Chapter 3. Basic Instrumentation for
Nuclear Technology
1. Accelerators
2. Detectors
3. Reactors
Outline of experiment:
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get particles (e.g. protons, …)
accelerate them
throw them against each other
observe and record what happens
analyse and interpret the data
1.Accelerators
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History-Why
Particle Sources
Acceleration stage
Space charge
Diagnostics
Application
2. Detectors
Gas-Filled Radiation Detectors
Scintillation Detectors
ionization chambers
proportional counters
Geiger-Muller counters
Photomultiplier tube
Semiconductor Detectors
Personal Dosimeters
Others
Particle identification
Measurement theory
Detection Equipment
photographic films
photographic emulsion plates
Cloud and Bubble Chambers
E-ΔE, TOF
3. Reactors
Reactions Involving Neutrons
Sustained, moderation
Thermal-Neutron Properties of Fuels
General features
The Neutron Life Cycle in a Thermal Reactor
Homogeneous and Heterogeneous Cores
Reflectors
Reactor Kinetics
Reactivity Effects (feedback)
n +
235U
 X + Y+ n + γ + E
200 MeV
“The energy produced by the breaking down of the atom
is a very poor kind of thing. Anyone who expects a source
of power from the transformations of these atoms is
talking moonshine.” Lord Ernest Rutherford, 1933.
Self-sustaining Chain reaction
Dec. 2, 1942, Fermi achieved
sustained chain reaction, and
the first fission reactor provided
data for future design of nuclear
reactors.
The Vision
• “It is not too much to expect that our children
will enjoy in their homes [nuclear generated]
electrical energy too cheap to meter.”
– Lewis Strauss, Chairman of the U.S.
Atomic Energy Commission (1954)
The total and fission cross section for 235U based on NJOYprocessed ENDF/B (version V) data.
Why neutron moderation is needed?
Fission neutron energy spectrum
The average energy of prompt fission neutrons is about 2 MeV
Reactions Involving Neutrons
Neutron Scattering
The elastic scattering is the main mechanism in
moderating neutrons in thermal nuclear reactors.
The corresponding neutron energy loss
Average Logarithmic Energy Loss
on a logarithmic energy
scale a neutron loses the
same amount of
logarithmic energy per
elastic scatter, regardless of
its initial energy
average number of scatters required to bring a neutron of
initial energy E1to a lower energy E2
Slowing of neutron (moderation) by various materials.
Here n is the number of elastic scatters to slow, on the
average, a neutron from 2 MeV to 0.025 eV
Is H2O a good moderator (慢化剂)
Thermal Neutrons Cross Sections
Thermal neutron capture cross sections (c)
Thermal neutron cross section for fission (f)
 c /b
1H
2H
12C
14N
0.33
0.00052 0.0034
1.82
16O
113Cd
0.0002 19,820
Moderators: H2O vs. D2O vs. C
Fermi’s used Cd for emergency
Nuclear Fission
15
Neutron Capture Reactions
Neutron leakage
Safety consideration
Spontaneous fission:
The fission produced in these cases is insignificant for
energy production However the phenomenon is important
since represents an uncontrollable source of neutrons in
a reactor and it is, furthermore, possible to make use of it
in the start-up stage. An example of the use of this fission
is the neutron source of 252 californium.
Induced fission:
Certain heavy nuclei can be induced to fission, as result of
one neutron capture. Consequently, several high-energy
neutrons are produced, which permit to maintain the chain
reaction process. The nuclei 235U,233U, 239Pu and 241Pu
experience fission with low-energy thermal neutrons and
they are called fissile materials.
The nuclei 238U and 232Th fission with fast neutrons. The
radiative capture of neutrons by 238U and 232Th leads to the
formation of the fissionable materials 239Pu and 233U, so they
are called fertile materials.
