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Title: Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?

Abstract

The power iteration method is the standard Monte Carlo approach for obtaining the eigenfunctions of a nuclear system, but the power method sometimes converges very slowly. Most discussions give a mathematical reason for the slow convergence of the Monte Carlo power method using the same concepts and terminology as when the power method is applied to a deterministic problem. This note first looks at why the convergence is slow from an intuitive Monte Carlo neutron perspective. Second, this note proposes building an eigenfunction intuitively in a cumulative (and noniterative) neutron by neutron manner that tends to better direct neutrons to where the neutrons need to be. Third, a very similar method for building the second eigenfunction is speculatively proposed.

Authors:
 [1]
  1. Los Alamos National Laboratory
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
DOE/LANL
OSTI Identifier:
1043017
Report Number(s):
LA-UR-12-21928
TRN: US1203078
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; EIGENFUNCTIONS; NEUTRONS

Citation Formats

Booth, Thomas E. Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?. United States: N. p., 2012. Web. doi:10.2172/1043017.
Booth, Thomas E. Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?. United States. doi:10.2172/1043017.
Booth, Thomas E. Tue . "Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?". United States. doi:10.2172/1043017. https://www.osti.gov/servlets/purl/1043017.
@article{osti_1043017,
title = {Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?},
author = {Booth, Thomas E},
abstractNote = {The power iteration method is the standard Monte Carlo approach for obtaining the eigenfunctions of a nuclear system, but the power method sometimes converges very slowly. Most discussions give a mathematical reason for the slow convergence of the Monte Carlo power method using the same concepts and terminology as when the power method is applied to a deterministic problem. This note first looks at why the convergence is slow from an intuitive Monte Carlo neutron perspective. Second, this note proposes building an eigenfunction intuitively in a cumulative (and noniterative) neutron by neutron manner that tends to better direct neutrons to where the neutrons need to be. Third, a very similar method for building the second eigenfunction is speculatively proposed.},
doi = {10.2172/1043017},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2012},
month = {6}
}

Technical Report:

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