4: Neutron-Induced Fission

1
4 Neutron-Induced Fission

• B. Rouben
• McMaster University
• Course EP 4P03/6P03
• 2008 Jan-Apr

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)

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(neutron-induced)
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.
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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.
• The process has the potential of being a chain
  reaction this can be self-perpetuating
  (critical) under certain conditions.
• 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.

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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!

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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.

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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
  neutrons 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.

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Energy from Fission

• Energy released per fission 200 MeV
  3.210-11 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.

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Schematic of a CANDU Nuclear Power Plant

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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

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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.

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Calculation of Reaction Rates

• How do we calculate the reaction rates of
  neutrons (in particular, the fission rate)?
• For this we need the concept of cross section,
  already introduced earlier, and the concept of
  neutron flux (see at right).

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Neutron Flux

• Imagine all neutrons in unit volume at a given
  instant.
• Let the neutron population density be n
  neutrons/cm3.
• Sum all the distances (path lengths) which would
  be traversed by these neutrons per unit time.
  This is defined as the total neutron flux,
  denoted f.
• In the (hypothetical) case in which all neutrons
  are travelling at the same speed v, the flux is
  the product of the density n of the neutron
  population and the speed v
• f(v) nv
• For a distribution of neutron speeds, integrate
  over v
• f has units of (neutrons.cm-3cm.s-1)
  (neutrons.cm-2.s-1)

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Calculating Reaction Rates

• Recall that the macroscopic cross section is the
  probability of reaction per distance travelled.
• ?Putting together the concepts of neutron flux
  and cross section, one can calculate reaction
  rates.
• The reaction rate for a given reaction type
  (e.g., fission) for neutrons of speed v is the
  product of the path length of neutrons of speed v
  i.e., the flux f(v) by the macroscopic cross
  section
• Rate of reactions of type i (per unit volume)
• for neutrons of speed v Si(v)f(v)
• If there is a distribution of neutron speeds,
• reaction rate must be integrated over
  speed v.

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Calculating Reaction Rates

• To calculate the reaction rates, we need
  therefore the macroscopic cross section 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 slide) gives the distribution of
  reaction rates, but the absolute value of the
  neutron flux is tied to the total reactor power.
  

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Concept of Irradiation

• 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.

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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)

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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 reactors
  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.

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Fuel Requirements

• Energy in fission immense
• 1 kg (U) in CANDU 180 MW.h(th)
• 60 MW.h(e).
• Typical 4-person households electricity use
• 1,000 kW.h/month 12 MW.h/year
• Then a mere 200 g (lt 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.

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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

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Reactor Multiplication Constant

• Three possibilities for keff
• keff lt 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 gt 1 More neutrons being produced than
  lost.
• Chain reaction more than
  self-sustaining,
• reactor power increases. Reactor is
  supercritical.

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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.

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Reactivity

• 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 lt 0 reactor subcritical
• r 0 reactor critical
• r gt 0 reactor supercritical

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Units of Reactivity

• Reactivity measured in milli-k (mk).
• 1 mk one part in one thousand
• 0.001
• r 1 mk means
• neutron production gt loss by 1 part in 1000
• 1 mk may seem small, but one must consider the
  time scale on which the chain reaction operates.
  

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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 lt 1
• done by inserting neutron absorbers, e.g. water,
  cadmium, boron, gadolinium.
• To increase power, we need to make keff slightly
  gt 1 for a short time
• usually done by removing a bit of absorption.

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Control of Chain Reaction

• In a reactor, we dont want to make keff much
  greater than 1, or gt 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.

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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.

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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.

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Decay Power vs. Time
0.03 0.02 0.01
0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01
Decay Heat ORIGEN includes actinides, and
fission products from U-238, U-235, Pu-239, Pu-241
Scale on right
Scale on left
1.0 10
102 103
104 105 Time After Shutdown (s)
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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.

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CANDU 6 Reactor(700-MWeClass)
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Calandria, Showing Fuel Channels
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Long-Term Reactivity Control

• For long-term maintenance of reactivity
• Refuelling is required because reactivity
  eventually decreases as fuel is irradiated
  fission products accumulate and total fissile
  content decreases.
• In CANDU 6, average refuelling rate 2 channels
  per Full-Power Day (FPD), using the
  8-bundle-shift refuelling scheme (8 new bundles
  pushed in channel, 8 irradiated bundles pushed
  out).
• 4-bundle-shift and 10-bundle-shift refuelling
  schemes have also been used in other CANDUs.
• Selection of channels is the job of the station
  physicist.

