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Backup shutdown systems proposed for future LMRs may employ discreet absorber particles to provide the negative reactivity insertion. When actuated, these systems release ACKNOWLEDGEMENT This research was performed under appointment to the Nuclear Engineering and Health Physics Fellowship Program administered by Oak Ridge Associated Universities for the U.S. Department of Energy. It has also been supported by the Rockford Technology Corporation of Vancouver, British Columbia. I am grateful to Dr. George Miley for our many hours of discussion and for his critique of the material. His advice and encouragement were instrumental in bringing this work to completion. Thanks also to Dr. Magdi Ragheb for his review and comments on the final draft. Finally, i wish to express my thankful appreciation to Dr. Barclay Jones and the staff of the Nuclear Engineering Department. Through their willing attention and cheerful assistance, they have facilitated the resolution of every problem I've encountered along the way. This supportive environment and the excellent facilities of the department were continually available to me and were frequently responsible for holding my frustration in check. v TABLE OF CONTENTS i