Stochastic equations in the invariant imbedding formulation of particle transport

• Invariant imbedding theory is an alternative formulation of particle transport theory. Although stochasticfoundations of invariant imbedding have been known from the beginnings, the method itself has so farexclusively been used for calculating first moments, i.e. expectations. The present paper attempts toset up a probability balance equation in the invariant imbedding approach from which equations forthe first and second order densities are derived. It is shown that only the equations for the first order densitiesare non-linear, while subsequent order densities obey linear equations. This is expected to considerablysimplify solution to those problems which involve second order density calculations whereinvariant imbedding techniques may be profitably used. Examples of such quantities are the varianceor correlations between particles detected at two different energies or angles or the higher momentsof 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 bythe active neutron assay technique. Another area is the study of particle cascade development in sputteringand positron backscattering from surfaces. The approach is illustrated by a simple forward–backwardscattering model for these two problems.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Annan teknik -- Övrig annan teknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Other Engineering and Technologies -- Other Engineering and Technologies not elsewhere specified (hsv//eng)

NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

Nyckelord

particle fluctuations

stochastic theory

sputtering

transport theory

Invariant imbedding

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