Phase diagram of water

Macroscopic cross-sections for natural
uranium (Σ t
= Σn i
σ ti
)
Factors affecting chain reaction
1) For each thermal neutron absorbed, η effective fast neutrons emitted
η < ν, mean number produced (ν =2.42 for 235 U), because not all
neutrons absorbed by fuel cause fission. Nat U (0.72% 235 U) η =1.33
2) Some fast neutrons cause fission before slowing down which
increases the number of neutrons by the fast fission factor ε
3) The probability that a neutron will avoid resonance capture by 238 U
the resonance escape probability p - depends on the moderator
4) The fraction of thermal neutrons that are absorbed by the fuel in the
core (fuel, moderator, can) is called the thermal utilization factor f
5) There are a fraction l f of fast neutrons and a fraction l t of thermal
neutrons that leak out of the reactor
The neutron multiplication factor k is therefore given by:
k = ηεpf(1− l f ) (1− l t )
For infinite core k ∞ = ηεpf
Four factors formula
Neutron Moderation
Moderator is a medium for reducing the kinetic energy of neutrons from
MeV to thermal level without losing many in the ‘resonant trap’ of 238 U
m
M
For 180 deg scattering
neutron
E s = [(M − m)/(M + m)] 2 E i = [(A − 1)/(A + 1)] 2 E i
For 0 deg scattering
E s = E i
Averaging, E s = ½{1 + [(A − 1)/(A + 1)] 2 }E s
nucleus
= [(A 2 + 1)/(A + 1) 2 ]E s
(Averaging over all angles gives the same result)
1
H
12
C
238
U
A 1 12 238
E s /E i 0.5 0.86 0.99
How many collisions required to reduce neutron energy from
2 MeV to 1 eV ? (factor of 2 10 6 )
Put (E s /E i ) n = 1/(2.10 6 ) = 5.10 −7
eg 1 H gives n ~ 21, 12 C gives n ~ 96
Moderating Ratio, MR
Good moderators require
• large σ elastic (σ el )
• low σ capture (σ c )
• significant loss in KE per collision
• chemical stability (in hot, radioactive environment)
Moderating ratio, MR = (1− E s /E i ) σ el /σ c
Reactor Control
H 2 O 62; D 2 O 4830; C 216
If the neutron flux increases to a higher level than that needed for a
stable chain reaction, how can the reactor be controlled, ie how can
equilibrium be restored?