TIME-DEPENDENT NEUTRON TRANSPORT. Thesis
The space and time dependence of the flex in onedimensional slab geometry is considered for nonmultiplying media. Time dependent approximations to the neutron transport equation, using a group representation for the energy dependence, were examined and are discussed. A formal, non-separable solution was obtained for slab geometry for diffusion theory, P/sub 1/ and DP/sub O/ approximations. An infinite sized medium and a finite sized medium subject to the boundary condition of zero flax at the extrapolated boundary were both considered. Homogeneous solutions and solutions due to arbitrary sources were obtained using the Laplace transform and Green's functions. A formulation of the problem is presented for P/sub 3/ theory. For the infinite sized medium diffusion theory and P/sub 1/ approximation solutions were compared and the wave- front corrections to diffusion theory are given and discussed. Eigenfunctions containing a separated real exponential time dependence were found for the P and the double P/sub L/ approximations. These solutions do not always form an infinite set. It is shown that solutions of this form do not exist in higher order approximations for slabs of small enough width. The solutions given by some low order approximations in these cases were of questionable significance. For these systems the higher approximations yield complex eigenvalues and give rise to traveling waves. The total number of eigenvalues was seen to increase with the order of the approximations in order to fit the more general initial conditions demanded by the higher order equations. In addition, for limiting cases, the eigenvalues are given as simple functions of the lifetimes for elementary processes. Some particularly interesting cases arise when an energy group is wealuly coupled to other groups. Also some aspects of simple lattices were treated by single thermal group theory. Application to and interpretations of lifetime and spectrum experiments in water and beryllium were used as numerical examples of hydrogenous and crystalline media. The influence of boundary conditions on the eigenvalues of the higher buckling modes is pointed out. (Dissertation Abstr., 24: No. 4, Oct. 1983.)
- Research Organization:
- Originating Research Org. not identified
- NSA Number:
- NSA-18-004523
- OSTI ID:
- 4131192
- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-64
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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