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University Ghent Reactortheory: Partim I History of nuclear fission
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University Ghent 2015-2016 Reactortheory: Partim I
1
Reactortheory: Partim IG. Janssens-Maenhout
Lecture 1 (24/09/2015)
University Ghent 2015-2016 Reactortheory: Partim I
Greet Maenhout (UGENT- European Commission/JRC)greet.maenhout@ugent,be or greet.maenhout@jrc.ec.europa.eu , 0039 0332 78 5831 (or 0039 3348013556)
ExercisesM. Vanderhaegen: discussed during the course/ by email
Exam: written 3hr
theory: 12pt: closed books (no ref. mat.)exercise: 8pt: open book (using ref. mat.)
Lectures: on Thursday afternoons 13:00 Partim I: 24/09 (S9); 15/10 (B913); 22/10; 05/11; 26/11; 3/12
Partim II: 01/10, 08/10, 29/10, 19/11, 10/12SCK.CEN Study trip/ Practicum: 12/11
Traineeship possibilities – JRC – Ispra (https://ec.europa.eu/jrc/en/research-topic/nuclear-safeguards-and-security)BNEN master after master (http://academy.sckcen.be)ESARDA course (https://esarda.jrc.ec.europa.eu/)
University Ghent 2015-2016 Reactortheory: Partim I
History of nuclear fission
University Ghent 2015-2016 Reactortheory: Partim I
Physical characteristics of a nucleus
Chemistry Nuclear physics radius atom: 10E-10m nucleus: 10E-14m
boundary vague clear, Volume~A
model cloud droplet model
proton p
neutron n
elektron e-
1u= 1.7 E-27kg
1.007 1.008 0.00055
1e-= 1.6 E-19 C
+1 0 -1
In a nucleus:
Nuclide X or A = (atomic) mass number
Z : for the chemical element Z = proton number A=Z+N = neutron number
Isotopes : nuclides with same Z : U-233, U-235, U-238,…
University Ghent 2015-2016 Reactortheory: Partim I
5
Eka-rhenium = Neptunium Eka-osmium = Plutonium
Glenn Seaborg (father of radio-
chemistry)
Periodic Table
University Ghent 2015-2016 Reactortheory: Partim I
Nuclides Chart
N=ZHeavy nucleimore neutrons
decay
decay -emitters
University Ghent 2015-2016 Reactortheory: Partim I
Radioactive decay
Radioactive decay : instable nuclei (in energy state, above their ground energy state) and
decay by emitting , n
time constant for decaying = Decay constant
After a Half life T1/2 only half of the original nuclei number remainedActivity = desintegration / second of the radioactive nuclide
1 Curie = activity of 1 g radium
)(BqNA BqECi 107.31
2N
example
Ground state
Excited states
Decay 1 with
Decay 2 withdttNtdN )()(
)exp()0()( tNtN
University Ghent 2015-2016 Reactortheory: Partim I
8
Relation between Mass and Energy
University Ghent 2015-2016 Reactortheory: Partim I
Mass defect :
Nuclear forces: mass defect
kernmNmZmm np
Nuclear forces are min. 100 x stronger than electromagnetic forces:nuclear fission releases much more energy than chemical reaction
Binding energy :
MeVummmUm nH 4.1789.114392)( A23592
)(931).(. umMeVEB
University Ghent 2015-2016 Reactortheory: Partim I
Nuclear forces: binding energy
NucleonEB ..
A
B.E. steadily increasing
Fe-56max.
fusion fission
Heavy nuclei fission spontaneously:
No natural nuclide with Z²/A>50
University Ghent 2015-2016 Reactortheory: Partim I
Nuclear forces: Bethe-Weiszäcker (emp.) mass formula
4/35
2
431332
21)(21..
Aa
AZAa
AZ²aAaAaEB /
/MeV
Volume term Coulomb term pairing term surface term asymmetric term
Coulombterm ~ 3/1
2
000 4²~
4.
AZ
re
RZeZe
Asymmetric term ~ Bv. He-4, C-6A
ZAZA 2)2(
Pairing term
Z pair A pair N pair = +1 P=155 Z pair A impair N impair = 0 P=53
Z impair A impair N pair = 0 P=50 Z impair A pair N impair = -1 P=4
University Ghent 2015-2016 Reactortheory: Partim I
Nuclear forces: empirical mass formula
3/23/2
4
3
4313
015.022
2max
2142..
AA
AaaAZif
AZa
AZa
ZEB
/
Good agreement between measured mass defect and the mass defect calculated with the empirical mass formulafor heavy nuclei.
