Nuclear Fission elementary principles

Nuclear Fission elementary principles

BNEN 2015-2016 IntroWilliam D’haeseleer

Mass defect & Binding energy

ΔΔE = E = ΔΔm cm c22

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

Nuclear fission

Nuclear Fission + products

Ref: Duderstadt & Hamilton

BNEN NRT 2009-2010William D’haeseleer

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Practical Fission Fuels

1 10

A Az zn X X → fission

fissile

fissile

fissile

U-233U-235

Pu-239

Ref: Lamarsh NRT

7


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)

23592 U

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Fertile nuclei

Nuclei that are not easily “fissile” (see further)but that produce fissile isotopesafter absorption of a neutron

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* Thorium-uranium

1 232 2330 90 90Th + Thn

23391Pa

β (22 min)

β (27 d)

23392 U

Fissile by slow (thermal) neutron

- not much used so far

- but large reserves of Th-232

- new interest because of ADS (cf. Rubbia)

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* Uranium-Plutonium

1 238 2390 92 92U + Un

23993 Np

23994 Pu

β (23 min)

β (2.3 d)

Fissile by slow (thermal) neutron

- 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”

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Fissionable nuclei

Th-232 and U-238 fissionable with threshold energy

U-233, U-235 & Pu 239 easily fissionable = “fissile”-- see Table 3.1 --


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1 10

A Az zn X X → fission

fissionable

fissionable

Th-232

U-238

Eth=0.6MeV

Eth=1.4 MeV

Fission Chain Reaction

Chain reaction235 U

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


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Probability for fission

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

Logarithmic scale !

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Cross Section of Fissionable Nuclei

• Thermal cross sectionImportant for “fissile” nuclei, is the so-called

thermal cross section

-- See Table 3.2 --

at 0.025 eVthf

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19


• 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

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Define

capture to fission ratiof

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U-235

α > 1 more chance for radiative capture

α < 1 more chance for fission

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f

a f Note

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Then with

Relative probability fission =

Relative probability rad. capture =

f

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f

f

1f

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

Fission products / fragments





Fission products generally radioactive

Dominantly neutron rich

Mostly β- decay

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The products of fission: neutrons

→ Besides fission also absorptionRecall

Therefore:

In U-235: 15% for low E1 n

1f

a

vv

f

See table 3.2

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

capture to fission ratiof

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1f

a

vv


32



1f

a

vv

η(E) for

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

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1f

a

vv

To be compared with curve for α (cfr before)

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

(25) (25)(25) (28)

f

a a

v

for material

for materialf i fi i

a i ai i

N i

N i

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

Production of transurans

Evolution

of 235U content

and Pu isotopes

in typical LWR

Production of transurans

Reactor power & burn up

● Fission Rate= # fissions per second

given: a reactor producing P MW

fission rate6

6 19

18 1

23

10 /10 1.6 10

6.25 10

5.4 10 fissions/day

R

R

R

P J sE J

P sE

PE


● 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/day1P gram/day

23 gram6.02 10A

0.895 gram/day

R

PAE

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


Hence, burn up

But fuel consumption is larger→ because of radiative capture

0.895 gram/dayR

PAE

Amount of fuel fissioned

Total absorption rate = fission ratea

f

1 fission rate

Reactor power & burn upconsumption rate

Energy “production” per fissioned amount of fuel:also often called Burn UpBurn Up: MWD/tonMWD/ton

- assume pure U-235, and assume that all U-235 is fissioned;- then: energy “production” 1MWD/g = 106 MWD/ton- but also radiative capture only 8 x 105 MWD/ton- but also U-238 in “fuel” in practice ~ 20 to 30 x 10³ MWD/ton

(however, recently more)

~ 50 to 60 x 103 MWD/ton

0.895 1 gram/dayR

PAE

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]

FP 33.6 46.1 61.4

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

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:

Then n emission rather than γ 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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Nuclear Fission elementary principles