3. Reactors
Reactions Involving Neutrons
Thermal-Neutron Properties of Fuels
General features
The Neutron Life Cycle in a Thermal Reactor
Homogeneous and Heterogeneous Cores
Reflectors
Reactor Kinetics
Reactivity Effects
Thermal-Neutron Properties of Fuels
σf and σγ are the cross-sections for fission and capture
v is the average number of emitted neutrons per nuclear fission
The number of neutrons emitted when one neutron is absorbed
in the nucleus expressed as η
1. 233U has the largest value of η, the number of fission
neutrons produced per thermal neutron absorbed, and
hence is the best prospect for a thermal breeder reactor (
增值反应堆）. A breeder reactor needs an η of at least
two since one neutron is needed to sustain the chain
reaction and one neutron must be absorbed in the fertile
material （增值材料） to breed a new fissile fuel atom.
Fertile materials are those such as 232Th and 238U that,
upon thermal neutron absorption, may yield fissile
materials
2. Although the plutonium isotopes produce almost 3
fission neutrons per thermal fission, their relatively high
radiative capture (n,γ) cross sections result in low values
of η.
E> ~100 keV, 239Pu and 241Pu, η >3. Thus fast reactors
using plutonium as fuel are attractive as breeder
reactors.
3. The fertile isotopes 232Th and 238U have absorption
cross sections of about 1% or less than those of their
conversion fissile isotopes
4. The fertile isotope 240Pu has a large capture cross
section for the production of the fissile isotope 241Pu.
η-values for important
fissile nuclides
3. Reactors
Reactions Involving Neutrons
Sustained, moderation
Thermal-Neutron Properties of Fuels
General features
The Neutron Life Cycle in a Thermal Reactor
Homogeneous and Heterogeneous Cores
Reflectors
Reactor Kinetics
Reactivity Effects
general features
Active core: (1) fissile fuel which through its fissioning is
the main source of neutrons, (2) moderator material if the
fission neutrons are to slow down, (3) coolant if the heat
generated by the fissions is to be removed from the core,
and (4) structural material which maintains the physical
integrity of the core.
Reflector: scatter neutrons back towards the core
Blanket region: captures neutrons leaking from the core
to produce useful isotopes such as 60Co
Shield
Control: allow the chain reaction to be started up,
maintained at some desired level, and safely shutdown
Reactors are broadly classified according to the
energy of the neutrons :
fast reactor, the fast fission neutrons do not slow
down very much before they are absorbed by the
fuel and cause the production of a new generation
of fission neutrons.
thermal reactor, almost all fissions are caused by
neutrons that have slowed down and are moving
with speeds comparable to those of the atoms of the
core material, i.e., the neutrons are in thermal
equilibrium with the surrounding material.
The fast fission cross section for three fissionable uranium
isotopes based on NJOY processed ENDF/B (version V) data
3. Reactors
Reactions Involving Neutrons
Thermal-Neutron Properties of Fuels
General features
The Neutron Life Cycle in a Thermal Reactor
Homogeneous and Heterogeneous Cores
Reflectors
Reactor Kinetics
Reactivity Feedback
The Neutron Life Cycle in a Thermal Reactor
The neutron life cycle in a thermal reactor showing the major mechanisms for
the loss and gain of neutrons. The n fast neutrons beginning the cycle produce
n‘ second-generation fast neutrons which, in turn, begin their life cycle
critical state
neutrons generated by nuclear fission +
neutrons increased by (n,2n), etc.
= absorbed neutrons + leaked neutrons
supercritical state
subcritical state
right side > left side
Quantification of the Neutron Cycle
1. fast fission factor ε （快中子增殖因数）: the ratio of the
total number of fast neutrons produced by both thermal and
fast fission to the number produced by thermal fission alone.
ε -> 1 238U
2. resonance escape probability p （逃脱共振俘获概率）:
the probability that a fast fission neutron slows to thermal
energies without being absorbed p -> 1 235U
This is the measure of how many neutrons can go
through resonances without being absorbed:
3. thermal utilization f （热中子利用系数）: probability that,
when a thermal neutron is absorbed, it is absorbed by the
"fuel" (F) and not by the "nonfuel" (NF)
Σ is called the macroscopic cross section
for a homogeneous(均匀的） core
=0->1
Example 10.1 what is the thermal utilization factor in a mixture of graphite
and natural uranium with a carbon-to-uranium atom-ratio
/
of 450?