For light nuclei and for magic nuclei, which are more stable: The shell model is more appropriate than the droplet model.
University Ghent 2015-2016 Reactortheory: Partim I
Fission and Fusion Reactions
)1(3,205421 0
001
10
13654
9842
10
23592
eVMeVQnXeMonU
fission
fusion
)1(6.17111 4
210
21
31
MeVMeVQHenHH
University Ghent 2015-2016 Reactortheory: Partim I
Nuclear reaction
4 Conservation laws
Conservation of number of nucleons
Conservation of electric charge
Conservation of momentum
Conservation of energy
Nuclear reactions and energy
dcbadcba ),(or
2331232::),( 23390
23290 nucleonsThnTh
UpnNp 23892
23893 ),( ),(235
92 fnUThnTh 23390
23290 ),(
19293::),( 23892
23893 chargeUpnNp
University Ghent 2015-2016 Reactortheory: Partim I
Mechanism to fission nucleus
Droplet model
If the nucleus deforms with contraction
then the nucleus fissions by repulsion of Coulomb forces
University Ghent 2015-2016 Reactortheory: Partim I
Fission threshold
Fission threshold:
minimal excitation energy
Q-value:
reaction energy
abd EEE
ac EEQ
University Ghent 2015-2016 Reactortheory: Partim I
Q-value of a nuclear reaction:
Q>0: exothermal reaction
Q<0: endothermal reaction
Examples: fission (reaction)
fusion (reaction)
chemical reaction
Nuclear reactions and energy: Q-value
22 )()( cmmcmmQ dcba
MeVQnDT 20
MeVQnXeMonU 200421 00
01
10
13654
9842
10
23592
eVQCOOC 422
University Ghent 2015-2016 Reactortheory: Partim I
Fission mechanism: fission parameter
Fission parameter x: = ratio Z² / (50A)
1. if (deformation remains constant and x increases) then E decreases2. if (A is large and x constant) then the impact of A is small
3. The height of fission threshold ~ deformation energy (surfaceterm+Coulombterm); experimentally determined as
AZ
MeVEd
²36.019
)( Z even A even N even = 0 Z even A odd N odd = 0.4
Z odd A odd N even = 0.4 Z odd A even N odd = 0.7
Bi-209 Th-232 U-235 U-238 Pu-239 Fm-254 x=0.66 x=0.70 x=0.72 x=0.71 x=0.74 x=0.79
University Ghent 2015-2016 Reactortheory: Partim I
Fission induced by absorbing neutrons
Heavy nuclei fission if excitation energy Ex > threshold Ed
Addition of excitation energy: with a neutron, approaching the nucleus and having the neutron taken up.
If (binding energy of latest n En (= 7 MeV) >
threshold energy (for U-235 (Z²/A=36) Ed =6 MeV)
then fission
QAZAZAZ
AZnAZ
),,(),(),()1,(
)1,(),(
2211*
*
University Ghent 2015-2016 Reactortheory: Partim I
Excitation energy of nucleus
Excitation energy = binding energy of last neutron absorbed
4/3
543/4
3313/1
232
1
4/34/315
22
4
3/13/13
3/23/221
1
)²/2(1²
)1(
211
21)1(
)1(²)1(
),.(.)1,.(.)(931)(
AaAZaAZaAaa
AAa
AZA
AZAa
AAZaAAaa
AZEBAZEBmmmMeVE
AA
AnAn
0.5MeV~33.5’A-3/4N even: ’=-1 ; N odd ’=+1
University Ghent 2015-2016 Reactortheory: Partim I
Thermal and fast fissioning
Thermal fissionable nuclide: if En Ed then the absorption of a thermal n suffices for fission (e.g. U233, U235, Pu239)
Fast fission: if En< Ed then additional energy is needed for excitation, for which n receives additional kinetic energy
Conservation of momentum
Energy
kinetic threshold energy: (Ed - En ) (A+1) /A
vMm
mV
nKEA
AmvA
A
mvMm
MVMmmvEK
1²
1
²²².).(
21
21
21
21
University Ghent 2015-2016 Reactortheory: Partim I
Fissile / fertile
Non-fissile nuclide not fissionable by thermal n, but possibly by fast n with KE > Ed
(fast fission)
Fissile nuclide is a thermally fissionable nuclide
(fissionable by thermal n with KE < 0.5eV )
U-233, U-235, Pu-239, …
Fertile nuclide: absorption of thermal n leads to a fissile nuclide, so that absorption of a second n induces fission U-238, Th-232, Pu-240, …
University Ghent 2015-2016 Reactortheory: Partim I
Experimental results of nuclear fission reactions
Experimental observations of a nuclear fission reaction:
a. Direct release: - 2 primary fission products with high Ex - 2-3 prompt neutrons (1.E-12s after fission) - prompt -photons (1.E-8s after fission)
