A STUDY OF THE VARIATIONAL PRINCIPLES OF NUCLEAR REACTOR PHYSICS
The application of the two main uses of the variational principle to reactor physics is explored. The two uses are first, to derive exact equations of motion from a stationary Lagrangian and to study the implications of the Lagrangian regarding constants of the motion, and second, to obtain approximate solutions to non-linear differential equations. Attention is restricted to diffusion theory, and hence the results are applicable only to reactors for which diffusion theory is adequate. Lagrangians for one- and two-group diffusion theory as well as one for the one-group theory including delayed neutron effects are presented and proved to be correct. From these Lagrangians the corresponding reactor Hamiltonians are found and used to determine the conjugate momenta'' and some constants of the motion for reactor diffusion theory. The implications or interpretations resultant from these constants and the conjugate momenta are discussed. The Hamilton-Jacobi equations for the one-group Hamiltonian were derived and shown to yield the expected results. Time-dependent perturbation theory is shown to be applicable to reactor problems to determine flux functions as a function of time. Variational theory is compared to the perturbation theory when carried to higher orders for the one-group case. Two-group variational theory is discussed in general terms. A modified form of variational theory which will delineate a lower bound to an eigenvalue was applied in general form to reactor problems. The standard upper bound variational theory and its lower bound form were then applied, using a one-parameter trial function, to many specific cases whose upper bounds are known from perturbation theory. Twoparameter one-group variational theory was considered. It was found that a two-parameter trial function yields quite accurate results even for heavily loaded reactors, if the poison is not too greatly concentrated. The special case of the reflected reactor was considered, and a correction to the perturbation theory determination of delta k/sub e//k/sub e/ was derived. A two-parameter variational technique was applied to this same problem and the correction required for reflected reactors is discussed. Two methods of attack, using the fourth-order differential equation and the matrix equation, on the two-group variational problem are presented. Solutions for several one- and two-parameter trial functions were determined for general poison distributions. An analytical solution for a perturbed reactor system was obtained, and the exact answer was compared with the variational answers for differential trial functions to demonstrate the validity of the method. (Dissertation Abstr.)
- Research Organization:
- Originating Research Org. not identified
- NSA Number:
- NSA-17-038511
- OSTI ID:
- 4657902
- Resource Relation:
- Other Information: Thesis. Orig. Receipt Date: 31-DEC-63
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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