Negative temperature feedback,
reactor stability and controllability –
an introduction
Jim Thomson
www.safetyinengineering.com
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lost
lost
Effective multiplication factor keff =
(no. of fissions in one generation)/(no. of fissions in succeeding generation)
Reactivity ρ = (keff - 1.0)/keff which is ~ (keff - 1.0) for practical purposes.
Prompt neutron lifetime (the time between a neutron being expelled from a nucleus, and hitting
another one) is typically about one-thousandth of a second.
The ‘lost’ neutrons are absorbed by non-fissionable materials. These include:
• Shielding,
• Structural steel,
• Moderator,
• Uranium-238
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Delayed neutrons
Some neutrons (typically 0.65%) emitted in the fission process
are delayed by up to several tens of seconds. The remaining 99.35%
are released immediately upon fission (‘prompt neutrons’).
This phenomenon gives a margin for control of nuclear reactors.
Reactors operate in a so-called ‘delayed critical’’ state, compared
to bombs which are ‘prompt critical’.
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1
Fission yield %
0.1
0.01
0.001
70
90
110
130
150
Mass number
The fission product spectrum for uranium-235
The fission product spectrum for uranium 235
Fission is a random process…………
all sorts of elements get produced as
fission products…………….
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0.4
0.3
S(E) = 0.771(Ee-0.776E) 0.5
S(E)
0.2
0.1
1
2
3
4
5
6
Neutron energy, E, MeV
The fission neutron energy spectrum
……and the neutrons get released at
a wide range of speeds (or energies)……...
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MaxwellBoltzmann
Spectrum
Hardened
spectrum
n(v)
Neutron speed (m/s)
The Maxwell-Boltzmann distribution for thermal neutrons
…….and even after the neutrons have been
slowed down (moderated) they still have a
wide range of speeds…………….
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1 barn = 10-28 m2
fission
crosssection
(barns)
Neutron energy
Neutron energy
Fission cross-sections for uranium-235 and uranium-238
…….and the chance that a neutron will hit
another uranium-235 nucleus (and hence
cause another fission) varies with the speed
of the neutron………...
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total
crosssection
(barns)
1 barn = 10-28 m2
Neutron energy
The total cross-section of uranium-238
……also the chance that the neutron will be
captured by uranium 238 (and not cause
fission) also varies with the neutron speed.
The peaks (‘resonances’) are important, and
are caused by quantum mechanics effects.......
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U238
capture
cross-section
Doppler broadening
of cross-section resonances
neutron energy
Doppler Broadening – as U-238 gets hotter, the
resonance peaks broaden due to vibration of the nuclei.
The nett effect is that U-238 absorbs more neutrons
(without causing fission) as the reactor temperature
increases. Hence an increase in reactor temperature
leads to a fall in reactivity.
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k-effective
1.006
Protection
System trip
settings
(notional)
1.0000
(normal
operation)
prompt
critical
Prompt criticality
increasing rate
of power increase
delayed
critical
Negative thermal feedback (passive)
or control system action (active)
or protection system action (emergency)
sub-critical
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The ways in which temperature effects reactivity – passive control mechanisms
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An increase in the
temperature of the
reactor leads to
FUEL
thermal feedback
Doppler broadening
More neutron capture by U238
(non-fissile, 97% of fuel)
very fast, negative
(fewer neutrons available for fission)
An increase in
mean neutron
thermal energy
Reduced neutron capture by U235
slow, negative
(less neutrons cause fission)
Increased neutron capture by Pu239
(due to 0.3eV resonance)
slow, positive
(more neutrons cause fission)
Fewer neutrons
absorbed in coolant
fast, positive
(more neutrons available for fission)
Longer neutron mean free path
fast/slow, negative
(more neutrons escape from reactor)
More neutrons captured
in control rods
slow negative
(more neutrons captured in CRA’s)
What happens to
the neutrons?
Effects on reactivity
MODERATOR
Increased steam
voidage in watercooled reactors
Expansion of the
reactor structure
STRUCTURE
Expansion of control
rods into the core
Physical effect
on reactor
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Passive thermal feedback
Reactivity ρ
+
Neutron
Kinetics
-
φ
Thermal
rating R
(watts/g)
Reactor power
δρ= α.δ T
Thermal
feedback
effects
δT
Fuel, coolant,
moderator and
structural
temperature
changes
∫
R dt
α = the temperature coefficient of reactivity
ρ = keff - 1
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SUMMARY
Delayed neutrons make a nuclear reactor controllable.
Doppler broadening makes a nuclear reactor stable.
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