b. Indirect release: primary fission products decay to second- ary fission products with - - decay: n p + - + - delayed neutrons, fraction 0.2% - 0.6%
Summarising: a fission reaction creates:
1. fission products, 2. energy, 3. prompt n, 4. delayed n
_
University Ghent 2015-2016 Reactortheory: Partim I
Experimental results: 1. Fission products
Yield: asymmetric fission
Remark:
- symmetric fission: rare
- Peaks at A=140 and A=95
- Z2/A only left peakA shifts to higher A
- If KE of n sym. fission more probable
- Evolution towards stable nucleithrough av. 3 decay (+)
U-235 Pu-239
University Ghent 2015-2016 Reactortheory: Partim I
Experimental results: 2. Energy released at fission
Energy Released
Kinetic energy of fission products
Energy of neutronsprompt -radiationFission products‘decay - - radiation - - radiation - Neutrino‘s
Secondary –radiationSecondary -radiation
168 MeV
5 MeV
7 MeV
8 MeV 7 MeV 12 MeV
(2 ~ 4 MeV)(3 ~ 6 MeV)
Total 200 MeV
Range (in U+air)
<0.01cm prompt
>10 cm prompt 100 cm prompt
<0.1 cm delayed100 cm delayed>100cm delayed
100 cm delayed<0.1cm delayed
About 1 gram fissile material supplies 1 MWth per day
University Ghent 2015-2016 Reactortheory: Partim I
Experimental results: 3. Fission neutrons
With the fission neutrons n we can control a chain reaction
Total number of free n: depends on - excitation energy Ex - deformation of the nucleus - fission products
Averaged total free n /fission:
Types of free n: - prompt n (fraction > 99%) - delayed n (fraction = 0.65%)
X-A(E)=0,X-A+aX-AE
2.9Pu-239
2.4U-2350
~1/8 ~1/7 E>1MeV ~1/15 E<1MeVa (1/MeV)
University Ghent 2015-2016 Reactortheory: Partim I
Experimental fission results: 3 Prompt fission neutrons
Kinetic energy of prompt n shows a continuous spectrum.
Fission spectrum (E)spectrum of which (E)dE represents the fraction of n with energy between E and E+dE.
properties of (E):
Independent of:- X-A- K.E. of n
max(E=0.72MeV)
E 2 MeV
cEbEa sinhexp
University Ghent 2015-2016 Reactortheory: Partim I
28
Einstein – Slizard:
Chain reaction
Basis for criticality: 1 neutron keeps reactions ongoing
System/mixture can be: subcritical: decliningcritical: stablesupercritical: exponentially growing
Chain Reaction
University Ghent 2015-2016 Reactortheory: Partim I
29
History of Nuclear Non-ProliferationFrom Einstein to Eisenhower
If the idea of world government is not realistic, then there is only one realistic view of our future: wholesale destruction of man by man A. Einstein
University Ghent 2015-2016 Reactortheory: Partim I
Mean neutron cycle: six factors model
Effective multiplication factor keff : number of thermal n
re-absorbed in fissile material after a mean cyclefthpLfLek
keff < 1 keff = 1 ke>1
Subcritical Supercritical mixture mixture
Critical mixture
Production factor
Fast fission factor
Fast neutron leakage
Resonance escape probability
Thermal neutron leakage
Thermal utilization factorfLp
L
th
f
University Ghent 2015-2016 Reactortheory: Partim I
31
n-leak
used n
2.4 kg 16 kg
Moderator: water
water left n-poison: B
geometry size mass
Water-reflector More leaking n N poisoning
Controlling a mixture of nuclear material around criticality
University Ghent 2015-2016 Reactortheory: Partim I
fast reactor: c = Na, Pb, PbBi s = Fe f = UO2, PuO2
The reactor as critical mixture: composition
coolant cstructure-material sfuel with
fissile material f
Fuel pin
thermal reactor: c = H2O, D2O, gas (CO2, He) s = Zr f = UO2,MOX m= H2O, C, D2O
moderator m
University Ghent 2015-2016 Reactortheory: Partim I
33
Chicago Pile 1
Rods were manually lifted on 2/12/42 9:45
History of nuclear fission reactors
University Ghent 2015-2016 Reactortheory: Partim I
Four generations of nuclear power plants
I
1942Prototype reactors:Chicago Pile
1,Dresden,Magnox
II
1965commercial
reactors:LWR
CANDUWWERRBMK...
