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Perturbation Theory Methods and Applications
Prof. John R. White

This is my area of specialty -- or at least it was for the first 18-20 years of my career in the nuclear field. However, even though I have not been very active in this area for the last 5-6 years or so (since I have been busy doing other things), it is still one of my favorite subjects.

A complete list of all my contributions to the field of generalized perturbation theory is given in reverse chronological order in my list of publications (see the Curriculum Vitae link). Here, I have tried to categorize the various papers, reports, and student theses (including my own) into selected sub-topics that represent various areas of focus for my work over the years. For example, much of my early work was focused on the development and application of multicycle depletion perturbation theory methods (i.e. the DEPTH-CHARGE system) and/or the use of perturbation theory for cross section sensitivity and uncertainty analyses -- with a considerable amount of overlap in the two areas, of course. In the mid-1980s, much of my work was re-directed towards the subject of PWR applications -- with fuel management optimization methods as the primary application area. This lead to the development of higher-order generalized perturbation theory methods so that the desired accuracy could be achieved. The time frame from the mid 1980s to the mid 1990s was an especially productive and fun period of work, where I had a number of UMass-Lowell students involved in this work -- I really had a great group of students to work with during the period!!! I have also been involved in several specialty topics, such as the 1-D exact analytical methods developed in the mid 1980s and the contributon theory visualization techniques from the mid to late 1990s, that rounded out my overall experiences in this field. Overall this research area has been exciting and challenging, and I hope that I have not seen the end of my work in this area -- time will tell…

Again, since most of these references are quite old, electronic versions of these documents are not available. The list here simply documents my involvement in these areas of research.

Depletion Perturbation Theory -- Development and Applications
M. L. Williams, J. R. White, J. H. Marable, and E. M. Oblow, "Sensitivity Theory for Depletion Analysis," Seminar-Workshop on the Theory and Application of Sensitivity and Uncertainty Analysis, Oak Ridge, Tennessee, ORNL/RSIC-42 (Aug. 1978).

M. L. Williams, J. R. White, and T. J. Burns, "A Technique for Sensitivity Analysis of Space- and Energy-Dependent Burnup Calculations," Trans. Am. Nuc. Soc., 32, 766 (June 1979).

J. R. White and T. J. Burns, "Development and Verification of Multicycle Depletion Perturbation Theory," Trans. Am. Nuc. Soc., 34, 824 (June 1980).

J. R. White, "The Development, Implementation, and Verification of Multicycle Depletion Perturbation Theory for Reactor Burnup Analysis," Oak Ridge National Laboratory, ORNL/TM-7305 (Aug. 1980). This was also my MS Thesis at the University of Tennessee.

J. R. White, T. J. Burns, and M. L. Williams, "On the Implementation, Verification, and Application of Multicycle Depletion Perturbation Theory," Topical Meeting on Advances in Reactor Physics and Shielding, Sun Valley, Idaho (Sept. 1980).

J. R. White, "The DEPTH-CHARGE Static and Time-Dependent Perturbation/Sensitivity System for Nuclear Reactor Core Analysis," Oak Ridge National Laboratory, ORNL/CSD-78 (Sept. 1981).

J. R. White, "The DEPTH-CHARGE Static and Time-Dependent Perturbation/Sensitivity System for Nuclear Reactor Core Analysis, Revision I," Oak Ridge National Laboratory, ORNL/CSD-78R (April 1985).

Cross Section Sensitivity and Uncertainty Analyses
J. M. Kallfelz, et al., "Design and Sensitivity Analysis of a CDS-Type Heterogeneous Core," ANS Topical Meeting on Advances in Reactor Physics and Shielding, Sun Valley, Idaho (Sept. 1980).

J. R. White, "Burnup Effects in Data Sensitivity Studies," Trans. Am. Nuc. Soc., 35, 587 (Nov. 1980).

D. Biswas, J. M. Kallfelz, and J. R. White, "Depletion Analysis and Sensitivity Study of PHENIX Fuel Irradiation Experiments," Trans. Am. Nuc. Soc., 38, 673 (June 1981).

J. M. Kallfelz, E. T. Tomlinson, D. Biswas, and J. R. White, "Preliminary Analysis and Sensitivity Study of PHENIX Fuel Irradiation Experiments," Oak Ridge National Laboratory, ORNL/TM-7505 (Sept. 1981).

J. R. White and R. E. Schenter, "Analysis of the Lumped Fission Product Uncertainty in CRBR," Trans. Am. Nuc. Soc., 39, 931 (Nov. 1981).

