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4: Neutron-Induced Fission. B. Rouben McMaster University Course EP 4P03/6P03 2008 Jan-Apr. 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.

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4 neutron induced fission

4: Neutron-Induced Fission

B. Rouben

McMaster University

Course EP 4P03/6P03

2008 Jan-Apr

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.



Radiative Capture: the neutron is captured and a gamma ray is emitted

from stainless steel


Fission (follows absorption)

Neutron Reactions with Matter


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.

outcome of neutron induced fission reaction
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.
fission process
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!
fissionable and fissile nuclides
Fissionable and Fissile Nuclides
  • Only a few nuclides can fission.
  • A nuclide which can be induced to fission by an incoming neutron ofany energy is calledfissile. 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.
fissile nuclides odd a
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.
energy from fission
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.
power from fission
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
  • 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.
calculation of reaction rates
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).
neutron flux
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]
  • fhas units of (neutrons.cm-3*cm.s-1) = (neutrons.cm-2.s-1)
calculating reaction rates
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 ratefor 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.

calculating reaction rates15
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.
concept of irradiation
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

  • fhas 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.
  • wthen hasunits ofneutrons per kilobarn [n/kb].
concept of fuel burnup
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)
fuel burnup
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.
fuel requirements
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.

reactor multiplication constant
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 effectivereactor multiplication constant:
reactor multiplication constant21
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.

critical mass
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 keffcannot 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.
  • Reactivity (r) is a quantity closely related to reactor multiplication constant. It is defined as

r= 1-1/ keff

= (Neutron production-loss)/Production

= Netrelative neutron production

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

Units of Reactivity
control of chain reaction
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 keffslightly > 1 for a short time:

usually done by removing a bit of absorption.

control of chain reaction26
Control of Chain Reaction
  • In a reactor, we don’t want to make keffmuch 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.
products of fission
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.
decay heat
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.
decay power vs time
Decay Power vs. Time












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)

formation of transuranics actinides

Transuranics areproduced 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 befertile because it yields fissile239Pu

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.

Formation of Transuranics (Actinides)
long term reactivity control

Long-Term Reactivity Control

For long-term maintenance of reactivity:

Refuellingis 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.

reactor regulating system

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.

special safety systems

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 > 50 mk of negative reactivity in approximately 1 s.

Next Figuresummarizes the reactivity worths and reactivity-insertion rates of the various CANDU-6 reactivity devices.

reactivity worths of candu reactivity devices




Total Reactivity Worth (mk)

Maximum Reactivity Rate (mk/s)


14 Zone Controllers




21 Adjusters




4 Mechanical Control Absorbers



- 3.5 (dropping)


Moderator Poison

-0.01 (extracting)


28 Shutoff Units




6 Poison-Injection Nozzles



candu reactivity devices

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.

liquid zone controllers
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 shape3-d power distribution towards desired reference shape
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.

Mechanical Control Absorbers
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 < 0.1 mk per second.

The adjusters also help toflatten the power distribution, so that more total power can be produced without exceeding channel and bundle power limits.

Adjuster Rods
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.

Moderator Poison
candu special shutdown systems
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.

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.

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.