Equation (1.3) is still space and time dependent even though the energy dependence can be averaged out by a judicious choice of the diffusion coefficient D. The main space dependent term is eliminated if the flux shape is assumed to remain constant as far as leakage is concerned during the kinetic calculation. The critical distribution derived from Fermi age theory

(3) may be assumed:

ГЦ = — ВЦ (1.9)

where В2 is the geometric buckling.

Then, with the following mathematical transformations

L2 = 2>/Га, /„ = 1/t;Г„ l* = /„/(1 + L2B% фі=р ехр(-£2т)Сі//0Га,

and assuming that the Fermi ages r and rD are equal and that the average neutron velocity is constant in time, we can further simplify Eq. (1.3).

In graphite-moderated systems typically r = 350 cm2 and rD = 333 cm2 so that the above assumption is reasonable. In water-moderated systems where r = 25 cm2 and rD = 14 cm2 the assumption is not so good. How­ever in the fast reactor r and rD are both very large and the assumption is excellent. Thus Eqs. (1.3) and (1.4) reduce to

дф/dt = [(<5& — /%efr) ф/П + £ Ліфі

,_1 (1.10)

дфі/dt = №<*Ф1П — Чі, і = 1,2,…, n v ‘

These equations are time dependent and ф may represent the total neutron flux in the system. In a fast system, which is relatively small, the approxima­tion is good.