4.5 The effective multiplication constant, ketf

In the foregoing the simplifying assumption has been made that the reactor has no boundary — an infinite reactor. This is not so for any real reactor, of course, and it is now necessary to include in the overall neutron balance of the fission chain reaction the possibility that some neutrons will ‘leak’ irreversibly out of the reactor — Fig 1.12. Thus, when considering finite sized reactors, the value of the infinite multi­plication constant will need to be modified to take into account those neutrons that are lost from the neutron life cycle through leakage. This is known as the ‘effective multiplication constant’ keff.

4.6 Non-leakage probability, PNL

By studying the neutron life cycle it was shown in Section 6.3 of this chapter that k® may be expressed as the product of four factors:

k® = рет/f

where the ‘infinity’ suffix is a reminder that the re­actor is presumed to be of infinite size. The possibility of neutrons diffusing out of the reactor or, more importantly, the proportion of neutrons that do not leak out may be incorporated in the multiplication constant by having a fifth factor: the non-leakage probability Pnl-

Thus keff = pei)f x Pnl = k® x Pnl

where keff is the effective multiplication constant for the finite reactor.

k® is the infinite multiplication constant for the equivalent reactor in terms of fuel and moderator materials and their basic incre­mental geometric arrangement within the core (i. e., the fundamental lattice cell ar­rangement) but of infinite size.

PNL is the non-leakage probability; that is the probability that a neutron remains in the reactor and is absorbed there.

number of neutrons absorbed

„ in the reactor

PNL = ———————————— IS < 1

number of neutrons absorbed

+ leaking out

Thus, keff is the product of four factors petjf (k*,) which describe the neutron behaviour inside the re­actor and a fifth factor Pnl which expresses the pro­bability that the neutrons remain in the reactor.

The probability that a neutron does leak out of a reactor, or the fraction of all neutrons that do leak, is:

Pl = 1 — Pnl