J. H. Marable, D. G. Cacuci, C. R. Weisbin, J. R. White, D. Biswas, J. M. Kallfelz, C. C. Cowan, and R. Protsik, "Sensitivities and Uncertainties of a Large LMFBR Using Adjusted Cross Section Library ORACLE-1," Topical Meeting on Reactor Physics and Core Thermal Hydraulics, Kiamesha Lake, New York (Sept. 1982).

J. R. White, J. H. Marable, and R. E. Schenter, "Sensitivity Analysis of the Inherent Neutron Source Strength," Trans. Am. Nuc. Soc., 43, 723 (Nov. 1982).

J. R. White, J. Konovalchick, J. H. Marable, and J. L. Lucius, "Sensitivity Analysis of the Doppler Coefficient in Heterogeneous LMFBRs," Trans. Am. Nuc. Soc., 45, 769 (Nov. 1983).

Thomas F. DeLorey, "Sensitivity and Uncertainty Analysis of the High Conversion Reactor Concept," MS Thesis, Energy Engineering (Nuclear Option), University of Lowell (Dec. 1989).

J. R. White and T. F. DeLorey, "Data Uncertainty Reduction in High Converter Reactor Designs Using PROTEUS Phase II Integral Experiments," International Conference on the Physics of Reactors: Operation, Design and Computation, Marseille, France (April 1990).

T. F. DeLorey and J. R. White, "Quantifying the Void Coefficient Uncertainty in High Conversion Reactor Systems," Trans. Am. Nucl. Soc., 61, 336 (June 1990).

J. R. White and T. F. DeLorey, "Sensitivity and Uncertainty Analysis of Integral Physics Parameters in High Conversion Reactors." Nuclear Technology, 95, 129 (Aug. 1991).

LWR Core Applications -- Fuel Management Optimization
J. R. White and M. L. Williams, "Application of Time-Dependent Generalized Perturbation Theory Methods in LWR Physics Analyses," Topical Meeting on Reactor Physics and Core Thermal Hydraulics, Kiamesha Lake, New York (Sept. 1982).

J. R. White, D. M. Chapman, and D. Biswas, "Development of a GPT-Based Optimization Algorithm," Trans. Am. Nuc. Soc., 50, 83 (Nov. 1985).

David M. Chapman, "GPT-Based Fuel Management Optimization," MS Thesis, Energy Engineering (Nuclear Option), University of Lowell (Sept. 1985).

J. R. White, D. M. Chapman, and D. Biswas, "Fuel Management Optimization Based on Generalized Perturbation Theory," Topical Meeting on Advances in Fuel Management, Pinehurst, North Carolina (March 1986).

J. R. White and B. R. Frank, "Static Generalized Perturbation Theory with Feedback Effects and Criticality Reset," Trans. Am. Nuc. Soc., 53, 433 (June 1986).

J. R. White and B. R. Frank, "Generalized Perturbation Theory for LWR Depletion Analysis and Core Design Applications," Topical Meeting on Advances in Reactor Physics and Safety, Saratoga Springs, New York (Sept. 1986).

J. R. White, "Conceptual Development of a Complete LWR Reload Design Methodology Based on Generalized Perturbation Theory," PhD Dissertation, University of Tennessee, Knoxville, TN. (March 1987).

B. R. Frank and J. R. White, "Implementation of Static Generalized Perturbation Theory for LWR Design Applications," International Topical Meeting on Advances in Reactor Physics, Mathematics, and Computations, Paris, France (April 1987).

Byron R. Frank, "Implementation of Generalized Perturbation Theory for LWR Design Applications," MS Thesis, Energy Engineering (Nuclear Option), University of Lowell (April 1987).

J. R. White and K. M. Avila, "Developing Feasible Loading Patterns Using Perturbation Theory Methods," International Conference on the Physics of Reactors: Operation, Design and Computation, Marseille, France (April 1990).

Kevin M. Avila, "In-Core Fuel Management Using Linear Optimization Techniques," MS Thesis, Energy Engineering (Nuclear Option), UMass-Lowell (Jan. 1994).

Philip M. Delmolino, "Development of Generalized Adjoint Capability in a Nodal Neutronics Code," DEng Dissertation, Mechanical Engineering (Nuclear Option), UMass-Lowell (April 1996).

P. M. Delmolino and J. R. White, "Development and Testing of a Generalized Adjoint Formulation Within the Framework of an Advanced Nodal Code," Advances in Nuclear Fuel Management II, Myrtle Beach, SC (March 1997).

