2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 1
Lecture 12
Applications of Nuclear Physics
Fission Reactors and Bombs
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.1 Overview 12.1 Induced fission
Fissile nuclei Time scales of the fission process Crossections for neutrons on U and Pu Neutron economy Energy balance A simple bomb
12.2 Fission reactors Reactor basics
Moderation Control Thermal stability
Thermal vs. fast Light water vs. heavy water Pressurised vs. Boiling water Enrichment
12.3 Fission Bombs Fission bomb fuels Suspicious behaviour
off syllabus, only in notes at end of slides
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.1 Induced Fission
(required energy)
Neutrons
Ef=Energy needed to penetrate fission barrier immediately ≈6-8MeV
A=238
Neu
tron
Nucleus Potential Energy during fission [MeV]
Esep≈6MeV per nucleon for heavy nuclei
Very slow n
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.1 Induced Fission
(required energy)
Spontaneous fission rates low due to high coulomb barrier (6-8 MeV @ A≈240)
Slow neutron releases Esep as excitation into nucleus
Excited nucleus has enough energy for immediate fission if Ef - Esep >0
We call this “thermal fission” (slow, thermal neutron needed)
But due to pairing term … even N nuclei have low Esep for additional n
odd N nuclei have high Esep for additional n Fission yield in n -absorption varies
dramatically between odd and even N
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.1 Induced Fission(fissile nuclei)
Esep(n,23892U) = 4.78 MeV only
Fission of 238U needs additional kinetic energy from neutron En,kin>Ef-Esep≈1.4 MeV
We call this “fast fission” (fast neutrons needed) Thermally fissile nuclei, En,kin
thermal=0.1eV @ 1160K 233
92U, 23592U, 239
94Pu, 24194Pu
Fast fissile nuclei En,kin=O(MeV) 232
90Th, 23892U, 240
94Pu, 24294Pu
Note: all Pu isotopes on earth are man made Note: only 0.72% of natural U is 235U
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.1 Induced Fission (Reminder: stages of the process up to a few seconds after fission
event)
t=0
t≈10-14 s
t>10-10 s
<# prompt n>prompt=2.5
<n-delay>d=few s
<# delayed n>d=0.006
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12.1 Induced Fission (the fission process)
Energy balance of 23592U induced thermal fission
MeV: Prompt (t<10-10s):
Ekin( fragments) 167 Ekin(prompt n) 5 3-12 from X+nY+ E(prompt ) 6 Subtotal: 178 (good for power production)
Delayed (10-10<t<): Ekin(e from -decays) 8 E( following -decay) 7 Subtotal: 15 (bad, spent fuel heats up)
Neutrinos: 12 (invisible) Grand total: 205
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12.1 Induced Fission
(n -induced fission crossections (n,f) )
23892U does nearly no n -induced fission below En,kin≈1.4
MeV 235
92U does O(85%) fission starting at very low En,kin
Consistent with SEMF-pairing term of 12MeV/√A≈0.8 MeV between
odd-even= 23592U and even-even= 238
92U
unre
solv
ed, n
arro
wre
sonance
s
unre
solv
ed, n
arro
wre
sonance
s
238U 235U
n -Energy
2 Dec 2005, Lecture 12 9
12.1 Induced Fission((n,f) and (n,) probabilities in natural Uranium)
23592U(n,f)
23592U(n,)
23892U(n,) 238
92U(n,f)235
92U(n,f)
23592U(n,)
23892U(n,)
23892U(n,)
en
erg
y r
ange o
f fi
ssio
n n
eutr
on
s
fastthermal
neutr
on a
bso
rbti
on p
robabili
t p
er
1
m
“bad-238”
“good 238 ”
“bad-235”
“good 235 ”
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.1 Induced Fission(a simple bomb)
mean free path for fission n:
235 238(1 )tot tot totc c 1 ( ) 3 cmnucl tot
Simplify to c=1 (the bomb mixture) prob(235U(nprompt ,f)) @ 2MeV ≈ 18% (see slide 8) rest of n scatter, loosing Ekin prob(235U(n,f)) grows most probable #collisions before 235U(n,f) = 6 (work it out!) 6 random steps of =3cm lmp=√6*3cm≈7cm in tmp=10-8 s
Uranium mix 235U:238U =c:(1-c) nucl(U)=4.8*1028 nuclei m-3
average n crossection:
mean time between collisions =1.5*10-9 s @ Ekin(n)=2MeV
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.1 Induced Fission(a simple bomb)
After 10-8 s 1n is replaced with =2.5 n, =average prompt neutron yield of this fission process
Let probability of new n inducing fission before it is lost = q
(others escape or give radiative capture) Each n produces on average (q-1) new such n in tp=10-8 s
(ignoring delayed n as bombs don’t last for seconds!)
