The transport and diffusion theory of a line source in an infinite half-space with internal reflection

A closed form analytical solution is obtained for a three-dimensional transport theory problem, namely that of a line source in a half-space in one-speed transport theory with an internally reflecting surface. The theory is developed by using Fourier transforms in the transverse directions and a Laplace transform in the axial direction, together with the Wiener–Hopf technique. Both specular and diffuse internal reflection are considered and it is shown that a closed form solution is not available for the specular case but is available for the diffuse case. The surface particle scalar intensity and current are obtained and their sensitivity to absorption and the reflection coefficient are assessed. We also obtain a number of analytic asymptotic estimates for the intensity valid at large distances from the source. Diffusion theory is also employed and compared numerically with the transport solution. In general, diffusion theory gives very satisfactory results within its regions of limitation. We also offer this paper as an exercise in analytical transport theory; an aspect of reactor physics which is not often seen in recent times.     

Accumulation dose factors for a plane isotropic γ source in an infinite air medium

Translated from Atomnaya Énergiya, Vol. 67, No. 1, pp. 51–52, July, 1989.     

Approximation theory for a certain class of operators and some of their applications to transport theory

The convergence of discrete-ordinates approximations under various assumptions on cross-section and source data has been shown in different function spaces by Anselone, Keller, Wendroff, Nestell, Madsen, Nelson, and Victory. For the establishment of the convergence theory of discrete-ordinates methods in higher spatial dimensions, we develop in this paper an approximation theory for a certain class of operators - - - naturally arising in conjunction with the transport equation. The theory developed in this paper is applied to proving that the critical parameter and critical flux computed by discrete-ordinate methods do converge to the corresponding quantities for the undiscretized, three-dimensional transport equation.     

One-speed neutron transport eigenvalues for an infinite, two-medium slab lattice

The monoenergetic transport equation with isotropic scattering is applied to an infinite, two-medium slab lattice. One of the media is assumed to have a multiplication factor larger than unity and the other smaller than unity. The two coupled integral equations that are derived are numerically solved using the spatial Legendre expansion method (Carlvik's method). Tables of seven eigenvalues for various dimensions of the bodies are given and the first four flux modes for some cases are plotted. In addition, simple formulae for very high-order eigenvalues are given.     

Explicit expressions for the moments of the monoenergetic neutron-transport equation for isotropic scattering in an infinite plane medium

The analytical determination of the spatial and angular moments of the monoenergetic neutron-transport equation in an infinite medium initiated by Case, de Hoffmann and Placzek 30 years ago is completed. Analytical expressions for the moments that are convenient for numerical evaluation are obtained, and several high-order moments are evaluated as a demonstration.     

Energy distribution of gamma quanta from a point source of gamma radiation in an infinite sandy medium

Gamma spectra from point sources (Cr⁵¹, Zn⁶⁵, Ra and MsTh) in an infinite sandy medium were studied with the aid of the scintillation spectrometer. The results obtained indicate that when gamma radiation passes through a thickness of sand there takes place an accumulation of soft scattered radiation of energy 50 kev independently of the energy of the initial radiation.In conclusion the authors wish to thank Professor I. I. Gurevice, Messrs, G. R. Golbeck, P. E. Stepanov and N. I. Laletin for their valuable advice during discussions in connection with this work.     

Identification and properties of the fundamental expansion functions for neutron transport in an infinite homogeneous medium

Starting from the basic expression for the neutron flux due to a point source in an infinite homogeneous scattering and absorbing medium, the first few fundamental expansion functions corresponding to successive collisions are identified, and their analytic properties are presented, in spherical and plane geometry. Various representations of the functions are obtained in the form of power series, an expansion in a series of exponential integrals, and other integrals. The adequacy of traditional asymptotic forms is considered.     

Spatial angular energy characteristic of the field of a plane isotropic γ source in an infinite air atmosphere

Translated from Atomnaya Énergiya, Vol. 65, No. 6, pp. 432–433, December, 1988.     

Evaluation of the integral quantities for incident fusion source neutrons in infinite medium

Integral neutronic quantities have been evaluated for incident 14.1 MeV (D,T) and 2.45 MeV (D,D) fusion source neutrons in infinite medium for the most important materials in fusion technology, namely lithium, beryllium, lead and thorium. The study covers the calculation of the integral tritium breeding ratio, the ²³³U breeding rate (when applicable), the neutron multiplication ratio through (n,x)-and fission-(when applicable) reactions, and the heat release in those mixtures which are composed when first thorium is mixed with natural lithium or ⁶Li for a volume fraction from 0% to 100% and then the variable thorium-lithium composition is mixed with Be or Pb for a volume fraction from 0% to 100%.