Some Considerations on Stochastic Neutron Populations

Conference · Sun Jun 13 04:00:00 EDT 2010

OSTI ID:983920

Prinja, Anil K. ^[1]; Souto, Francisco J. ^[2]

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1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); University of New Mexico, Albuquerque, NM (United States)
2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

The neutron population in a multiplying body containing a weak random source may depart considerably from its average or expected value. The resulting behavior of the system is then unpredictable, and a fully stochastic description of the neutron population becomes necessary. Stochastic considerations are especially important when dealing with pulsed reactors or in the case of criticality excursions in the presence of a weak source. Using the theory of discrete-state continuous-time Markov processes, and subject to some physical approximations, Bell obtained approximate solutions for the neutron number probability distributions (pdf), with and without an intrinsic random neutron source, that were valid at late times and/ large neutron populations. In recent work, we obtained exact solutions for Bell's model problem, and in this paper we use these exact probability distributions to: (I) assess the accuracy of Bell's asymptotic solutions and show how the latter follow from the exact solutions, (2) rigorously examine the probability of obtaining a divergent chain reaction, and (3) demonstrate the existence of an abrupt transition from a stochastic to a deterministic phase with increasing source strength.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA), Nuclear Criticality Safety Program (NCSP)
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 983920
• Report Number(s): LA-UR--10-00264; LA-UR--10-264
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCURACY
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
Abrupt Transition Determination
Bell's Asymptotic Solutions Accuracy
CHAIN REACTIONS
CRITICALITY
Divergent Chain Reaction
EXACT SOLUTIONS
NEUTRON SOURCES
NEUTRONS
Nuclear Criticality Safety Program (NCSP)
PROBABILITY
PULSED REACTORS