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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


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.


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.


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

© 2010, Carl Hanser Verlag, München