1: Backgrounder on Fission & CANDU
B. Rouben
McMaster University
Nuclear Power Plant Systems & Operation
EP 4P03/6P03
2016 Jan-Apr
2016 January
1
Neutron Reactions with Matter

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
Scattering: the neutron
bounces off, with or without
the same energy (elastic or
inelastic scattering)
Activation: the neutron is
captured, & the resulting
nuclide is radioactive, e.g.
16O(n,p)16N

10B(n,)7Li

Radiative Capture: the
neutron is captured and a
gamma ray is emitted
 from stainless steel
40Ar(n,)41Ar

Fission (follows absorption)
2016 January
Inelastic Scattering:
Scattered neutron, E2
elec tron
neutron
Incident neutron, E1
p roton
Gamma Photon, E
E1 = E + E2
Scattered neutron, E2
Elastic Scattering:
elec tron
neutron
p roton
Incident neutron, E1
a EA
E1 = EA + E2
Gamma Photon, E
E  ~ 7 MeV
Neutron Absorption:
elec tron
neutron
p roton
Incident thermal neutron, E
2
Neutron Absorption in Nuclear Fuel


When a neutron is absorbed in a fuel nuclide, the
2 most important (although not the only)
consequences which can follow are neutron
capture and fission.
The competition between neutron capture and
fission, along with the neutron reactions with
other materials in the reactor, determines
whether the fission chain reaction can be selfsustaining.
2016 January
3
(neutron-induced)
A neutron splits a
uranium nucleus,
releasing energy (quickly
turned to heat) and more
neutrons, which can
repeat the process.
2016 January
The energy appears
mostly in the kinetic
energy of the fission
products and in the beta
and gamma radiation. 4
Outcome of Neutron-Induced Fission Reaction

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Energy is released (a small part of the nuclear mass is
turned into energy).
One neutron enters the reaction, 2 or 3 (on the average)
emerge, and can induce more fissions.
This chain reaction can be self-perpetuating (“critical”)
if at least one of the neutrons released in fission is able
to induce more fissions.
By judicious design, research and power reactors can be
designed for criticality; controllability is also important.
The energy release is open to control by controlling the
number of fissions.
This is the operating principle of fission reactors.
2016 January
5
A Nuclear Generating Station
2016 January
6
Components of a Nuclear Plant
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What are the basic components of a nuclear
generating station?
They consist of the nuclear reactor and the
Balance of Plant.
The reactor must contain:

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Nuclear fuel
Coolant (Heat-Transport System)
Moderator (in thermal reactors only)
Control and Shutdown Mechanisms
2016 January
cont’d
7
Components of a Nuclear Plant

The Balance of Plant must contain:

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
One or more Steam Generators (Boilers) to turn
water into steam (unless the primary coolant is
turned into steam in the reactor itself, and unless a
gas coolant is used)
A Turbine-Generator to turn mechanical energy
into electricity
Connections to the outside electrical grid.
2016 January
8
Reactor Components

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Nuclear fuel: Only very heavy nuclei are
fissionable; these are isotopes of uranium and of
plutonium and other transuranics.
Some nuclides can be fissioned by neutrons of
any energy; these nuclides are called fissile; e.g.,
235U, 239Pu, 241Pu, 233U. 235U is the only naturally
occurring fissile nuclide.
Fissionable but non-fissile nuclides, e.g., 238U,
can be fissioned by neutrons of energy greater
than some specific threshold.
cont’d
2016 January
9
Reactor Components (Cont’d)


Fissile nuclides are easier to fission than nonfissile nuclides, and furthermore the fission cross
section of fissile nuclides is much much greater
for slow (thermal) neutrons. Therefore it is
much easier to build a reactor which relies on
fissions induced by thermal neutrons.
Such a reactor is called a thermal reactor. It
requires a moderator, which is a light material,
with atoms of low mass number, used to slow
neutrons down to thermal energies.
cont’d
2016 January
10
Reactor Components (Cont’d)