III
1995advanced reactors:
AP600System 80+
ABWREPR ...
IV
2020Future reactors:• economically performant• inherently safe (passive systems, operator-friendly)• minimal waste (with solution for HLR waste)• proliferation-resistent
University Ghent 2015-2016 Reactortheory: Partim I
Schematics: PWR: Pressurised Water Reactor
fuel:
cladding:moderator:
coolant:
UO2 , MOXU-235 3,2%ZrH2OH2O
efficiency=33% 4 circuitspprim= 150 bar, Tin=290°C, Tout=320°C
P / V = 100 MW/m³example T.M. I. ReactorSuccessor: APWR
University Ghent 2015-2016 Reactortheory: Partim I
Reactor vessel: internals
1 Control rod drive mechanism3 Vessel head 4 outlet (+ seal)6 Fuel assembly7 Internal basket (fuel support barrel)8 Bolds (fixing vessel head )10 Control rod cluster voor 1 bundel11 Reactor vessel12 Support plate 13 Guide thimbles for core instrumentation
14
University Ghent 2015-2016 Reactortheory: Partim I
Primaire circuit: Primary pump
1 Flywheel 2-3 Radial upper bearings4-5 Motor rotor and stator7 Radial lower bearing8 Seal No. 3 with controlled leak 9 Seal No. 2 with controlled leak 10 Pump axis11 Coolant inlet (thermal barrier)12 Orifice 13 Suction14-15 Motor 16 Seals17 Seal No. 1 with controlled leak 20-22 Metallic can protecting pump23 Diffuser
University Ghent 2015-2016 Reactortheory: Partim I
Primary Circuit: Pressurizer
To regulate 150 bar in the primary circuit
University Ghent 2015-2016 Reactortheory: Partim I
Primary circuit: Steam generator
1 Steam outlet2 Steam dryers (pos. entrainment)3 Upper shell4 Cyclone5 Moisture separator (scrubbers)6 Bottom shell 7 Bundle of steam generator tubes8 Support plates 9 Feedwater inlet 10 Lower tube sheet 11 Divider plate (separating primary water inlet and outlet)12 Outlet primary coolant 13 Inlet primary coolant
University Ghent 2015-2016 Reactortheory: Partim I
Heat transfer from primary circuit to secondary circuit
University Ghent 2015-2016 Reactortheory: Partim I
Cooling of secundary circuit
University Ghent 2015-2016 Reactortheory: Partim I
BWR: Boiling Water Reactor
Fuel:
Cladding:Moderator:
Coolant:
UO2
U-235 2,6%ZrH2OH2O
Efficiency=33% 3 Circuitspprim= 70 bar, Tin=290°C, Tout=320°C
P / V = 60 MW/m³Successor: ABWR
University Ghent 2015-2016 Reactortheory: Partim I
SGHWR: Steam Generating Heavy Water Reactor
Fuel:
Cladding:Moderator:
Coolant:
UO2
U-235 2,24%ZrD2OH2O
P / V = 15 MW/m³
Efficiency=32% Pressure Tubespprim= 60 bar, Tin=240°C, Tout=270°C
University Ghent 2015-2016 Reactortheory: Partim I
CANDU: Canadian Deuterium Reactor
Fuel:
Cladding:Moderator:
Coolant:
UO2
U nat: U-235 0,7%ZrD2OD2O
P / V = 11 MW/m³Successor: CANDU-3
Efficiency=30% Pressure Tubespprim= 85 bar, Tin=270°C, Tout=300°C
University Ghent 2015-2016 Reactortheory: Partim I
Fuel:
Cladding:Moderator:
Coolant:
U MetalU MetalU nat.U nat.Magn.Ox.Magn.Ox.CCCOCO22
Magnox: Gas Cooled Graphite Reactor
P / V = 1 MW/m³
Efficiency=31% 14mx8m C-Blockpprim= 20 bar, Tin=200°C, Tout=370°C
University Ghent 2015-2016 Reactortheory: Partim I
AGR: Advanced Graphite Reactor
Fuel:
Cladding:Moderator:
Coolant:
UO2U-235 2,3%aust. steelCCO2
P / V = 2,8 MW/m³
Efficiency=42% 9mx9m C-Blockpprim= 40 bar, Tin=450°C, Tout=670°C
CO2 gas evaporates water
steam drives turbine
University Ghent 2015-2016 Reactortheory: Partim I
HTR: High Temperature Reactor
Fuel:
Cladding:Moderator:
Coolant:
UO2 - UCU-235 10%SiCCHe
P / V = 6,3 MW/m³Successor: MHTGR
Efficiency=40% 10mx6m C-Blockpprim= 50 bar, Tin=300°C, Tout=800°C
University Ghent 2015-2016 Reactortheory: Partim I
FBR: Fast Breeding Reactor
Fuel:
Cladding: Moderator:
Coolant:
UO2 - PuO2
Pu-239 20%aust. steel----Na
P / V = 650 MW/m³Successor: EFR, BREST
Efficiency=43% Blancket enriched Upprim= 5 bar, Tin=500°C, Tout=600°C
University Ghent 2015-2016 Reactortheory: Partim I
RBMK: Water Cooled Graphite Reactor
Fuel:
Cladding:Moderator:
Coolant:
UO2
U-235 2,0%ZrCH2O
P / V = 1,3 MW/m³
e.g. Tschernobyl Unit 4
Efficiency=31% 12mx7m C-Blockpprim= 70 bar, Tin=220°C, Tout=280°C
University Ghent 2015-2016 Reactortheory: Partim I
Nuclear Power Plants in Europe
LWR
WWERRBMK
GCR, FR,...
