terms of an image source. The results, combined with earlier calculations of the radiation flux reflected from a condensed medium, such as ground, predict the effect of the ground-air interface on radiation fluxes in air near the interface. The results are extrapolated to source-detector separation of the order of a mean-free-path by using infinite-medium buildup factors. Comparisons with experiment show that the model produces results that are in qualitative agreement with experiment.

ISSN:0029-5639    

DOI:10.13182/NSE68-A19729

出版商:Taylor&Francis    

年代:1968

数据来源: Taylor

摘要:

AbstractA formalism is developed from observable systematics and elementary energetics of nuclear reactions for the calculation of neutron induced gamma-ray production cross sections and spectra. The calculations are compared with experiments performed at several laboratories. The comparison shows a mean deviation of 18%.

ISSN:0029-5639    

DOI:10.13182/NSE68-A19730

出版商:Taylor&Francis    

年代:1968

数据来源: Taylor

摘要:

AbstractThe method of invariant imbedding has been applied to the problem of penetration of gamma rays through slabs. The accuracy of the method was examined by comparison with other reliable calculations and proved to be competitive with other well-developed methods. The method has the advantages that it is much more efficient than the Monte Carlo method and that it is readily applicable to the multilayer problems. An extensive series of calculations on the transmission of gamma rays through homogeneous slabs was carried out. The energy and angular distributions of transmitted photons from monoenergetic and oblique sources were obtained for slab thickness up to 15 mean-free-paths and for 7 materials. The results of calculations were compared with experiments and found to be in good agreement.

ISSN:0029-5639    

DOI:10.13182/NSE68-A19731

出版商:Taylor&Francis    

年代:1968

数据来源: Taylor

摘要:

AbstractThe cross sections for the reactions111Cd(n,n′)111mCd,112Cd(n,2 n)111mCd,87Sr(n,n′)87mSr,58Ni(n,p)58m + gCo,58Ni(n,2n)57Ni, and58Ni[n,d) + (n,np) + (n,pn)]57Co have been measured by the activation method. Measurements were performed in the energy regions from 2.2 to 3.5 MeV and from 13.7 to 14.8 MeV. The cross sections obtained for the111Cd and87Sr reactions indicate that both these isotopes should prove useful as neutron flux monitors. The cross sections obtained for the58Ni reactions are in good agreement with the results of recent investigations.

ISSN:0029-5639    

DOI:10.13182/NSE68-A19732

出版商:Taylor&Francis    

年代:1968

数据来源: Taylor

摘要:

AbstractWith a view to a detailed study of heterogeneity effects in lattices, and in particular of the streaming effects introduced by the presence of channels, a project has been undertaken in France for studying graphite lattices by the pulsed source technique. The aim of the project is to obtain experimental data on clean simple systems for testing the methods used in lattice calculations. The project comprises three progressive stages: study of lattices of empty channels, followed by lattices of non-fissile material, and finally by multiplying lattices. This article presents the results obtained in the study of empty-channel lattices. Regarding the theoretical aspects of the project, the expressions involved are somewhat different, depending on whether one is dealing with stationary or with non-stationary systems. The point of view adopted in the theoretical studies presented in this article, as well as in a related article that has appeared inNuclear Science and Engineering, has been to consider stationary systems as particular cases of non-stationary ones. In the present article, detailed expressions are obtained for non-multiplying lattices, and wherever it was possible without digressing too much from the context, multiplying lattices have also been discussed. In one of the Appendixes in particular, a method is presented for the direct calculation of decay constants in multiplying or non-multiplying lattices, a particular form of which can be used for the calculation of critical bucklings. The main part of the article deals with the axial and the transversal diffusion coefficients in empty-channel lattices. Experiments have been performed on lattices with a square pitch of 20-cm side, the channel radii studied being 1.5, 2.5, 3.5, 4.5, 5.5, and 7 cm. Since the object was to determine if the anisotropy effects introduced in the diffusion coefficients by the cell geometry could be properly interpreted, the theoretical calculations have been limited to one-velocity treatments, which should be adequate for empty-channel systems. The comparison between experiment and theory is quite satisfactory, though some discrepancy is observed with the axial diffusion coefficient in the case of the large channel radii. The experiments indicate, furthermore, that the diffusion cooling coefficients vary very rapidly with channel radius. The theoretical treatment of cooling coefficients in lattices is very complex, and has not been attempted. One section of the article has been devoted to the consideration of extrapolation lengths of empty-channel graphite systems. Approximate analytical calculations as well as a numerical calculation utilizing the TDC code have been presented. They indicate that it is reasonable to consider the extrapolation length as being equal to 0.71 times the cell mean-free-path associated with the direction considered. This expression has been utilized to define the bucklings of the blocks studied. However, a more detailed study of extrapolation lengths would be very useful. The theoretical studies presented are based on the classical approach of expressing the finite medium decay constant as a power series of the buckling. This approach is strictly valid only if the corresponding infinite lattice has an asymptotic decay constant. The conditions necessary for its existence are considered and it is seen that configurations of non-multiplying lattices can very easily be such that the required conditions are not satisfied. A satisfactory treatment of such“singular”cases would require a theoretical approach that treats the finite system directly without calling upon the corresponding infinite one.