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Fission processes transform some small fraction
of the mass of the fuel to energy (E = mc2).
In a nuclear reactor, most of this energy is turned
very quickly into heat (random kinetic energy).
Therefore a coolant is required to take away the
heat and turn water into steam to feed the
turbine-generator.
Finally, any reactor needs control mechanisms to
control the fission chain reaction. Some reactors
have independent shutdown systems.
2016 January
11
Fission Process
The fission process occurs when the nucleus
which absorbs the neutron is excited into an
“elongated” (barbell) shape, with roughly half
the nucleons in each part.
 This excitation works against the strong force
between the nucleons, which tends to bring the
nucleus back to a spherical shape  there is a
“fission barrier”
 If the energy of excitation is larger than the
fission barrier, the two parts of the barbell have
the potential to completely separate: binary
fission!

2016 January
12
Fissionable and Fissile Nuclides

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Only a few nuclides can fission.
A nuclide which can be induced to fission by an
incoming neutron of any energy is called fissile. There
is only one naturally occurring fissile nuclide: 235U.
Other fissile nuclides: 233U, isotopes 239Pu and 241Pu of
plutonium; none of these is present in nature to any
appreciable extent.
Fissionable nuclides: can be induced to fission, but only
by neutrons of energy higher than a certain threshold.
e.g. 238U and 240Pu.
2016 January
13
Fissile Nuclides: Odd-A
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Notice, from the previous slide, that fissile nuclides generally have
an odd value of A. This is not a coincidence.
The binding energy is greater when there are pairs of nucleons.
When a neutron is absorbed in an odd-A (fissile) nucleus, its “drop”
in energy is relatively large (= to the binding energy of the last
nucleons in the even-A nucleus).
The energy released by this “drop” of the neutron’s energy (even if
the neutron brought no kinetic energy) is now available to change
the configuration of the nucleus  the nucleus can “deform” by
stretching and can surmount the fission barrier.
If the neutron is absorbed in an even-A (fissionable) nucleus, its
binding energy in the odd-A nucleus is smaller, and is not sufficient
for the nucleus to surmount the fission barrier. To induce fission,
the neutron needs to bring in some minimum (threshold) kinetic
energy.
2016 January
14
Energy from Fission
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Energy released per fission ~ 200 MeV [~ 3.2*10-11 J].
This is hundreds of thousands, or millions, of times
greater than energy produced by combustion, but still
only ~0.09% of mass energy of uranium nucleus!
The energy released appears mostly (85%) as kinetic
energy of the fission fragments, and in small part (15%)
as the kinetic energy of the neutrons and other particles.
The energy is quickly reduced to heat (random kinetic
energy) as the fission fragments are stopped by the
surrounding atoms.
The heat is used to make steam by boiling water,
The steams turns a turbine and generates electricity.
2016 January
15
Power from Fission
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Total power (energy per unit time) generated in a
nuclear reactor depends on the number of fissions per
second.
Quantities of interest:
 Fission power (total power generated in fission)
 Thermal power (the power (heat) removed by the
coolant)
 Electric power (the power changed to electrical
form)
In the CANDU 6:
 Fission power
= 2156 MWf
 Thermal Power = 2061 MWth
 Gross Electric Power  680-730 MWe
2016 January
16
Exercises
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Given that one fission releases 200 MeV, how
many fissions occur per second in a CANDU 6 at
full power?
How many fissions occur in 1 year at full power?
Compare this to the number of uranium nuclei in
the reactor.
2016 January
17
Intensity of a Neutron Beam
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Consider the concept of a neutron beam, i.e., a number of
neutrons all moving in the same direction towards a target
of some material.
The intensity I of the beam represents the number of
neutrons crossing a unit area in a plane perpendicular to
the beam direction per unit time.
Typical units for I are neutrons.cm-2.s-1.
If the “density of neutrons in the beam is n neutrons.cm-3
and we imagine them all to be travelling at the same
speed v, i.e., the beam is monoenergetic, then it is easy to
see (figure next slide) that the neutrons crossing the area
per s will be those within a distance v from the target, i.e.,
2016 January
18
I = nv.
Intensity of a Neutron Beam
Density of
neutrons in beam
is n per cm3
Unit Area
of Target
Speed of neutrons = v
All neutrons within a
distance (v*1 s) will cross
the area within 1 s,
i.e., I = nv
2016 January
19
Macroscopic Cross Section

