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Nuclear Fission elementary principles

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Mass defect & Binding energy

ΔE = Δm c2

Nuclear Fission

- Heavy elements may tend to split/fission
- But need activation energy to surmount potential barrier
- Absorption of n sufficient in
233U 235U 239Pu … fissile nuclei

- Fission energy released ~ 200 MeV
- Energetic fission fragments
- 2 à 3 prompt neutrons released upon fission

Ref: Duderstadt & Hamilton

Practical Fission Fuels

→fission

Ref: Lamarsh NRT

fissile

U-233

fissile

U-235

fissile

Pu-239

BNEN NRT 2009-2010

William D’haeseleer

Practical Fission Fuels

From these, only appears in nature (0.71%)

The other fissile isotopes must be “bred”

out of Th-232 (for U-233)

out of U-238 (for Pu-239)

Practical Fission Fuels

Fertile nuclei

Nuclei that are not easily “fissile” (see further)

but that produce fissile isotopes

after absorption of a neutron

Practical Fission Fuels

* Thorium-uranium

β (22 min)

β (27 d)

- not much used so far

- but large reserves of Th-232

- new interest because of ADS (cf. Rubbia)

Fissile by slow (thermal) neutron

Practical Fission Fuels

* Uranium-Plutonium

β (23 min)

β (2.3 d)

- up till now mostly used for weapons

- is implicitly present in U-reactors

- now also used as MOX fuels

- the basic scheme for “breeder reactors”

Fissile by slow (thermal) neutron

Practical Fission Fuels

Fissionable nuclei

Th-232 and U-238 fissionable with threshold energy

U-233, U-235 & Pu 239 easily fissionable = “fissile”

-- see Table 3.1 --

Practical Fission Fuels

→fission

Eth=1.4 MeV

fissionable

Th-232

U-238

fissionable

Eth=0.6MeV

BNEN NRT 2009-2010

William D’haeseleer

Fission Chain Reaction

- k= multiplication factor
- k= (# neutrons in generation i) /
(# neutrons in generation i-1)

- k= 1 critical reactor
- k>1 supercritical
- k<1 subcritical

Critical mass

- Critical mass is amount of mass of fissile material, such that
Neutron gain due to fission

=

Neutron losses due to leakage & absorption

- Critical mass
= minimal mass for stationary fission regime

Probability for fission

Logarithmic scale !

Comparison fission cross section U-235 and U-238 [Ref Krane]

BNEN NRT 2009-2010

William D’haeseleer

Cross Section of Fissionable Nuclei

- Thermal cross section
Important for “fissile” nuclei, is the so-called

thermal cross section

-- See Table 3.2 --

Cross Section of Fissionable Nuclei

- Absorption without fission
σγ for these nuclei ~ other nuclei

behaves like 1/v for small v

at low En, inelastic scattering non existing

only competition between -fission

-radiative capture

Cross Section of Fissionable Nuclei

α > 1 more chance for radiative capture

U-235

α < 1 more chance for fission

Cross Section of Fissionable Nuclei

Then with

Relative probability fission =

Relative probability rad. capture =

Thermal reactors

- Belgian fission reactors are “thermal reactors”
- Neutrons, born with <E>=2MeV to be slowed down to ~ 0.025 eV
- By means of moderator:
- Light material: hydrogen, deuterium, water
graphite

- Light material: hydrogen, deuterium, water

Fission products / fragments

Fission products generally radioactive

Dominantly neutron rich

Mostly β- decay

The products of fission: neutrons

→ Besides fission also absorption

Recall

Therefore:

See table 3.2

η=number of n ejected per n absorbed in the “fuel”

The products of fission: neutrons

η(E) for

U-233, U-235, Pu-239 & Pu-241

BNEN NRT 2009-2010

William D’haeseleer

Ref: Duderstadt & Hamilton

The products of fission: neutrons

To be compared with curve for α(cfr before)

Ref: Duderstadt & Hamilton

The products of fission: neutrons

η usually also defined for mixture U-235 and U-238

Enrichment

- Natural U consist of 99.3% 238U & 0.7% 235U
- NU alone cannot sustain chain reaction
- NU in heavy water moderator D2O can be critical (CANDU reactors)
- Light water (H2O) moderated reactors need enrichment of fissile isotope 235U
- Typically in thermal reactors 3-5% 235U enrichment
- For bombs need > 90% enrichment

Reactor power & burn up

● Fission Rate

= # fissions per second

given: a reactor producing P MW

fission rate

Reactor power & burn up

● Burn up

= amount of mass fissioned per unit time

Burn up = fission rate * mass of 1 atom

Burn up =

for A = 235 ; ER = 200 MeV … Burn Up = 1P gram/day

! For a reactor of 1 MW, 1 gram/day U-235 will be fissioned !

Reactor power & burn up

Hence, burn up

But fuel consumption is larger

→ because of radiative capture

Amount of fuel fissioned

Reactor power & burn up

consumption rate

Energy “production” per fissioned amount of fuel:

MWD/tonne

- assume pure U-235, and assume that all U-235 is fissioned;

- then: energy “production” 1MWD/g = 106 MWD/tonne

- but also radiative capture only 8 x 105 MWD/tonne

- but also U-238 in “fuel” in practice ~ 20 to 30 x 10³ MWD/tonne

(however, recently more)

~ 50 to 60 x 103 MWD/tonne

Actinide Buildup [Ref: CLEFS CEA Nr 53]

Total U 955 746 941 026 923 339

Total Pu 9 737 11 338 13 000

Composition of spent fuel

- Typical for LWR:

Fission Products [Ref: CLEFS CEA Nr 53]

TOTAL 33,6 46,1 61,4

Fission Products [Ref: CLEFS CEA Nr 53]

Category UOX 33 GWa/tUi UOX 45 GWa/tUi UOX 60 GWa/tUi

Enr 3.5% Enr: 3.7% Enr: 4,5%

Amount kg/tUi Amount kg/tUi Amount kg/tUi

Uranium 955.746 941.026 923.339

Plutonium 9.737 11.338 13.0

FP 33.6 46.1 61.4

TOTAL 999.083 998.464 997.739

Remainder converted to energy via E=∆m c2

Delayed neutrons

- Recall 2 à 3 prompt neutrons, released after ~10-14 sec
- Thermalized after ~1 μsec
- Absorption after ~200 μs ~ 10-4 s
- Difficult to control
- Nature has foreseen solution! Delayed Neutrons
- Recall β decay from some fission products

Neutron emission after β decay

After β decay, if energy excited state daughter larger than “virtual energy” (binding energy weakest bound neutron) in neighbor:

Thenn emissionrather thanγ emission

Called “delayed neutrons”

Delayed neutrons

- Small amount of delayed neutrons suffices (fraction ~0.0065) to allow appropriate control of reactor
- Easy to deal with perturbations

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