First-flight transport model

For the cases to which the first-flight transport model is applicable, there is a relation between the transmission coefficient a and the over-all self-shielding factor/o this is... 

If it is appropriate to use the first-flight transport model for the material of this sphere, then Eq. (5.303) may be used for a, and we have finally [using Eqs. (5.338) and (5.344) for 3D, and denoting moderator quantities by the index M and absorber quantities by the index A]... 

Application of Diffusion Approximation for Current from Moderator to Absorber, (a) Diffusion theory applicable to both moderator and absorber Here we drop the restrictive assumption of an isotropic flux incident upon the absorber and consider the angular distribution given in Eq. (5.334) which is appropriate to the diffusion approximation. We consider first the results when diffusion theory is also assumed to hold in the absorber region and subsequently discuss the first-flight transport model for the absorber. 

It is of some interest to compare the results for a using the diffusion-theory and first-flight transport models for a thin fuel plate. These are found to be, with 2a2/ [Pg.653]

The use of this model involves the choice of the proper a from Sec. 5.8a, on the basis of either the diffusion approximation or the first-flight transport approximation, depending on the nature of the absorber. It should not be expected to give good results in cases where the angular distribution in the moderator, near the lump, differs appreciably from isotropic, as it would, for example, near a small, highly absorbing lump. 

About the turn of the century cuid shortly thereafter, certain developments in mathematical physics and in physical chemistry were realized which were to prove important in the theory of mass and charge transport in solids, later. Einsteinand Smoluchowski( ) initiated the modern theory of Brownian motion by idealizing it as a problem in random flights. Then some seventeen years or so later, Joffee A proposed that interstitial defects could form inside the lattice of ionic crystals and play a role in electrical conductivity. The first tenable model for ionic conductivity was proposed by Frenkel, who recognized that vaccin-cies and interstitials could form internally to account for ion movement. 

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