University Ghent 2015-2016 Reactortheory: Partim I
51
Where to situate the Nuclear Power ?
University Ghent 2015-2016 Reactortheory: Partim I
52
The Nuclear Club
University Ghent 2015-2016 Reactortheory: Partim I
Belgian Reactors
Nuclear share48%
Permanent shutdown
University Ghent 2015-2016 Reactortheory: Partim I
Reactor core: refueling
Pressurised Water Reactor: refueling after 12-18 months
RBMK large graphite watercooled reactor: online refueling
Fuel Assembly of a Pressurised Water Reactor
University Ghent 2015-2016 Reactortheory: Partim I
Reactor vessel : vertical cross section
1 Reactor vessel head bolt 2 Upper support plate3 1 of the 4 hot legs (outlet)4 Reactorsteel sample 5 radial support6 Control rod guiding tube 7 Spring to counteract lift force 8 O-ring for reactor vessel head9 Support column10 Lower control rod guiding tube 11 Support barrel 12 Core shell (+ rad. refl. / therm. shield)13 Lower support plate14 Diffuser plate (vortex)15 Secondary support
1
2
3
4
5
7
8
9
10
11
12
13
14
6
15
University Ghent 2015-2016 Reactortheory: Partim I
Reactor core : horizontal cross sectionPWR core
radial reflector (thermal shield)Support barrelReactor vessel
Zone 1: 1e cycle:Fresh fuel: UO2/MOX
Zone 2: 2e cycle
Zone 3: 3e cycle
With control rods
157 fuel assemblies
University Ghent 2015-2016 Reactortheory: Partim I
Reactor core: fuel assemblies configuration
Fuel assembly
(typical MOX: UO2 +PuO2)
17x17Pin lattice
o o oo o
o o o oo o
o o o o o o oo o o o
o o o oo o o o
o o o o o o oo o
o o o oo o
o o o
zone 1 nieuwe splijtstof UO2/MOX
zone 2 2e cyclus
zone 3 3e cyclus
o met controlestaven
o o oo o
o o o o o
o o x o o
o o o o o
o oo o o
zone 1 12 stiften 4.12 % Pu
zone 2 68 stiften 5.54 % Pu
zone 3 8.70 % Pu
o geleidingsbuis voor controlestaaf
x geleiding voor instrumentatiebuis
PWR core
Fresh fuel
2nd cycle fuel
3rd cycle fuel
pin
pin
Guiding tube for control rod
Guide thimble for core instrumentationWith control rods
University Ghent 2015-2016 Reactortheory: Partim I
Reactor core: fuel pin1
2
3
4
5
78
6
Pin of 9.5-12 mm thickness, 4m lengthUnder pressure (in cold condition 20-30 bar)Filled with He (heat conducting tracer gas)
1 Upper plug 2 Expansion room with spring3 Zircaloy cladding (0.5 mm)4 Isolating upper pellet5 Fuel pellets6 Isolating lower pellet 7 Supporting tube 8 Lower plug
Quality requires no leak (controlled by means of Sippingtest)
University Ghent 2015-2016 Reactortheory: Partim I
Reactor core: fuel assembly or fuel element
1 Control rod cluster 2 Control rods3 Head with spring4 Upper lattice5 Intermediate lattice support keeping fuel pins in position6 Guiding tube for control rods 7 Lower lattice8 Sole with damper
1
2
3 4
5
6
7 8
University Ghent 2015-2016 Reactortheory: Partim I
Example of Sellafield reprocessing plant: spent fuel storage
Reactor core: refueling
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