A Semianalytical Analysis of Transient Supercritical Assembly Extinction Probabilities

References

• L. PÁL, “On the Theory of Stochastic Processes in Nuclear Reactors,” Il Nuovo Cimento, Suppl. VII, 25 (1958).
   Google Scholar
• L. PÁL, “Statistical Theory of Neutron Chain Reactions,” Proc. 3rd Int. Conf. Peaceful Uses of Atomic Energy, Geneva, Switzerland, August 31–September 9, 1964, Vol. 2, p. 218, International Atomic Energy Agency (1964).
   Google Scholar
• L. PÁL, “Neutron Noise and Random Trees: Links Between Past and Present,” Prog. Nucl. Energy, 43, 5 (2003).
   Web of Science ®Google Scholar
• G. I. BELL, “On the Stochastic Theory of Neutron Transport,” Nucl. Sci. Eng., 21, 390 (1965).
   Web of Science ®Google Scholar
• G. I. BELL, “Stochastic Formulations of Neutron Transport,” Proc. Transport Theory Symp. Applied Mathematics, New York, 1967.
   Google Scholar
• G. I. BELL and C. E. LEE, “On the Probability of Initiating a Persistent Fission Chain,” LA-2608 (DEL), Los Alamos National Laboratory (1976).
   Google Scholar
• D. R. HARRIS, “Neutron Fluctuations in a Reactor of Finite Size,” Nucl. Sci. Eng., 21, 369 (1965).
   Web of Science ®Google Scholar
• S. P. FRANKEL, “The Statistics of the Hypocritical Gadget,” LAMS-36 (Series C), Los Alamos National Laboratory (1948).
   Google Scholar
• D. HAWKINS and S. ULAM, “Theory of Multiplicative Processes, I,” LA-171, Los Alamos National Laboratory (1944).
   Google Scholar
• W. M. STACEY, Space-Time Nuclear Reactor Kinetics, Academic Press, New York (1970).
   Google Scholar
• R. SANCHEZ, “An Analysis of the Stochasticity of the Transport Equation,” Transp. Theory Stat. Phys., 26, 4&5, 469 (1997).
   Google Scholar
• M. M. R. WILLIAMS, “The Extinction Problem in a Super-Critical Sphere of Fissile Material,” Ann. Nucl. Energy, 31, 933 (2004).
   Web of Science ®Google Scholar
• J. MUÑOZ-COBO, R.B. PEREZ, and G. VERDU, “Stochastic Neutron Transport Theory: Neutron Counting Statistics in Nuclear Assemblies,” Nucl. Sci. Eng., 95, 83 (1987).
   Web of Science ®Google Scholar
• G. I. BELL, “Probability Distribution of Neutrons and Precursors in a Multiplying Assembly,” Ann. Phys. (N.Y.), 21, 243 (1963).
   Web of Science ®Google Scholar
• F. NORELLI, V. M. JORIO, and N. PACILIO, “Stochastic Kinetics: Analytical Solutions of Detailed Probability Balance Equations,” Ann. Nucl. Energy, 2, 67 (1975).
   Web of Science ®Google Scholar
• M. ASH, Nuclear Reactor Kinetics, McGraw-Hill, New York (1965).
   Google Scholar
• R. P. FEYNMAN, “Statistical Behavior of Neutron Chains,” LA-591 (DEL), Los Alamos National Laboratory (1946).
   Google Scholar
• D. R. HARRIS, “Analysis of Reactor Fluctuations,” Trans. Am. Nucl. Soc., 4, 317 (1961).
   Google Scholar
• G. E. HANSEN, “Assembly of Fissionable Material in the Presence of a Weak Neutron Source,” Nucl. Sci. Eng., 8, 709 (1960).
   Web of Science ®Google Scholar
• J. G. HAYES and E. J. ALLEN, “Stochastic Point-Kinetics Equations in Nuclear Reactor Dynamics,” Ann. Nucl. Energy, 32, 572 (2005).
   Web of Science ®Google Scholar
• G. I. BELL, W. A. ANDERSON, and D. GALBRAITH, “Probability Distribution of Neutrons and Precursors in Multiplying Medium, II,” Nucl. Sci. Eng., 16, 118 (1963).
   Web of Science ®Google Scholar
• H. HURWITZ, Jr., “Kinetics of Low Source Reactor Startups. Part I,” Nucl. Sci. Eng., 15, 166 (1963).
   Web of Science ®Google Scholar
• H. HURWITZ, Jr., “Kinetics of Low Source Reactor Startups. Part II,” Nucl. Sci. Eng., 15, 187 (1963).
   Web of Science ®Google Scholar
• D. B. MACMILLAN and M. L. STORM, “Kinetics of Low Source Reactor Startups—Part III,” Nucl. Sci. Eng., 16, 369 (1963).
   Web of Science ®Google Scholar
• G. A. CAMPBELL, V. CHAN, and J. D. LEWINS, “An Exact Special Case Solution of the Neutron Stochastic Equations at Low Power,” Ann. Nucl. Energy, 8, 1 (1981).
   Google Scholar
• S. D. NOLEN, “The Chain-Length Distribution in Subcritical Systems,” LA-13721-T, Los Alamos National Laboratory (2000).
   Google Scholar
• W. L. MYERS, “A Stochastic, Four Energy Group Model of a Nuclear Assembly,” PhD Thesis, University of Illinois at Urbana-Champaign (1995).
   Google Scholar
• S. D. RAMSEY, “The Extinction Probabilities of Nuclear Assemblies: A Sensitivity Study,” PhD Thesis, University of Illinois at Urbana-Champaign (2009).
   Google Scholar
• J. L. HILL, “Advances in the Theory of Persistent Neutron Chains,” PhD Thesis, University of Illinois at Urbana-Champaign (1998).
   Google Scholar
• J. D. LEWINS, “Variational Method in Neutron Stochastics,” Ann. Nucl. Energy, 5, 141 (1978).
   Google Scholar
• F. CARLONI and M. MARSEGUERRA, “Influence of the Quadratic Approximation on the Moments of the Neutron and Count Distributions in a Multiplying System,” Ann. Nucl. Energy, 6, 327 (1979).
   Google Scholar
• M. M. R. WILLIAMS, “An Exact Solution of the Extinction Problem in Supercritical Multiplying Systems,” Ann. Nucl. Energy, 6, 463 (1979).
   Google Scholar
• J. D. LEWINS, “Stochastic Distribution of Prompt Neutrons in a Super-Critical Reactor,” Ann. Nucl. Energy, 8, 15 (1981).
   Google Scholar
• G. T. PARKS and J. D. LEWINS, “An Exact Transient Stochastic Solution for Low-Power Neutron Multiplication,” Ann. Nucl. Energy, 12, 2, 65 (1985).
   Google Scholar
• G. D. SPRIGGS, R. D. BUSCH, K. J. ADAMS, D. K. PARSONS, L. PETRIE, and J. S. HENDRICKS, “On the Definition of Neutron Lifetimes in Multiplying and Non-Multiplying Systems,” LA-UR-97-1073, Los Alamos National Laboratory (1997).
   Google Scholar
• N. E. HOLDEN and M. S. ZUCKER, “A Re-Evaluation of the Average Prompt Neutron Emission Multiplicity (Nubar) Values from Fission of Uranium and Transuranium Nuclides,” BNL-NCS-35513-R, Brookhaven National Laboratory (1986).
   Google Scholar