Fermi age

The lattice mimtlon area deduced from an exponential experiment Is 6k6 cv (see Section 2.6 2) this Is separable Into a.Fermi age ( t and a diffusion area (L ) of l60 cm at room teoqperature At operating tempera-ture Increases by 109.  

The age of neutrons in a heterogeneous reactor and particularly N Reactor Is not readily calculable with any precision. The complex stzuctuxe of the R moderator and the large amount of water in the N lattice make the calculation of difficult. The Farml age may be estimated by the equation 

Dhe sum. over 1 is over all lattice cell regioi the sum over Is over only moderator cell regioiais and the sum k Is over o non-moderator cell regions  

The aiUAtities and i, g have been defined previously and the r ji s are the ages to thermal for each moderator Inelastic scattering In the ure um fuel must be considered and the ZT s are given by 

The coUlslon probability Pg is the fast neutron collision probability in the fuel and can be obtained from previously defined quantities. 

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Derivation of the Fermi age equation. The Boltzmann equation is an integro-dififerential equation involving distance, energy and directional variables. By making suitable approximations we shall now proceed to reduce this equation to a set of coupled differential equations in which the spatial coordinates are the only independent variables. These are the so-called multigroup diffusion equations. But first we discuss the so-caUed age theory. 

This last equation is known as the Fermi age diffusion equation. It is a partial differential equation involving only spatial and lethargy coordinates. In any region where the material properties (in particular fiTr) are constant, we may also write... 

Fermi age equation (3.3) and integrate over a lethargy interval uj,Uj+ ). We find that... 

In order to illustrate the numerical problems involved, I will restrict myself to a discussion of the Fermi age-diffusion equation for the neutron flux (f)(r,u) ... 

This error is attributable to two sources The Fermi age calculation in metal-water mixtures by the moments method spears to give values lower than experimentally observed and calculations of thermal utilization by the one-group Ps method results in high values. Both effects contribute in varying amounts to the overestimate of buckling however, the trends are predictable and the overall calculatlan is sufficiently accurate for criticality control purposes. 

The variation in the Fermi age, T, vith graphite temperature arises from the fact that the neutrons have to slow down over a smaller energy range as the neutron temperature increases. The coefficient is small and positive and for a hetereogeneous reactor is difficult to calculate. For these reasons it can be neglected. 

The differential equation (6.19) may be reduced to a more elementary form by applying a Laplace transform ( ) to the Fermi age variable r. 

The linear dependence of the average r u) on r u) is a general result. The constant of proportionality is determined by the source distribution. Thus, in general, the square root of the Fermi age is a measure of the slowing-down length of a neutron. 

Better to demonstrate some of the suggestions on the use of the Fermi age model, let us consider the problem of determining the critical size and minimum fuel mass of a uniform bare reactor. For simplicity, assume that the basic constituents fuel, moderator, structure, and coolant have all been selected and an estimate of the relative proportions of these materials in the reactor is available. Our problem is to find the dimensions of the reactor with these basic characteristics which has the smallest fuel mass. The procedure is straightforward and involves the calculation of a number of systems each of different size. 

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