Phd records
https://feeds.library.caltech.edu/people/Erdmann-R-C/Phd.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 19:05:02 +0000Time-dependent monoenergetic neutron transport in two adjacent semi-infinite media
https://resolver.caltech.edu/CaltechTHESIS:10022015-101429428
Authors: {'items': [{'id': 'Erdmann-R-C', 'name': {'family': 'Erdmann', 'given': 'Robert C.'}}]}
Year: 1966
DOI: 10.7907/00R6-9A13
<p>An exact solution to the monoenergetic Boltzmann equation is
obtained for the case of a plane isotropic burst of neutrons introduced
at the interface separating two adjacent, dissimilar, semi-infinite
media. The method of solution used is to remove the time dependence
by a Laplace transformation, solve the transformed equation by the
normal mode expansion method, and then invert to recover the time
dependence.</p>
<p>The general result is expressed as a sum of definite, multiple
integrals, one of which contains the uncollided wave of neutrons
originating at the source plane. It is possible to obtain a simplified
form for the solution at the interface, and certain numerical calculations
are made there.</p>
<p>The interface flux in two adjacent moderators is calculated and
plotted as a function of time for several moderator materials. For
each case it is found that the flux decay curve has an asymptotic slope
given accurately by diffusion theory. Furthermore, the interface current
is observed to change directions when the scattering and absorption
cross sections of the two moderator materials are related in a
certain manner. More specifically, the reflection process in two
adjacent moderators appears to depend initially on the scattering
properties and for long times on the absorption properties of the media.</p>
<p>This analysis contains both the single infinite and semi-infinite
medium problems as special cases. The results in these
two special cases provide a check on the accuracy of the general
solution since they agree with solutions of these problems obtained
by separate analyses.</p>
https://thesis.library.caltech.edu/id/eprint/9192