Higher-Order GPT Methods and Applications
J. R. White and G. A. Swanbon, "A Practical Approach to Higher Order Generalized Perturbation Theory," ANS Topical Meeting on Advances in Nuclear Engineering Computation and Radiation Shielding, Santa Fe, New Mexico (April 1989).

Glenn A. Swanbon, "The Development, Testing, and Implementation of a Second Order Correction to Generalized Perturbation Theory," MS Thesis, Energy Engineering (Nuclear Option), University of Lowell (May 1989).

J. R. White and P. M. Delmolino, "Accurate LWR Assembly Power Distributions Based on Generalized Perturbation Theory," International Conference on the Physics of Reactors: Operation, Design and Computation, Marseille, France (April 1990).

Philip M. Delmolino, "Development of a User Friendly Computer Code for Performing Fuel Reload Analysis," MS Thesis, Energy Engineering (Nuclear Option), UMass-Lowell (May 1990).

J. R. White and G. A. Swanbon, "Development of a Technique for the Practical Implementation of Higher-Order Perturbation Methods," Nuc. Sci. Eng., 105, 160 (June 1990).

J. R. White and P. M. Delmolino, "An Implicit High-Order GPT Method for LWR Reload Design Applications," Trans. Am. Nucl. Soc., 61, 159 (June 1990).

J. R. White and P. M. Delmolino, "RESCUE - A PC-Based Interactive Reload Design Tool," Trans. Am. Nuc. Soc., 62, 551 (Nov. 1990).

J. R. White, K. R. Robinson, and P. M. Delmolino, "Implicit Versus Explicit Perturbation Methods for the Efficient Evaluation of Alternative Core Designs," International Topical Meeting on Advances in Mathematics, Computations, and Reactor Physics, Pittsburgh, Pennsylvania (April 1991).

J. R. White and P. M. Delmolino, "LWR Core Design and Analysis Using the RESCUE Interactive Reload Design Tool," AI 91: Frontiers in Innovative Computing for the Nuclear Industry, Jackson, Wyoming (Sept. 1991).

Keith R. Robinson, "A Comparison of Explicit and Implicit Perturbation Methods for Use in Reactor Core Reload Optimization," MS Thesis, Energy Engineering (Nuclear Option), UMass-Lowell (April 1992).

J. R. White and P. M. Delmolino, "Simple Heuristics: A Bridge Between Manual Core Design and Automated Optimization Methods," International Conference on Mathematical Methods and Super Computing in Nuclear Applications, Karlsruhe, Germany (April 1993).

Specialty Topics
J. R. White, B. R. Frank, and J. Pappas, "Analytic Solution for the Fundamental and Higher Harmonics of the 1-D Diffusion Equation," Trans. Am. Nuc. Soc., 46, 408 (June 1984).

J. R. White, T. J. Cahill, and B. R. Frank, "Exact Analytic Solution for the Generalized Flux in 1-D Cartesian Geometry," Trans. Am. Nuc. Soc., 49, 220 (June 1985).

Thomas J. Cahill, "An Analytical Solution Technique for One-Dimensional Generalized Perturbation Theory Analyses," MS Thesis, Energy Engineering (Nuclear Option), University of Lowell (April 1986).

J. R. White and B. R. Frank, "Analytic Solutions to Several Forms of the One-Dimensional Multigroup Diffusion Equation," International Topical Meeting on Advances in Reactor Physics, Mathematics, and Computations, Paris, France (April 1987).

D. Biswas, W. P. Kovacik, and J. R. White, "Evaluation of the Delayed Neutron Importance Factor with ENDF/B-V Data," Trans. Am. Nucl. Soc., 59, 318 (June 1989).

Barbara Y. Hubbard, "The Development and Evaluation of a Shutdown Margin Estimator Using First Order Perturbation Theory," MS Thesis, Energy Engineering (Nuclear Option), University of Lowell (Dec. 1991).

Erkut Gungordu, "Visualization of Two-Dimensional Particle Transport Calculations with the Use of Generalized Contributon Theory," by MS Thesis, Energy Engineering (Nuclear Option), UMass-Lowell (Sept 1997).

Erkut Gungordu, "Visualization of Three-Dimensional Particle Transport Calculations with the Use of Generalized Contributon Theory," by PhD Dissertation, Applied Physics (Nuclear Option), UMass-Lowell (Sept. 2000).

Last updated by Prof. John R. White (January 2003)

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