## Nuclear Engineering ETDs

#### Publication Date

7-8-2009

#### Abstract

Sandia National Laboratories has successfully operated fast burst reactors over the past four decades. Fast burst reactors refer to a type of reactor that is able to achieve intense neutron pulses in very short periods of time using fissile material. Typically these systems are comprised of enriched metallic uranium fuel. During operation of a fast burst reactor, a phenomena known as a pre-initiation has been known to take place. A pre-initiation occurs when the neutron population exceeds some fiducial prior to achieving the final reactivity state in a pulse operation. Reactivity is determined from the physical configuration of the reactor and governs the average neutron population behavior. The purpose of this study is to examine the probability of initiation (or the pre-initiation probability) for a fast burst type of system, with emphasis on the Sandia Pulse Reactor-III (SPR-III) for physics parameters. The magnitude of the pre-initiation problem for SPR-III was examined to establish the magnitude of the phenomena. This work focuses on developing and numerically solving an equation that describes the non-extinction probability in a prompt critical assembly when the population is so low that it deviates from the average behavior. A zero dimensional (0-D) model is derived to describe the neutron non-extinction probability in a system where the reactivity is changing as a function of time. Analytical solutions to the model are provided where solutions could be found. Numerical solutions were obtained for a variety of cases applicable to fast burst reactor operation. Use of 0-D Monte Carlo techniques is also presented as a means to examine the low population stochastic behavior and for comparison to the deterministic solution. The 1-D time dependent equation for slab geometry was evaluated to highlight the importance of neutron leakage. The non-extinction probability equation was solved using a modified form of the standard fixed point iteration method. Other iteration techniques were also analyzed. Particular emphasis was extended to a linearized routine since the performance can be analyzed analytically and it allows for development of acceleration techniques. An accelerated routine was then developed and analyzed. The numerical performance between the iteration routines was thoroughly investigated. The impact of the acceleration routine on the iteration count and the associated decrease in runtime was evaluated.

#### Keywords

Pulsed reactors--Mathematical models., Nuclear reactors--Reactivity--Mathematical models., Nuclear reactor kinetics--Mathematical models.

#### Sponsors

Sandia National Laboratories

#### Document Type

Dissertation

#### Language

English

#### Degree Name

Nuclear Engineering

#### Level of Degree

Doctoral

#### Department Name

Nuclear Engineering

#### First Advisor

Prinja, Anil

#### First Committee Member (Chair)

Cooper, Gary

#### Second Committee Member

Ueki, Taro

#### Third Committee Member

Coutsias, Evangelos

#### Recommended Citation

Gregson, Michael. "Time dependent non-extinction probability for fast burst reactors." (2009). https://digitalrepository.unm.edu/ne_etds/50