ISSN:0029-5639    

DOI:10.13182/NSE68-A19733

出版商:Taylor&Francis    

年代:1968

数据来源: Taylor

摘要:

AbstractIn a new method of approximation of the Boltzmann equation, one starts from a particular form of the equation that involves only the angular flux at the boundary of the considered medium and where the space variable does not appear explicitly. Expansion of the angular flux of neutrons leaking from the medium, in spherical harmonics with no assumption about the angular flux within the medium, gives a very good approximation of several classical plane geometry problems. These problems include the albedo of slabs and the transmission by slabs, the extrapolation length of the Milne problem, and the spectrum of neutrons reflected by a semi-infinite slowing down medium. The method may be extended to other geometries.

ISSN:0029-5639    

DOI:10.13182/NSE68-A19734

出版商:Taylor&Francis    

年代:1968

数据来源: Taylor

摘要:

AbstractFew-group diffusion equations are derived from variational principles. It is shown that by proper choice of trial function it is possible to derive a few-group theory in which interface boundary conditions of continuity of few-group fluxes and currents are obtained, even when the few-group constants are obtained by flux-adjoint weighting. The analysis is facilitated by the use of functionals that incorporate the interface condition of flux continuity by means of Lagrange multipliers. Two functionals are used to give two variants of the theory. Both functionals have as Euler equations theP-1 approximation to the time-independent, eigenvalue form of the energy-dependent transport equation. In addition, the current and flux interface boundary conditions are part of the complement of Euler conditions of the functionals. The functionals admit trial functions discontinuous in space and energy. The two functionals differ in that one has both flux and current arguments, whereas the other has only flux arguments, and yields theP-1 equations in second-order diffusion form.

ISSN:0029-5639    

DOI:10.13182/NSE68-A19735

出版商:Taylor&Francis    

年代:1968

数据来源: Taylor

摘要:

AbstractA complete inverse mass expansion is derived for the difference-differential equation describing neutron moderation in infinite homogeneous media, far energetically from the sources. We consider slowing down equations with different values of the nucleus-to-neutron mass ratio, and a common value of the capture-to-scattering cross-section ratio. The latter is assumed to be an analytic function of lethargy. A preliminary analysis suggests the functional form of the leading term of the expansion. Further treatment leads to a first-order, linear, inhomogeneous, ordinary differential equation satisfied by the expansion terms. Different terms of the expansion correspond to different free terms of the differential equation. Imposing a normalization condition, the solution of the differential equation is made unique, and a formal, practically effective solution to the general asymptotic moderation problem is obtained.

ISSN:0029-5639    

DOI:10.13182/NSE68-A19736

出版商:Taylor&Francis    

年代:1968

数据来源: Taylor

摘要:

AbstractThis paper presents a method for solving multiregion transport problems which is a generalization of integral transport theory as typified by the well-known Amouyal-Benoist-Horowitz method. The theorem of uniqueness of the solution of Boltzmann equation is used to reduce the problem to a series of associated problems, the Green's functions of which are supposed to be known, with appropriate sources at region boundaries. A system of integral equations is obtained for the sources. The present paper is restricted to one-speed, plane geometry, and infinite medium problems as associated ones. The numerical results presented appear to be very good compared with other methods. Our method provides the advantage of reducing the number of unknowns by an order of magnitude and can therefore provide a comparable reduction in computing time.

ISSN:0029-5639    

DOI:10.13182/NSE68-A19737

出版商:Taylor&Francis    

年代:1968

数据来源: Taylor