Transport Theory and Spectral Problems
- Univ. of New Mexico, Albuquerque, NM (United States)
A simple model of time-independent neutron transport on a line as a stochastic process, using the method of invariant imbedding, is considered. Non-linear equations for the expected values (flux) are also obtained and solved, the results are compared with the ordinary linear theory, and possible advantages of the new formulation are cited. Generalizations to a large class of transport problems are discussed. The nonlinear time-dependent operator for transport in one dimension is considered in detail. It has a pure point spectrum, and expansion theorems can be proved. These results contrast with those for isotropic one-velocity neutron transport in the infinite slab. Here there are only a finite number of points in the point spectrum, with a half-plane in the continuous spectrum. Approximations to the eigenvalues and eigenfunctions for the slab case, as well as extensions to the multivelocity problem, are mentioned. There is a brief discussion of recent spectral and expansion theorems for very general geometries.
- Research Organization:
- Univ. of New Mexico, Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA), Nuclear Criticality Safety Program (NCSP)
- NSA Number:
- NSA-13-018477
- OSTI ID:
- 4259132
- Report Number(s):
- SCR--88
- Country of Publication:
- United States
- Language:
- English
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