Vol. XXI, No. 2, Pp. 1101
December 2006
UDC 621.039+614.876:504.06
YU ISSN 14513994
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Pages: 3  13
Authors: Malin WAHLBERG, Imre PÁZSIT
Abstract
The purpose of this paper is to demonstrate the use of the invariant embedding method in a few model transport problems for which it is also possible to obtain an analytical solution. The use of the method is demonstrated in three different areas. The first is the calculation of the energy spectrum of sputtered particles from a scattering medium without absorption, where the multiplication (particle cascade) is generated by recoil production. Both constant and energy dependent crosssections with a power law dependence were treated. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and in a halfspace are interrelated through embeddinglike integral equations, by the solution of which the flux reflected from a halfspace can be re constructed from solutions in an infinite medium or vice versa. In all cases, the invariant embedding method proved to be robust, fast, and monotonically converging to the exact solutions.
Key words: invariant embedding method, synthetic scattering kernel, sputtering spectrum, path length distribution
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