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Fuelling machines at both ends of the reactor
remove spent fuel, insert new fuel.
35
Reactor Regulating System

• The reactivity devices used for control purposes
  by the Reactor Regulating System (RRS) in the
  standard CANDU-6 design are the following
• 14 liquid-zone-control compartments (H2O filled)
• 21 adjuster rods
• 4 mechanical control absorbers
• moderator poison.

36
Special Safety Systems

• There are in addition two spatially, logically,
  and functionally separate special shutdown
  systems (SDS)
• SDS-1, consisting of 28 cadmium shutoff rods
  which fall into the core from above
• SDS-2, consisting of high-pressure poison
  injection into the moderator through 6
  horizontally oriented nozzles.
• Each shutdown system can insert gt 50 mk of
  negative reactivity in approximately 1 s.
• Next Figure summarizes the reactivity worths and
  reactivity-insertion rates of the various CANDU-6
  reactivity devices.

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REACTIVITY WORTHS OF CANDU REACTIVITY DEVICES

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CANDU Reactivity Devices

• All reactivity devices are located or introduced
  into guide tubes permanently positioned in the
  low-pressure moderator environment.
• These guide tubes are located interstitially
  between rows of calandria tubes (see next
  Figure).
• Maximum positive reactivity insertion rate
  achievable by driving all control devices
  together is about 0.35 mk/s, well within the
  design capability of the shutdown systems.

39
Liquid Zone Controllers

• For fine control of reactivity
• 14 zone-control compartments, containing
  variable amounts of light water (H2O used as
  absorber!)
• The water fills are manipulated
• all in same direction,
• to keep reactor critical for steady operation,
  or
• to provide small positive or negative reactivity
  to increase or decrease power in a controlled
  manner
• differentially, to shape 3-d power distribution
  towards desired reference shape

40
Liquid Zone-Control Units
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Liquid Zone-Control Compartments
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Mechanical Control Absorbers

• For fast power reduction
• 4 mechanical absorbers (MCA), tubes of cadmium
  sandwiched in stainless steel physically same
  as shutoff rods.
• The MCAs are normally parked fully outside the
  core under steady-state reactor operation.
• They are moved into the core only for rapid
  reduction of reactor power, at a rate or over a
  range that cannot be accomplished by filling the
  liquid zone-control system at the maximum
  possible rate.
• Can be driven in pairs, or all four dropped in by
  gravity following release of an electromagnetic
  clutch.

43
X Mechanical Control Absorbers
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Adjuster Rods

• When refuelling unavailable (fuelling machine
  down) for long period, or for xenon override
• 21 adjuster rods, made of stainless steel or
  cobalt (to produce 60Co for medical
  applications).
• Adjusters are normally in-core, and are driven
  out (vertically) when extra positive reactivity
  is required.
• The reactivity worth of the complete system is
  about 15 mk.
• Maximum rate of change of reactivity for 1 bank
  of adjusters is lt 0.1 mk per second.
• The adjusters also help to flatten the power
  distribution, so that more total power can be
  produced without exceeding channel and bundle
  power limits.

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Top View Showing Adjuster Positions
46
Face View Showing Adjuster Positions
47
Moderator Poison

• Moderator poison is used to compensate for excess
  reactivity
• in the initial core, when all fuel in the core
  is fresh, and
• during and following reactor shutdown, when the
  135Xe concentration has decayed below normal
  levels.
• Boron is used in the initial core, and gadolinium
  is used following reactor shutdown. Advantage of
  gadolinium is that burnout rate compensates for
  xenon growth.

48
CANDU Special Shutdown Systems
Two independent, fully capable shutdown
systems SDS-1 (rods enter core from top) SDS-2
(injection of neutron poison from side.
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SDS-1

• SDS-1 28 shutoff rods, tubes consisting of
  cadmium sheet sandwiched between two concentric
  steel cylinders.
• The SORs are inserted vertically into perforated
  circular guide tubes which are permanently fixed
  in the core.
• See locations in next Figure.
• The diameter of the SORs is about 113 mm.
• The outermost four SORs are 4.4 m long, the rest
  5.4 m long.

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Top View Showing Shutoff-Rod Positions (SA 1
28)
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SDS-2

• SDS-2 high-pressure injection of solution of
  gadolinium into the moderator in the calandria.
• Gadolinium solution normally held at high
  pressure in vessels outside of the calandria.
  Concentration is 8000 g of gadolinium per Mg of
  heavy water.
• Injection accomplished by opening high-speed
  valves which are normally closed.
• When the valves open, the poison is injected into
  the moderator through 6 horizontally oriented
  nozzles that span the core (see next Figure).
• Nozzles inject poison in four different
  directions in the form of a large number of
  individual jets.
• Poison disperses rapidly throughout large
  fraction of core.

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Positions of Liquid-Poison-Injection Nozzles
53

• END