Neutron Life Cycle

1Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Neutron Life Cycle

Why should we worry about these?

How?

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

2

k = fp(1-lfast)(1-lthermal)

Controlled Fission

• Thermal utilization factor f can be changed, as an example, by adding absorber to coolant (PWR) (chemical shim, boric acid), orby inserting movable control rods in & out.• Reactors can also be controlled by altering neutron leakages using movable neutron reflectors.• f and p factors change as fuel is burned.• f, p, η change as fertile material is converted to fissilematerial.


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Controlled Fission

• Attention should be paid also to the fact that reactor power changes occur due to changes in resonance escape probability p. If Fuel T↑, p↓ due to Doppler broadening ofresonance peaks.


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Controlled Fission• Note that is greater than 2 at thermal energies andalmost 3 at high energies.• These “extra” neutrons are Used to convert fertile into fissile fuel.• Efficiency of this process is determined by neutronenergy spectrum.

Variations in Variations in


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Controlled Fission

• Conversion ratio Conversion ratio CR is defined as the average rate of fissile atom production to the average rate of fissile atom consumption.• For LWR's CR 0.6.• CR is called BR for values > 1.• Fast breeder reactors have BR > 1.• They are called “fast” because primary fissions inducing neutrons are fast not thermal, thus η > 2.5 but σf is only a few barns.

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Controlled Fission

Time scale for neutron multiplicationTime scale for neutron multiplication• Time constant includes moderation time (~10-6 s) and diffusion time of thermal neutrons (~10-3 s).

Time Average number of thermal neutrons t nt + knt + 2 k2n

• For a short time dt

• Show thatShow that

nkn

dt

dn

tkentn )1(0)(


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• k = 1 n is constant (Desired).• k < 1 n decays exponentially.• k > 1 n grows exponentially with time constant / (k-1).• k = 1.01 (slightly supercritical) e(0.01/0.001)t = e10 = 22026 in 1s. in 1s. • Cd is highly absorptive of thermal neutrons.• Design the reactor to be slightly subcritical for prompt neutrons.• The “few” “delayed” neutrons will be used to achieve criticality, allowing enough time tomanipulate the controlrods.

Controlled Fission

Dan

gero

us

Dan

gero

us

Cd control rodsCd control rods


tkentn )1(0)(

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Fission Reactors

Essential elements:Essential elements:• Fuel (fissile material).• Moderator (not in reactors using fast neutrons).• Reflector (to reduce leakage and critical size).• Containment vessel (to prevent leakage of waste).• Shielding (for neutrons and ’s).• Coolant.• Control system.• Emergency systems (to prevent runaway during failure).

Core


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Fission Reactors

Types of reactors:Types of reactors:Used for what?Used for what?• Power reactors: extract kinetic energy of fragments as heat boil water steam drives turbine electricity.• Research reactors: low power (1-10 MW) to generate neutrons (~1013 n.cm-2.s-1 or higher) for research.• Converters and breeders: Convert non-thermally-fissionable material (non-fissile) to a thermally-fissionable material (fissile).


What are neutron generators?What are neutron generators?

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Fission Reactors

What neutron energy?What neutron energy?• Thermal, intermediate (eV – keV), fast reactors.• Large, smaller, smaller but more fuel.

What fuel?What fuel?• Natural uranium, enriched uranium, 233U, 239Pu.

From converter or breeder reactor.How???


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Fission ReactorsWhat assembly?What assembly?• Heterogeneous: moderator and fuel are lumped. • Homogeneous: moderator and fuel are mixed together.• In homogeneous systems, it is easier to calculate p and

f for example, but a homogeneous natural uranium-graphite mixture can not go critical.

What coolant?What coolant?• Coolant prevents meltdown of the core.• It transfers heat in power reactors.• Why pressurized-water reactors.• Why liquid sodium?


What moderator?What moderator?1. Cheap and abundant.2. Chemically stable.3. Low mass (high logarithmic energy decrement).4. High density.5. High s and very low a.• Graphite (1,2,4,5) increase amount to compensate 3.• Water (1,2,3,4) but n + p d + enriched uranium.• D2O (heavy water) (1!) but has low capture cross

section natural uranium, but if capture occurs, produces tritium.

• ….. 12

More on Moderators


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More on Moderators


Moderating ratio

Calculate both moderating power and ratio for water, heavy water, graphite, polyethylene and boronboron.Tabulate your results and comment.

a

s

Moderating power

HW 12HW 12 LiBnB 7*1110

B-10

1/v region

Good absorber,

Good absorber, bad moderator.

bad moderator.

Never consider this only!

For a compound?

1010BB


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More on Moderators

1

1ln

2

)1(1ln

2

\

A

A

A

A

E

Eu

av

nEEn lnln \

)/ln( \

nEEn Recall

After n collisions

)/ln( thf EE

n

Total mean free path = n s

Is it random walk or there is a preferred direction???

creation

absorption

After one collision

f

th

Assumptions:Assumptions:1.1.Elastic scattering. Elastic scattering. E2.2.Target nucleus at rest. Target nucleus at rest. E3.3.Spherical symmetry in Spherical symmetry in CM.CM.

Recall (head-on). Then the maximum energy loss is (1-)E, or E E\ E. For an ss-wave-wave collision:

show that

Obviously


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More on ModeratorsHW 13 (or 6HW 13 (or 6\\))

EEA

AE

2

min\

1

1

EEEPdEEEP

E

E )1(

1)(1)( \\\

EE )1(21\

otherwise

EEEE

E

dE

dEE

ss

s

0)1(

)()(

|

|\

Scattering Kernel?Scattering Kernel?

E


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More on Moderators

2

222

2

2\

)1(

sincos

cos)1()1(2

1

)1(

cos21

A

A

A

AA

E

E CMCM

(Re)-verify

For doing so, you need to verify and use

CM

CM

AA

A

cos21

cos1cos

2

HW 13 (or 6HW 13 (or 6\\) ) continued…continued…


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More on Moderators


• Forward scattering is preferred for “practical” moderators (small A).• If isotropic neutron scattering (spherically symmetric) in the laboratorylaboratory frame average cosine of the scattering angle is zero.

Show that A3

2)(cos


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More on Moderators

Spherically symmetric in CM

Show that

)(4

1)( E

d

ds

CMsCM

s

CM

CMs

s A

AAE

cos1

)1cos2(

4

)()(

1

2312

Try to sketch.


• Neutron scatteringscattering is isotropic in the laboratory system?! valid for neutron scattering with heavy nuclei, which is not true for usual thermal reactor moderators (corrections are applied);

Distinguish fromDistinguish from

• Angular neutron distribution.distribution.

Neutron Life Cycle

Documents

saed dababneh

thatnuclear reactors

corenuclear reactors

fast breeder reactors

fast neutrons

absorptive of thermal

prompt neutrons

extra neutrons