Time-dependent Behavior of the Neutron Flux with Delayed Neutrons Neglected

1 Time-dependent Behavior of the Neutron Flux with Delayed Neutrons Neglected 

Apart from this limitation, the principal restriction in the use of the Fermi age model is due to the large number of conditions which must be satisfied by the physical system if the model is to be valid (see Sec. 7.3i). However, even with this shortcoming, the model is still very useful for preliminary studies and for gaining insight into the essential features of many reactor problems. The Fermi age or continuous-slowing-down diffusion theory, then, offers some generality without introducing excessive computational difficulties. 

The appropriate time-dependent differential equations for the com-bined-slowing-down diffusion theory may be obtained by recognizing that the time rate of change of the neutron density is given by the difference between the rates of disappearance and appearance of neutrons from sinks and sources. Thus we write 

The various functions which appear in these relations are defined by 

4 TyUyt) = neutron flux per unit lethargy around r at time t S TyUyi) = number of neutrons produced by sources per unit volume per unit lethargy per unit time around (r,z ) at time t q TyUyt) = number of neutrons slowing down past lethargy u per unit volume per unit time around (TyU) at time t nth Tyi) = number of neutrons of thermal speed per unit volume around r at time t 

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