Page 264 - Dynamics and Control of Nuclear Reactors

APPENDIX C Basic reactor physics 265

Define the multiplication factor (gain)

Number of neutrons generated in the present generation n p
k ¼ (C.13)
Number of neutrons generated in the previous generation nðÞ
If k¼1, the chain reaction is sustained, and the reactor is said to be critical. If k<1,
the number of neutrons from one generation to the next decreases. Such a reactor is
said to be sub-critical. If k>1, the number of neutrons from one generation to the
next increases without bound, and such a reactor is said to be super-critical.
In summary:
• k¼1, critical reactor
• k<1, sub-critical reactor
• k>1, super-critical reactor

C.9 Computing effective multiplication factor
The following factors determine the magnitude of the multiplication factor k:

1. Thermal fission factor, η: The factor, η, is defined as the number of fast neutrons
produced per thermal neutron absorption in the fuel. That is:
σ fuel
η ¼ ν f
fuel
σ a
2. ν ¼ number of neutrons produced per fission.
A typical value for η is around 1.65 for a U-235-fueled thermal reactor.

3. Thermal utilization factor, f: The factor, f, is defined as the number of neutron
absorptions in the fuel per total number of neutron absorptions. That is:
Σ fuel
f ¼ a
Σ total
a
A typical value for f is around 0.71 for a U-235-fueled thermal reactor.
4. Resonance escape probability, p: The factor, p, is equal to the number of
neutrons that reach thermal energy per fast neutron born. It accounts for
neutron losses in resonances during slowing down. A typical value for p is around
0.87 for a U-235-fueled thermal reactor.
5. Fast fission factor, ε: This factor is defined as the total number of neutrons from
both thermal and fast fissions per number of neutrons from thermal fissions.
A typical value for ε is around 1.02 for a U-235-fueled thermal reactor

Using the above four factors we define the effective multiplication of an infinite
size core as
k ∞ ¼ ηfp ε (C.14)