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Recall (from nuclear physics) the concept of
macroscopic cross section  (units cm-1) - for a
given reaction type.
This is the probability of reaction of 1 particle in
the beam (1 neutron here) with nuclides of the
target per distance travelled into the target (note:
this really applies to infinitely small distances).
Since the intensity I counts all the neutrons in the
beam and the distance they travel per s, we can
see that the total rate R of reactions (of the type
-3.s-1)
considered)
will
be
R
=
I

(reactions.cm
2016 January
20
Neutron Flux
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Now say that you do not have a beam of neutrons, but that
you have a number n of neutrons in a unit volume, all
moving at speed v in different directions.
Consider each neutron as if it is in a “beam” of its own, of
intensity 1*v.
Imagine “adding up” the intensity of all these beams even if they are not parallel; then the total “beam
intensity” is still I = nv neutrons.cm-2.s-1.
The reason that it makes sense to add the intensities this
way, even if the areas that the neutrons are crossing are at
different angles, is that the nuclides don’t really care from
which direction the neutrons are coming.
2016 January
21
Neutron Flux


The neutron flux for speed v is denoted f(v) and is
defined as the total intensity of all these disparate beams,
i.e.,
f(v) = nv
If the neutrons have different speeds (energies), then we

can define a total flux
f   f (v dv
0

(Or, if we are interested in only a range of neutron
energies, we can customize the range of integration.)
2016 January
22
Neutron Flux
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An equivalent way to define the neutron flux is
to visualize an arrow associated with each
neutron. The arrow shows the direction of
motion of the neutron, and its length denotes the
neutron’s speed.
The sum of all the arrow lengths is the flux f
(see figure in next slide).
It is also the sum of the distances (path lengths)
which would be traversed by the neutrons per
unit time.
A flux f has units of neutrons.cm-2.s-1, also
-2.s-1.
abbreviated
as
of
n.cm
2016 January
23
Neutron Flux
Unit
Volume
Total flux f =
sum of all
arrow lengths
in unit volume
2016 January
24
Reaction Rate
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The Reaction Rate R of neutrons with the nuclides
of the material, for a given reaction type, is a very
important quantity.
Since the nuclides don’t care about the direction of
motion of the neutrons, then as shown for a beam
of neutrons of speed v, R is given by:
R(v) = (v)f(v), where  (v) is the material’s
macroscopic cross section for neutrons of speed v.
If the neutrons are not monoenergetic, then the

total reaction rate is
R   (v f (v dv
2016 January
0
25
Energy Instead of Speed

It is important to remember that in any and all of
the treatment in the previous slides, neutron
energy E can be used as the independent variable
instead of the neutron speed v, since these two
quantities are directly related to one another by
1 2
E  mv
2
2016 January
26
Reaction-Rate Equation
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The general equation for a reaction rate must be
stressed, as it is extremely important:
R(v) = (v)f(v)
Remember that the macroscopic cross section 
depends on the type of nuclide (the material), the
type of reaction, and the speed v of the neutrons
relative to the nuclides.
This is a basic equation!
The reaction rate can be integrated over any
range considered for the neutron energies.
Typical units for R are reactions.cm-3.s-1.
2016 January
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Example: Fission Rate



Let us consider the fission reaction. The fission
cross section is written f. This is a function of
neutron energy E and can be (and usually is) a
function of position r, because there may be
different materials at different points.
Then Fission rate at point r = f(E, r)f(E, r).
And the total fission rate in the reactor would be
obtained by integrating this quantity over the
reactor volume.
2016 January
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Neutron-Production Rate
If the average number of neutrons produced in a fission
is  (don’t confuse this with neutron speed), we can
define a new quantity, the “production” (or “yield”)
cross section f(E, r).
 Then
Production rate of neutrons at r = f(E, r)f(E, r)
This can also be called the “volumetric source” of
neutrons.
 The total neutron production rate in the reactor can be
obtained by integrating the above quantity over r.
 It is of course important to distinguish between
fission rate and yield rate (volumetric source).

