Generalized perturbation theory using twodimensional, discrete ordinates transport theory
Abstract
Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using twodimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions GAMMA and GAMMA*. Demonstration calculations were performed for changes in a reactionrate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions.
 Authors:
 Publication Date:
 Research Org.:
 Oak Ridge National Lab., TN (USA)
 OSTI Identifier:
 5261569
 Report Number(s):
 ORNL/CSD/TM127
TRN: 80013535
 DOE Contract Number:
 W7405ENG26
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 22 GENERAL STUDIES OF NUCLEAR REACTORS; REACTOR KINETICS; PERTURBATION THEORY; NEUTRON FLUX; POWER DENSITY; REACTIVITY WORTHS; TWODIMENSIONAL CALCULATIONS; KINETICS; RADIATION FLUX; 220100*  Nuclear Reactor Technology Theory & Calculation
Citation Formats
Childs, R.L. Generalized perturbation theory using twodimensional, discrete ordinates transport theory. United States: N. p., 1980.
Web. doi:10.2172/5261569.
Childs, R.L. Generalized perturbation theory using twodimensional, discrete ordinates transport theory. United States. doi:10.2172/5261569.
Childs, R.L. Sun .
"Generalized perturbation theory using twodimensional, discrete ordinates transport theory". United States.
doi:10.2172/5261569. https://www.osti.gov/servlets/purl/5261569.
@article{osti_5261569,
title = {Generalized perturbation theory using twodimensional, discrete ordinates transport theory},
author = {Childs, R.L.},
abstractNote = {Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using twodimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions GAMMA and GAMMA*. Demonstration calculations were performed for changes in a reactionrate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions.},
doi = {10.2172/5261569},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Jun 01 00:00:00 EDT 1980},
month = {Sun Jun 01 00:00:00 EDT 1980}
}

Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using twodimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions ..lambda.. and ..lambda..*. Demonstration calculations were performed for changes in a reactionrate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed tomore »

Exponential characteristic spatial quadrature for discrete ordinates neutral particle transport in twodimensional cartesian coordinates. Doctoral thesis
The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport with rectangular cells is developed. Numerical problems arising in the derivation required the development of exponential moment functions. These functions are used to remove indeterminant forms which can cause catastrophic cancellations. The EC method is positive and nonlinear. It conserves particles and satisfies first moment balance. Comparisons of the EC method's performance to other methods in optically thin and thick spatial cells were performed. For optically thin cells, the EC method was shown to converge to the correct answer, with third order truncation error in the thin cell limit.more »