The joint probability distribution function for transport in a random medium
- Univ. of New Mexico, Albuquerque, NM (United States)
In a recent paper, the transport of neutral particles in the presence of randomly fluctuating cross sections was considered in one-dimensional rod geometry. Specifically, the total cross section was assumed to exhibit Gaussian distributed fluctuations about a mean value with an otherwise arbitrary spatial correlation function, and the object of the investigation was to construct exact equations for the ensemble averaged forward and backward components of the angular flux. Exact closure was possible only in semi-infinite rods, in which case the scalar flux was shown to satisfy a renormalized diffusion-drift equation. It was concluded that fluctuations have an antidamping effect by lowering the effective absorption. Furthermore, in this geometry, an exactly closed Fokker-Planck equation was derived for the joint probability distribution function (pdf) P({phi},J,x) for the scalar flux {phi} and current J evolving with distance x. An exact solution to this equation was not possible at the time, and analysis was restricted to the second order moments of {phi} and J as well as the correlation between them. In this paper, the author shows that the Fokker-Planck equation can indeed by solved exactly once a crucial, general simplifying observation is made.
- OSTI ID:
- 426401
- Report Number(s):
- CONF-961103--
- Journal Information:
- Transactions of the American Nuclear Society, Journal Name: Transactions of the American Nuclear Society Vol. 75; ISSN TANSAO; ISSN 0003-018X
- Country of Publication:
- United States
- Language:
- English
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