#### Presentation Title

Strongly Stochastic Neutron Populations in Multiplying Systems With Weak Sources

#### Start Date

8-11-2017 8:30 AM

#### End Date

8-11-2017 12:30 PM

#### Abstract

The neutron population in multiplying systems containing a weak random source departs significantly from its 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 for describing preinitation of neutron bursts in pulsed nuclear reactors and for assessing criticality excursions, both in the presence of a weak neutron source. Weak sources lead to well separated neutron chains in which some chains are short lived while others propagate for unusually long times, leading to large fluctuations in the neutron population. The fate of individual chains then plays a defining role in the evolution of the neutron population in strongly stochastic systems, and of particular interest and importance in supercritical systems is the extinction probability, defined as the probability that the neutron chain will be extinguished at a particular time, or its complement, the time-dependent survival probability. The time-asymptotic limit of the latter, the probability of divergence, gives the probability that the neutron population will grow without bound. The ability to numerically compute these probabilities, with high accuracy and without introducing overly restrictive physical approximations is essential in developing an understanding of the behavior of strongly stochastic systems. Here we use the theory of discrete-state continuous-time Markov processes to develop forward and backward Master Equation models for the probability distribution of neutron numbers, in both lumped and unlumped (full phase-space) settings. Approximate closed form solutions are obtained for the number distributions and benchmarked against Monte Carlo simulations of the neutron population. In the phase space case, an eigenfunction expansion approach is used to demonstrate significant increase in efficiency for computing the neutron survival probability over direct solution of the nonlinear backward Master equation.

Strongly Stochastic Neutron Populations in Multiplying Systems With Weak Sources

The neutron population in multiplying systems containing a weak random source departs significantly from its 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 for describing preinitation of neutron bursts in pulsed nuclear reactors and for assessing criticality excursions, both in the presence of a weak neutron source. Weak sources lead to well separated neutron chains in which some chains are short lived while others propagate for unusually long times, leading to large fluctuations in the neutron population. The fate of individual chains then plays a defining role in the evolution of the neutron population in strongly stochastic systems, and of particular interest and importance in supercritical systems is the extinction probability, defined as the probability that the neutron chain will be extinguished at a particular time, or its complement, the time-dependent survival probability. The time-asymptotic limit of the latter, the probability of divergence, gives the probability that the neutron population will grow without bound. The ability to numerically compute these probabilities, with high accuracy and without introducing overly restrictive physical approximations is essential in developing an understanding of the behavior of strongly stochastic systems. Here we use the theory of discrete-state continuous-time Markov processes to develop forward and backward Master Equation models for the probability distribution of neutron numbers, in both lumped and unlumped (full phase-space) settings. Approximate closed form solutions are obtained for the number distributions and benchmarked against Monte Carlo simulations of the neutron population. In the phase space case, an eigenfunction expansion approach is used to demonstrate significant increase in efficiency for computing the neutron survival probability over direct solution of the nonlinear backward Master equation.