Neutron, balance equation thermal

The thermal-neutron balance equation for the reference design condition states that the rate of production of thermal neutrons equals the rate of consumption ... 

We are now in position to derive equations that will give the degree uf bumup nuclear fuel can experience before it ceases to be critical. First, we must determine how the concentration of each nuclide that affects the neutron balance changes with time. We consider fuel that at time zero contains N s atoms of U per cubic centimeter, atoms of U, and no other uranium isotopes, plutonium, or fission products. This fuel is then exposed to a thermal-neutron flux 0(0, which may be a function of time. The variation in concentration of each nuclide in this fuel with time is obtained as follows. 

Equation (4.5) may be put in another form by introducing the neutron balance condition for the critical reactor. The production rate of thermal neutrons, which is given by the product rjaL25 P is equal to the thermal neutron loss rate due to absorption in U , moderator, and fission product poisons, and to leakage. Hence,... 

The exact form of the solution is strongly dependent on the geometry. It can be shown that for a large subcritical assembly the thermal-neutron balance in a region far from the source, where essentially all the neutrons have resulted from fissions, can be represented by equation (l) with the source term S(r) equal to zero. The wave equation for the flux distribution is given to a good approximation by... 

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