4. thermal fission factor η （热裂变中子数）: number of fast
fission neutrons produced per thermal neutron absorbed by the
"fuel."
Equivalently, η is the average number of neutrons per thermal
fission (v) times the probability a fission occurs when a
thermal neutron is absorbed by the fuel,
η > 1, sustaining chain reaction
is a property of the fuel material alone and is unaffected by
the type and amount of nonfuel material in the core.
5. thermal non-leakage probability
（热中子在扩散过程
中不泄漏概率） :
probability a thermal neutron does not leak from the core
before it is absorbed.
R: spherical core of radius
there is no leakage
临界屈曲
for a homogeneous mixture of fuel (F) and moderator
(M)
D is the thermal diffusion coefficient
Moderator properties for thermal (0.00253 eV) neutrons. L is
the thermal diffusion length.
（快中子在慢化过程中不泄漏概率）
the probability a fast neutron does not leak from the core
as it slows to thermal energies.
Г is the Fermi age from fission to thermal energies
Г ：one-sixth the mean squared distance between the point at
which a fast fission neutron is born and begins to slow down
and the point at which it reaches thermal energies.
thermal utilization
fastabso
rp.
Effective Multiplication Factor （有效增殖因数）
For an infinite medium, there is no neutron leakage.
"four-factor formula"
is a property of only the core material and is independent of the
size and shape of the core.
Variation of Keff and its factors with the fuel-to-moderator
ratio. This example is for a homogeneous mixture of water and
2%-enriched uranium. Here NF /NM = atom density of uranium
to molecular density of water.
subcritical
supercritical
critical
self-sustaining
What is
of a homogeneous mixture of 235U and graphite
with an atomic uranium to carbon ratio of 1 to 40,000?
For such a dilute mixture of fully enriched uranium and carbon,
so that
What is the radius R of a critical bare sphere composed of
a homogeneous mixture of 235U and graphite with a
uranium to carbon atom ratio of 1 to 40,000?
For criticality,
R = 125 cm
fastabso
rp.
3. Reactors
General features
Reactions Involving Neutrons
Thermal-Neutron Properties of Fuels
The Neutron Life Cycle in a Thermal Reactor
Homogeneous and Heterogeneous Cores
Reflectors
Reactor Kinetics
Reactivity Effects
Fission Product Poisons
Homogeneous and Heterogeneous Cores
The least expensive fuel to use in a reactor assembly is
natural uranium (0.72 atom-% 235U). But
a fast fission neutron would lose so little energy in each scatter
from a uranium nucleus that over 2000 scatters would be
required to slow the neutron to thermal energies
238U
has large absorption cross sections,
for a pure natural uranium core, the resonance escape
probability p would be very small so that
<<1
The simplest assembly is a homogeneous mixture of
natural uranium and a moderator material
Small, too little moderation, p is very small
Large, the thermal neutrons are not absorbed
easily by the fuel, f is small
Optimum moderator-fuel ratios for a homogeneous mixture
of natural uranium and moderator
Conclusion? Ways for improvement?
heterogeneous core
the fast neutrons are thermalized in the moderator away from
the 238U and hence they can slow through the energy
ranges of the 238U resonances with little likelihood of being
captured
increase p
Fast neutrons born in the fuel lumps have a greater probability
of causing fast fissions in 238U if they are surrounded by only
uranium atoms. In a homogeneous system, a fast fission
neutron may first encounter a moderator atom, scatter, and
lose so much energy that it is no longer capable of causing fast
fission.
Increase fast fission factor ε
Cross-section of a heterogeneous core. Each unit cell of pitch a
contains a 1.25-cm radius fuel rod (black circles) of natural
uranium metal.
The remainder of each lattice cell is graphite.
