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Benchmarking the invariant embedding method against analytical solutions in model transport problems

Malin Wahlberg (Institutionen för teknisk fysik, Nukleär teknik) ; Imre Pázsit (Institutionen för teknisk fysik, Nukleär teknik)
Nuclear Technology and Radiation Protection (1451-3994). Vol. 21 (2006), 2, p. 3 - 13 .
[Artikel, refereegranskad vetenskaplig]

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 cross sections 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 half-space are interrelated through embedding-like integral equations, by the solution of which the flux reflected from a half-space can be reconstructed 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.

Nyckelord: Invariant embedding, reflected flux, sputtering, path length distribution, analytical solutions, transport theory.

Denna post skapades 2007-01-08. Senast ändrad 2014-09-02.
CPL Pubid: 24980


Institutioner (Chalmers)

Institutionen för teknisk fysik, Nukleär teknik (2006-2015)


Atom- och molekylfysik och optik
Matematisk fysik

Chalmers infrastruktur