Abstract
A method has been developed for the solution of the monoenergetic critical problem for a slab or a sphere. The method utilizes an expansion of the flux density in Legendre polynomials of the coordinate. It is equivalent to the usual variational method using powers of the coordinate, but the use of Legendre polynomials makes it possible to calculate most of the elements of the resulting matrix by means of recurrence formulae. A series of calculations has been performed for slabs and spheres with d {<=} 5, where d is the thickness of the slab or the diameter of the sphere measured in mean free paths. The critical problem is equivalent to the problem of determining the decay constant of a subcritical system with an exponentially decaying flux density. In consequence the calculations also give a series of decay constants for subcritical slabs and spheres. Comparisons with diffusion theory show that large errors can result from uncritical application of diffusion theory to small assemblies. The author would recommend that measurements on small pulsed assemblies be analyzed by means of more accurate methods, for example the present method extended to multi-group treatment of the energy dependence. The results of the calculations show
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Citation Formats
Carlvik, I.
Monoenergetic Critical Parameters and Decay Constants for Small Spheres and Thin Slabs.
Sweden: N. p.,
1967.
Web.
Carlvik, I.
Monoenergetic Critical Parameters and Decay Constants for Small Spheres and Thin Slabs.
Sweden.
Carlvik, I.
1967.
"Monoenergetic Critical Parameters and Decay Constants for Small Spheres and Thin Slabs."
Sweden.
@misc{etde_20949450,
title = {Monoenergetic Critical Parameters and Decay Constants for Small Spheres and Thin Slabs}
author = {Carlvik, I}
abstractNote = {A method has been developed for the solution of the monoenergetic critical problem for a slab or a sphere. The method utilizes an expansion of the flux density in Legendre polynomials of the coordinate. It is equivalent to the usual variational method using powers of the coordinate, but the use of Legendre polynomials makes it possible to calculate most of the elements of the resulting matrix by means of recurrence formulae. A series of calculations has been performed for slabs and spheres with d {<=} 5, where d is the thickness of the slab or the diameter of the sphere measured in mean free paths. The critical problem is equivalent to the problem of determining the decay constant of a subcritical system with an exponentially decaying flux density. In consequence the calculations also give a series of decay constants for subcritical slabs and spheres. Comparisons with diffusion theory show that large errors can result from uncritical application of diffusion theory to small assemblies. The author would recommend that measurements on small pulsed assemblies be analyzed by means of more accurate methods, for example the present method extended to multi-group treatment of the energy dependence. The results of the calculations show clearly the interesting fact that the exponentially decaying flux of very small spheres has a minimum at the center.}
place = {Sweden}
year = {1967}
month = {Apr}
}
title = {Monoenergetic Critical Parameters and Decay Constants for Small Spheres and Thin Slabs}
author = {Carlvik, I}
abstractNote = {A method has been developed for the solution of the monoenergetic critical problem for a slab or a sphere. The method utilizes an expansion of the flux density in Legendre polynomials of the coordinate. It is equivalent to the usual variational method using powers of the coordinate, but the use of Legendre polynomials makes it possible to calculate most of the elements of the resulting matrix by means of recurrence formulae. A series of calculations has been performed for slabs and spheres with d {<=} 5, where d is the thickness of the slab or the diameter of the sphere measured in mean free paths. The critical problem is equivalent to the problem of determining the decay constant of a subcritical system with an exponentially decaying flux density. In consequence the calculations also give a series of decay constants for subcritical slabs and spheres. Comparisons with diffusion theory show that large errors can result from uncritical application of diffusion theory to small assemblies. The author would recommend that measurements on small pulsed assemblies be analyzed by means of more accurate methods, for example the present method extended to multi-group treatment of the energy dependence. The results of the calculations show clearly the interesting fact that the exponentially decaying flux of very small spheres has a minimum at the center.}
place = {Sweden}
year = {1967}
month = {Apr}
}