2016 January
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Note on Calculating Reaction Rates
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To calculate reaction rates, we need the macroscopic cross
sections and the neutron flux.
These are calculated with the help of computer programs:
 The cross sections are calculated from international databases
of microscopic cross sections
 The neutron flux distribution in space (the “flux shape”) is
calculated with specialized computer programs, which solve
equations describing the transport or diffusion of neutrons
[The diffusion equation is an approximation to the more
accurate transport equation.]
The product of these two quantities (as per previous slides) gives
the distribution of reaction rates, but the absolute value of the
neutron flux is tied to the total reactor power.
2016 January
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Concept of Irradiation
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The irradiation w (or exposure, or fluence) of the reactor
fuel or other material is a measure of the time spent by the
material in a given neutron flux f. Mathematically, it is
defined as the product of flux by time:
w = f.t
f has units of neutrons.cm-2.s-1
Therefore the units of irradiation w are neutrons/cm2.
In these units, w has very small values. It is more
convenient therefore to use the “nuclear” unit of area, the
“barn” (b) = 10-24 cm2, or even the kb = 1,000 b.
w then has units of neutrons per kilobarn [n/kb].
2016 January
31
Concept of Fuel Burnup
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Fuel burnup is defined as the (cumulative) quantity of
fission energy produced per mass of uranium during its
residence time in the reactor.
Fuel burnup starts at 0 for fuel which has just entered the
reactor, and builds up as the fuel produces energy.
The exit (or discharge) burnup is the burnup of the fuel as
it exits the reactor.
The two most commonly used units for fuel burnup are
Megawatt-hours per kilogram of uranium, i.e.,
MW.h/kg(U), and Megawatt-days per Megagram (or
Tonne) of uranium, i.e., MW.d/Mg(U).
1 MW.h/kg(U) = 1,000/24 MW.d/Mg(U) = 41.67 MW.d/Mg(U)
2016 January
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Fuel Burnup
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The exit fuel burnup is an important economic quantity: it
is essentially the inverse of fuel consumption [units, e.g.,
Mg(U)/GW(e).a].
For a given fissile content (fuel enrichment), a high
burnup signifies low fuel consumption, and therefore a
small refuelling-cost component.
Note, however: the true measure of a reactor’s efficiency
is not fuel burnup, but uranium utilization, the amount of
uranium “from the ground” needed to produce a certain
amount of energy.
Typical fuel burnup attained in CANDU 6 = 7,500
MW.d/Mg(U), or 175-180 MW.h/kg(U).
However, this can vary, because burnup depends on
operational
parameters,
mostly
the
moderator
purity.
2016 January
33
Fuel Requirements
Energy in fission immense:
1 kg (U) in CANDU = ~180 MW.h(th)
= 60 MW.h(e).
Typical 4-person household’s electricity use
= 1,000 kW.h/month = 12 MW.h/year
Then a mere 200 g (< 0.5 lb) (U) [6 to 8 pellets]
serves 1 household for an entire year. [Cf: If from
fossil, ~ 30,000 times as large, ~ 6,000 kg coal.]
 Cost of nuclear electricity insensitive to
fluctuations in price of U.
2016 January
34
Reactor Multiplication Constant
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Several processes compete for neutrons in a nuclear
reactor:
 “productive” absorptions, which end in fission
 “non-productive” absorptions (in fuel or in
structural material), which do not end in fission
 leakage out of the reactor
Self-sustainability of chain reaction depends on
relative rates of production and loss of neutrons.
Measured by the effective reactor multiplication
constant:
Rate of neutron production
keff 
2016 January
Rate of neutron loss (absorptions  leakage)
35
Reactor Multiplication Constant

