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The time-dependent P1 model for the neutronics of multiplying systems: a review

G. G. M. Coppa, S. Dulla and P. Ravetto
From the journal Kerntechnik

Abstract

The derivation of the time-dependent P1 model by the spherical harmonics expansion approach to solve the neutron transport equation is reviewed and its main features and physical characteristics are illustrated. The telegrapher's equation is presented and its formulation for multiplying systems is discussed. In particular, it is evidenced that the presence of a time derivative of the source terms in the telegrapher's equation implies the appearance of time derivatives of the flux and of the precursor concentrations. The role of these terms is evaluated and discussed.

Kurzfassung

Das zeitabhängige P1 Modell für das neutronische Verhalten in multiplizierenden Systemen: eine Übersicht. Die Ableitung des zeitabhängigen P1 Modells mit Hilfe der sphärischen harmonischen Expansion zur Lösung der Neutronentransportgleichung wird bewertet und die wichtigsten Merkmale und physikalischen Eigenschaften werden erläutert. Die Telegraphengleichung wird vorgestellt und ihre Formulierung für multiplizierende Systeme diskutiert. Insbesondere wird nachgewiesen, dass das Vorhandensein einer Zeitableitung des Quellterms bei der Telegraphengleichung das Auftreten von Zeitableitungen des Flusses und der Dichte der Vorläuferkerne impliziert. Die Bedeutung dieser Terme wird bewertet und diskutiert.

References

1 Merk, B.: An analytical approximation solution for a time-dependent neutron transport problem with external source and delayed neutron production, Nuclear Science and Engineering, 161 (2009) 4967 Search in Google Scholar

2 Merk, B.: An analytical solution for a one dimensional time-dependent neutron transport problem with external source, Transport Theory and Statistical Physics, 37 (2009) 535549 Search in Google Scholar

3 Dulla, S.; Ganapol, B. D.; Ravetto, P.: Space asymptotic methods for the study of neutron propagation, Annals of Nuclear Energy, 33 (2006) 93294010.1016/j.anucene.2006.04.001 Search in Google Scholar

4 Dulla, S.; Ravetto, P.: Numerical aspects in the study of neutron propagation, Annals of Nuclear Energy, 35 (2008) 65666410.1016/j.anucene.2007.08.009 Search in Google Scholar

5 Weinberg, A. M.; Wigner, E. P.: The physical theory of neutron chain reactors, University of Chicago Press, Chicago (1958) Search in Google Scholar

6 Di Pasquantonio, F.: Propagation of monokinetic neutron waves in dissipative media, Energia Nucleare, 9 (1964) 465494 Search in Google Scholar

7 Mortensen, G. A.; Smith, H. P.: Neutron wave propagation using the P1 approximation, Nuclear Science and Engineering, 22 (1965) 321327 Search in Google Scholar

8 Coppa, G.; Corno, S. E.; Ravetto, P.: Analytical solution and physical interpretation of the P-1 approximation in local reactor dynamics, Energia Nucleare, 27 (1980) 92108 Search in Google Scholar

9 Mark, C.: The neutron density near a plane surface, Physical Review, 72 (1947) 558564 Search in Google Scholar

10 Marshak, R. E.: Note on the spherical harmonic method as applied to the Milne problem for a sphere, Physical Review, 71 (1947) 558564 Search in Google Scholar

11 Meghreblian, R. V.; Holmes, D. K.: Reactor analysis, McGraw-Hill, New York (1960) Search in Google Scholar

12 Davison, B.: Neutron transport theory, Clarendon Press, Oxford (1968) Search in Google Scholar

13 Morse, P. M.; Feshbach, H.: Methods of theoretical physics, McGraw-Hill, New York, (1953) Search in Google Scholar

14 Shin, U.; MillerJr., W. F.; Morel, J. E.: Asymptotic analysis of the several competitive equations to solve the time-dependent neutron transport equation, Proceedings of the International Conference on Mathematics and Computations, Reactor Physics, and Environmental Analyses, Portland (1995) Search in Google Scholar

Received: 2010-2-15
Published Online: 2013-04-05
Published in Print: 2010-08-01

© 2010, Carl Hanser Verlag, München