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AbstractAbstract

[en] The discrete eigenvalue problem associated with the one-speed azimuthal Fourier harmonics in plane geometry is discussed. An explicit expression, well-suited to numerical evaluation, is given for the dispersion function, and the reality and maximum number of discrete eigenvalues are demonstrated. From numerical examples, it is found that quite often there are no discrete eigenvalues, particularly for the higher harmonics

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Planar geometry

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Journal Article

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Nuclear Science and Engineering; v. 59(1); p. 53-56

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[en] Using slab geometry, generalized rebalance is presented as a class of iteration acceleration schemes applicable to the neutron transport equation. It is demonstrated that the diffusion-synthetic, variable-Eddington-factor, and conventional-rebalance schemes can be shown to be special cases of generalized rebalance. Expressing these schemes within the generalized-rebalance framework leads one to consider a new scheme labeled third-moment rebalance. Numerical results are presented that indicate that Alcouffe's diffusion-synthetic schemes are presently the best available methods

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Nuclear Science and Engineering; v. 65(2); p. 226-236

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[en] The mathematical problem of approximating the neutron escape probability function is studied through an analysis of the moment expansion of the function. The problem with possible divergence of the expansion is identified and avoided by devising an alternative based on physical arguments. An approximation of general validity for any convex geometry is thus deduced that is simple, accurate, and convenient for use. As examples, numerical results are presented for three geometries: a sphere, a cylinder, and a slab

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Nuclear Science and Engineering; v. 66(2); p. 254-258

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[en] A general systematic method to reduce multiregion problems in plane geometry to regular integral equations for the coefficients of singular-eigenfunction expansions is proposed. The method is based on the half-range orthogonality relations of the eigenfunctions and is applicable in two-group as well as one-group theory. The method is used to solve two problems in one-group theory for isotropic scattering: the Milne problem for a half-space bounded by a slab of dissimilar medium and a problem of neutron transmission through two slabs. Numerical results are reported for several sets of parameters

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Published in summary form only.

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Journal Article

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Nuclear Science and Engineering; v. 65(1); p. 191-196

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No abstract available

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Nuclear Science and Engineering; v. 50(1); p. 10-19

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[en] The main features of this paper are the utilization of inherent two-dimensional symmetries and the development of accurate angular quadrature coordinates and weights especially suited for the net and/or partial currents and all the net and/or partial moments of the neutron flux up to a given order. Three classes of true analogs of the one-dimensional single-Gauss and double-Gauss are considered for two-dimensional x-y problems with rectangular spatial mesh subdivisions. The first is single-range quadrature, most suitable for the asymptotic regions where the vector flux of neutrons can be well approximated by polynomials in Ω/sub x/ and Ω/sub y/ defined over the entire unit sphere of angular directions Ω. This quadrature can be used whenever distances between material interfaces are large with respect to the neutron mean-free-path (mfp). The second is double-range quadrature, most suitable at material interfaces where the unit sphere can be split into two hemispheres, one in each material region, and the vector flux can be well approximated by two possibly distinct polynomials in Ω/sub x/ and Ω/sub y/, one in each hemisphere. This quadrature can be used whenever material interfaces and currents are important along either the x or the y direction but not both. The third is quadruple-range quadrature, most suitable at corners where the unit sphere can be split into four quadrants and the vector flux can be well approximated by four possibly distinct polynomials in Ω/sub x/ and Ω/sub y/, one in each quadrant. This quadrature explicitly allows for discontinuities at corners and is appropriate for highly heterogeneous problems where distances between material corners are small with respect to the mfp. For simplicity, only product formulas are considered, where the angular integrals are split into separate integrals over polar and azimuthal directions

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Nuclear Science and Engineering; v. 64(2); p. 299-316

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[en] The inverse problem for multigroup transport theory is solved for the cases of plane and spherical symmetry

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Nuclear Science and Engineering; v. 63(1); p. 95-96

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[en] It is well known that for a large reactor a diffusion calculation of the system eigenvalue (criticality) is weakly dependent on the linear extrapolation distance /gamma/. This weak dependence is characterized by a smallness parameter /epsilon/. A perturbation method is used to quantify the errors in the eigenvalue resulting from the use of approximate boundary conditions in this paper. An explicit formula is derived which gives an energy independent extrapolated endpoint in terms of the energy-dependent linear extrapolation distance. 8 refs

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Nuclear Science and Engineering; ISSN 0029-5639; ; v. 77(4); p. 438-443

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[en] The one-speed transport equation is solved for a ring reactor. A complete solution is obtained for the space-time relaxation of a pulse of neutrons in a multiplying medium in which delayed neutrons are neglected. The solution consists of a fundamental mode, a finite number of harmonics, and an integral transient. A condition is deduced, which gives the maximum number of harmonics that can exist for a given ring circumferenced. The limitations of diffusion theory are pointed out with particular reference to the shortcomings of that theory in dealing with the early stages of evolution of the pulse. Delayed neutrons are included and a complete solution is obtained by means of the prompt jump approximation. The results are illustrated by numerical calculations designed to show the onset of instabilities in the harmonics when the reactor is sufficiently large

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AbstractAbstract

No abstract available

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Nuclear Science and Engineering; v. 51(1); p. 76-78

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