If we assume the separability of time and space dependence in the flux, for a step change of dk at t = 0, the flux and the precursor concentrations will eventually attain a steady period

Ф(Е, t) = ф0 exp(/a>) фі(Е, t) = фі0 exp (no)

After substitution in the single-point Eqs. (1.10) and cancelation of фі01ф0 and exp(/co), the in-hour equation is obtained:

q = dk/keS = (l*(o/keff) + £ «&/((о + A*) (1.12)

i-l

This equation relates all the N + 1 time constants of transient ф and фі behavior for the reactivity level q. Thus

A+l A+l

Ф=Фо^ап exp(/ft>„), фі = фі0 £ bin exp(ton)

n—1 П“1

For Q > 1 there is at least one dominant positive root m0 and the neutron flux increases with time. Figure 1.3 shows co0 as a function of q.