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Neutron-Transport-IntroRev0

Neutron-Transport-IntroRev0 - Introduction to Neutron...

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Introduction to Neutron Transport 36

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Determination of the neutron distribution in the reactor system, leading to analysis of the fission power in the reactor. The Neutron Transport equation describes the precise behavior of in system (Boltzmann transport Eqn (BTE)). In some reactor systems, the diffusion equation offers an approximation n 1 0 to the transport equations . ”Diffusion” from high density to low density Limited validity. mfp for materials t 1 are 0(cm) also, PWR fuel pins <0(cm) Neutron Transport equation fully describes neutron population elegantly. But it is difficult to solve by hand! we define a number of simplifying assumptions to make it treatable. Transport common sense... Neutron diffusion has been used for years to solve for neutron population; but it is inaccurate in places where the flux can change radically , e.g. i) where two different materials meet ii) strong absorbers (control rods) iii) boundary of system 37
Many times diffusion cross sections are “tuned” to give “transport-corrected” fluxes, rxn rates. Why? Diffusion equation is easier (cheaper) to solve. Neutron Density Consider the case where all neutrons in the system have speed v Recall the interaction frequency Consider reaction rate density t r F , # Rxns in about r d 3 r at time t r d t r r d t r N v r d t r F 3 3 3 , , , (D&H p.105, Eq 4-3) Consider a neutron traveling with speed v Recall that the direction is ˆ E v m n 2 2 1 so 2 1 2 m E v 38

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Angular Neutron Density “Vector” Angular current density: t E r t E r n v t
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Neutron-Transport-IntroRev0 - Introduction to Neutron...

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