Three possibilities for keff:
 keff < 1: Fewer neutrons being produced than lost.
Chain reaction not self-sustaining, reactor
eventually shuts down. Reactor is subcritical.
 keff = 1: Neutrons produced at same rate as lost.
Chain reaction exactly self-sustaining, reactor
in steady state. Reactor is critical.
 keff > 1: More neutrons being produced than lost.
Chain reaction more than self-sustaining,
reactor power increases. Reactor is supercritical.
2016 January
36
Critical Mass

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Because leakage of neutrons out of reactor
increases as size of reactor decreases, reactor
must have a minimum size for criticality.
Below minimum size (critical mass), leakage is
too high and keff cannot possibly be equal to 1.
Critical mass depends on:




shape of the reactor
composition of the fuel
other materials in the reactor.
Shape with lowest relative leakage, i.e. for which
critical mass is least, is shape with smallest
surface-to-volume ratio: a sphere.
2016 January
37
Reactivity
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
Reactivity (r is a quantity closely related to
reactor multiplication constant. It is defined as
r = 1-1/ keff
= (Neutron production-loss)/Production
= Net relative neutron production
“Central” value is 0:



r < 0 : reactor subcritical
r = 0 : reactor critical
r > 0 : reactor supercritical
2016 January
38
Units of Reactivity
Reactivity measured in milli-k (mk).
1 mk = one part in one thousand
= 0.001
r = 1 mk means
neutron production > loss by 1 part in 1000
1 mk may seem small, but one must consider the time
scale on which the chain reaction operates.
2016 January
39
Control of Chain Reaction
To operate reactor:
 Most of the time we want keff = 1 to keep power
steady.
 To reduce power, or shut the reactor down, we
need ways to make keff < 1:
done by inserting neutron absorbers, e.g. water,
cadmium, boron, gadolinium.
 To increase power, we need to make keff slightly >
1 for a short time:
usually done by removing a bit of absorption.
2016 January
40
Control of Chain Reaction



In a reactor, we don’t want to make keff much greater than
1, or > 1 for long time, or power could increase to high
values, potentially with undesirable consequences, e.g.
melting of the fuel.
Even when we want to keep keff = 1, we need reactivity
devices to counteract perturbations to the chain reaction.
The movement of reactivity devices allows absorption to
be added or removed in order to manipulate keff.
Every nuclear reactor contains regulating and shutdown
systems to do the job of keeping keff steady or increasing
or decreasing it, as desired.
2016 January
41
Products of Fission
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
The fission products (fission fragments) are nuclides of
roughly half the mass of uranium.
They are not always the same in every fission. There are
a great number of different fission products, each
produced in a certain percentage of the fissions (their
fission “yield”).
Most fission-product nuclides are “neutron rich”; they
disintegrate typically by - or - decay, and are therefore
radioactive, with various half-lives.
2016 January
42
Decay Heat
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Many fission products are still decaying long after the originating
fission reaction.
Energy (heat) from this nuclear decay is actually produced in the
reactor for many hours, days, even months after the chain reaction
is stopped. This decay heat is not negligible.
When the reactor is in steady operation, decay heat represents
about 7% of the total heat generated.
Even after reactor shutdown, decay heat must be dissipated
safely, otherwise the fuel and reactor core can seriously overheat.
Next Figure shows the variation of decay heat with time.
Also, the used fuel which is removed from the reactor must be
safely stored, to cool it and to contain its radioactivity.
2016 January
43
Decay Power vs. Time
Figure from E.E. Lewis, “Fundamentals of Nuclear Reactor
2016 January Physics”, Academic Press, ISBN: 978-0-12-370631-7
44
Formation of Transuranics (Actinides)
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Transuranics are produced in the reactor by absorption of
neutrons by 238U: plutonium, americium, curium, etc.
e.g., production of 239Pu:
238U +n
239U
239Np + 
239Pu + 2 
238U is said to be fertile because it yields fissile 239Pu
239Pu can participate in fissions; it can also continue to
absorb neutrons to yield 240Pu and 241Pu (latter is fissile)
Half the energy eventually produced in CANDU is from
plutonium created “in situ”!
Actinides tend to have long half-lives, e.g. for 239Pu
24,000 y.
2016 January
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END
2016 January
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