2015 January 1

1: Backgrounder on Fission & CANDU

B. Rouben

McMaster University

Nuclear Power Plant Systems & Operation

EP 4P03/6P03

2015 Jan-Apr

2015 January 2

Neutron Reactions with Matter 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)

e le c tro n ne utro n

p ro to n In c id e n t n e u tr o n , E 1

S c a tte r e d n e u tr o n , E 2

a E A

E 1 = E + E 2

In e la s t ic S c a tte r in g :

e le c tro n ne utro n

p ro to n

E la s tic S c a tte r in g :

In c id e n t n e u tr o n , E 1

S c a tte r e d n e u tr o n , E 2

E 1 = E A + E 2

e le c tro n ne utro n

p ro to n

N e u tr o n A b so r p tio n :

In c id e n t th e r m a l n e u tr o n , E

G a m m a P h o to n , E

G a m m a P h o to n , E

E ~ 7 M e V

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 self-sustaining.

2015 January 3

2015 January 4

A neutron splits a uranium nucleus, releasing energy (quickly turned to heat) and more neutrons, which can repeat the process.

The energy appears mostly in the kinetic energy of the fission products and in the beta and gamma radiation.

(neutron-induced)

2015 January 5

Outcome of Neutron-Induced Fission Reaction

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.

A Nuclear Generating Station

2015 January 6

Components of a Nuclear Plant

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: Nuclear fuel Coolant (Heat-Transport System) Moderator (in thermal reactors only) Control and Shutdown Mechanisms cont’d

2015 January 7

Components of a Nuclear Plant

The Balance of Plant must contain: 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.

2015 January 8

Reactor Components

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

2015 January 9

Reactor Components (Cont’d)

Fissile nuclides are easier to fission than non-fissile 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

2015 January 10

Reactor Components (Cont’d)

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.

2015 January 11

2015 January 12

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!

2015 January 13

Fissionable and Fissile Nuclides

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.

2015 January 14

Fissile Nuclides: Odd-A 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.

2015 January 15

Energy from Fission 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.

2015 January 16

Power from Fission

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

2015 January 17

Exercises

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.

Intensity of a Neutron Beam 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.,

I = nv. 2015 January 18

Intensity of a Neutron Beam

2015 January 19

Unit Area of Target

Density of neutrons in beam is n per cm3

Speed of neutrons = vAll neutrons within a distance (v*1 s) will cross the area within 1 s, i.e., I = nv

Macroscopic Cross Section 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 considered) will be R = I (reactions.cm-3.s-1)

2015 January 20

2015 January 21

Neutron Flux

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.

2015 January 22

Neutron Flux

The neutron flux for speed v is denoted v) and is defined as the total intensity of all these disparate beams, i.e., (v) = nv

If the neutrons have different speeds (energies), then we can define a total flux

(Or, if we are interested in only a range of neutron energies, we can customize the range of integration.)

0

dvv

Neutron Flux 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 (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 has units of neutrons.cm-2.s-1, also abbreviated as of n.cm-2.s-1.2015 January 23

Neutron Flux

2015 January 24

Unit Volume

Total flux = sum of all arrow lengths in unit volume

Reaction Rate 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)(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

2015 January 25

0

dvvvR

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

2015 January 26

2

2

1mvE

Reaction-Rate Equation The general equation for a reaction rate must be

stressed, as it is extremely important:R(v) = (v)(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.

2015 January 27

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)(E, r). And the total fission rate in the reactor would be

obtained by integrating this quantity over the reactor volume.

2015 January 28

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)(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).2015 January 29

2015 January 30

Note on Calculating Reaction Rates

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.

2015 January 31

Concept of Irradiation

The irradiation (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 . Mathematically, it is defined as the product of flux by time:

= .t

has units of neutrons.cm-2.s-1

Therefore the units of irradiation are neutrons/cm2. In these units, 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.

then hasunits of neutrons per kilobarn [n/kb].

2015 January 32

Concept of Fuel Burnup 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)

2015 January 33

Fuel Burnup 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.

2015 January 34

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/yearThen 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.

2015 January 35

Reactor Multiplication Constant

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:

)( leakagesabsorptionlossneutronofRate

productionneutronofRatekeff

2015 January 36

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.

2015 January 37

Critical Mass

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.

2015 January 38

Reactivity

Reactivity ( is a quantity closely related to reactor multiplication constant. It is defined as

= 1-1/ keff = (Neutron production-loss)/Production= Net relative neutron production

“Central” value is 0: < 0 : reactor subcritical = 0 : reactor critical > 0 : reactor supercritical

2015 January 39

Units of Reactivity

Reactivity measured in milli-k (mk).

1 mk = one part in one thousand

= 0.001

= 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.

2015 January 40

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.

2015 January 41

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.

2015 January 42

Products of Fission

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.

2015 January 43

Decay Heat 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.

2015 January 44

Decay Power vs. Time

Figure from E.E. Lewis, “Fundamentals of Nuclear Reactor Physics”, Academic Press, ISBN: 978-0-12-370631-7

2015 January 45

Formation of Transuranics (Actinides)

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.

2015 January 46

END