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Stochastic equations in the invariant imbedding formulation of particle transport

Shashikant Degweker (Institutionen för teknisk fysik, Nukleär teknik) ; Imre Pázsit (Institutionen för teknisk fysik, Nukleär teknik)
Annals of Nuclear Energy (0306-4549). Vol. 36 (2009), 8, p. 1108-1119.
[Artikel, refereegranskad vetenskaplig]

Invariant imbedding theory is an alternative formulation of particle transport theory. Although stochastic foundations of invariant imbedding have been known from the beginnings, the method itself has so far exclusively been used for calculating first moments, i.e. expectations. The present paper attempts to set up a probability balance equation in the invariant imbedding approach from which equations for the first and second order densities are derived. It is shown that only the equations for the first order densities are non-linear, while subsequent order densities obey linear equations. This is expected to considerably simplify solution to those problems which involve second order density calculations where invariant imbedding techniques may be profitably used. Examples of such quantities are the variance or correlations between particles detected at two different energies or angles or the higher moments of the emitted multiplicity distribution such as the variance from a target bombarded by incident particles. One possible area of application of our equations is non-destructive estimation of fissile material by the active neutron assay technique. Another area is the study of particle cascade development in sputtering and positron backscattering from surfaces. The approach is illustrated by a simple forward–backward scattering model for these two problems.

Nyckelord: Invariant imbedding, transport theory, particle fluctuations, stochastic theory, sputtering



Denna post skapades 2009-12-20. Senast ändrad 2014-09-02.
CPL Pubid: 104452

 

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Institutioner (Chalmers)

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

Ämnesområden

Statistisk fysik
Annan fysik
Matematisk fysik
Övrig teknisk fysik

Chalmers infrastruktur