Variation of core parameters with cell size for the natural
uranium and graphite core
Reflectors
Most reactor cores are surrounded by some material that has a
high scattering to-absorption cross section ratio (typical of
moderators). This material, called a reflector
it reflects some of the neutrons which would escape or leak
from a bare core back into the core, thereby increasing the
nonleakage probabilities.
raise the thermal flux density near the core edges. For heattransfer purposes it is desirable to maintain as constant a
thermal flux profile
general features
Active core: (1) fissile fuel which through its fissioning is
the main source of neutrons, (2) moderator material if the
fission neutrons are to slow down, (3) coolant if the heat
generated by the fissions is to be removed from the core,
and (4) structural material which maintains the physical
integrity of the core.
Reflector: scatter neutrons back towards the core
Blanket region: captures neutrons leaking from the core
to produce useful isotopes such as 60Co
Shield
Control: allow the chain reaction to be started up,
maintained at some desired level, and safely shutdown
3. Reactors
Reactions Involving Neutrons
Sustained, moderation
Thermal-Neutron Properties of Fuels
General features
The Neutron Life Cycle in a Thermal Reactor
Homogeneous and Heterogeneous Cores
Reflectors
Reactor Kinetics
Reactivity Effects
Reactor Kinetics
A Simple Reactor Kinetics Model
Consider a core in which the neutron cycle takes l'
seconds to complete
The change Δn in the total number of thermal
neutrons in one cycle at time t
n(t) is the number of neutrons
at the beginning of the cycle
or
the neutron population (and hence the reactor power)
varies exponentially in time if keff≠1.
=1.001
Uncontrollable !
瞬发中子
A small fraction β (0.65% for 235U) of fission neutrons are
emitted, not during the fission event, but by the radioactive
decay of daughters of certain fission products at times up to
minutes after the fission event that created the fission
products.
The fission products, whose daughters decay by neutron
emission, are called delayed neutron precursors and the
emitted neutrons are called delayed neutrons.
An example of a fission product
whose decay leads to a delayed
neutron.
Delayed-neutrons are grouped by the apparent half-lives of
the observed emission rates
β delayed-neutron fraction
proportion β of delayed neutrons is insignificant. For 235U, it
is 0.65%, while the proportion of the prompt neutrons is
99.35%. Though the proportion of delayed neutrons is
small but they have a very important effect in the control
of the reactor.
Delayed neutrons, the average energy being
about one-half of that for prompt fission neutrons.
lengthening of the neutron cycle time , causes the neutron
population and reactor power to vary sufficiently slowly
that control of the chain reaction is possible.
Reactivity and Delta-k
the degree of departure from criticality
reactivity
The factor that determines how subcritical or supercritical a
reactor may be is
They are all positive for a supercritical system, negative for
a subcritical reactor, and zero at criticality
Revised Simplified Reactor Kinetics Models
Consider a thermal reactor fueled with 235U
Delayed neutron average lifetime is
A fraction β of the fission neutrons
requires a cycle time of
while a fraction (1 -β) is the
prompt-neutron fraction and
requires a cycle time of only
The average or effective generation time required for all the
neutrons produced in a single neutron cycle is thus
=0.083 s
-> 0.083 s
controllable !
3. Reactors
General features
Reactions Involving Neutrons
Thermal-Neutron Properties of Fuels
The Neutron Life Cycle in a Thermal Reactor
Homogeneous and Heterogeneous Cores
Reflectors
Reactor Kinetics
Reactivity Effects
REACTIVITY EFFECTS
Poisoning effect
Fission product mass yield per fission
induced by thermal neutrons for important
fissile nuclides[2]. Total yield is 200%.
135Xe
has a large thermal neutron cross-section, and it
greatly affects the reactivity control of the reactor
Fission products decay chain including
135Xe
Fission product yield and decay constant for 135I
and 135Xe in the fission of 235U
will generally cause a divergent oscillation in the output power
Fuel burn-up
The reactivity when all control material is removed
from the core is called the excess reactivity
Excess reactivity change during burnup
The following conditions have to be satisfied
for nuclear reactor
① Exoergic reaction
n +
235U
 X + Y+ ηn + E
200 MeV
② Sustainable as a chain reaction
③ Moderator
④ Controllable
Delayed neutron
⑤ Safety
Neutron evolution in a nuclear reactor