0
( 1)
( ) ( ) ( 1) ( ) ( )
( ) 1lim ( )
solved by: ( ) (0) mp
mp
tmp
tq t
n t t n t q n t t t
dn t qn t
dt t
n t n e if q>1 exponential growths of neutron number For 235U, =2.5 if q>0.4 you get a bomb
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.1 Induced Fission(a simple bomb)
If object dimensions << lmp=7 cm
most n escape through surface q << 1
If Rsphere(235U)≥8.7cm M(235U)≥52 kg
q = 1 explosion in < tp=10-8 s
little time for sphere to blow apart significant fraction of 235U will do fission
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12.2 Fission Reactors(not so simple)
Q: What happens to a 2 MeV fission neutron in a block of natural Uranium (c=0.72%)?
A: In order of probability Inelastic 238U scatter (slide 8) Fission of 238U (5%) rest is negligible
as Eneutron decreases via inelastic scattering (238
92U(n,)) increases and becomes resonant (238
92U(n,f)) decreases rapidly and vanishes below 1.4 MeV only remaining chance for fission is (235
92U(n,f)) which is much smaller then (238
92U(n,)) Conclusion: piling up natural U won’t make a reactor
because n get “eaten” by (n,) resonances. I said it is not SO simple
23592U(n,f)
23592U(n,)
23892U(n,) 238
92U(n,f)235
92U(n,f)
23592U(n,)
23892U(n,)
23892U(n,)
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors(two ways out)
Way 1: Thermal Reactors bring neutrons to thermal energies without
absorbing them = moderate them use low mass nuclei with low n-capture
crossection as moderator. (Why low mass?) sandwich fuel rods with moderator and
coolant layers when n returns from moderator its energy is
so low that it will predominantly cause fission in 235U
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors(two ways out)
Way 2: Fast Reactors Use fast neutrons for fission Use higher fraction of fissile material,
typically 20% of 239Pu + 80% 238U This is self refuelling (fast breeding) via:
23892U+n 239
92U + 239
93Np + e- + e
23994Pu + e¯ + e
Details about fast reactors later
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12.2 Fission Reactors (Pu fuel)
239Pu fission crossection slightly “better” then 235U Chemically separable from 238U (no centrifuges) More prompt neutrons (239Pu)=2.96 Fewer delayed n & higher n-absorbtion, more later
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (Reactor control)
For bomb we found: “boom” if: q > 1 where was number of prompt n we don’t want “boom” need to get rid of most
prompt n Reactors use control rods with large n-capture
crossection nc like B or Cd to regulate q Lifetime of prompt n:
O(10-8 s) in pure 235U O(10-3 s) in thermal reactor (“long” time in moderator)
not “long” enough Far too fast to control … but there are also delayed neutrons
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12.2 Fission Reactors (Reactor control)
Fission products all n -rich all - active Some - decays have excited states as daughters These can directly emit n (see table of nuclides, green at bottom of
curve)
Group Half-Life
(sec)
Delayed Neutron Fraction
Average Energy (MeV)
1 55.7 0.00021 0.252 22.7 0.00142 0.463 6.2 0.00127 0.414 2.3 0.0026 0.455 0.61 0.00075 0.416 0.23 0.00027 -
Total - 0.0065 -
Delayed Neutron Precursor Groups for Thermal Fission in 235-U
several sources of delayed n typical lifetimes ≈O(1 sec) Fraction d ≈ 0.6%
Energ
y
off
sylla
bus
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (Reactor control)
Since fuel rods “hopefully” remain in reactor longer then 10-2 s must include delayed n fraction d into our calculations
New control problem: keep (+d)q = 1 to accuracy of < 0.6% at time scale of a few seconds
Doable with mechanical systems but not easy
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12.2 Fission Reactors (Reactor cooling)
As q rises during control, power produced in reactor rises we cool reactor and drive “heat engine” with coolant coolant will often also act as moderator
Coolant/Moderator choices:
Material
State n-abs reduce En
chemistry
other coolant
H2O liquid
small
best reactive cheap good
D2O liquid
none
2nd best reactive rare good
C solid mild medium reactive cheap medium
CO2press. gas mild medium passive cheap ok
He gas mild 3rd best very passi.
leaks ok
Na liquid
small
medium very react.
difficult excellent
off
sylla
bus
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (Thermal Stability)
Want dq/dT < 0 Many mechanical influences via thermal
expansion Change in n-energy spectrum Doppler broadening of 238U(n,) resonances
large negative contribution to dq/dT due to increased n -absorbtion in broadened spectrum
Doppler broadening of 239Pu(n,f) in fast reactors gives positive contribution to dq/dt
Chernobyl No 4. had dq/dT >0 at low power … which proved that you really want dq/dT < 0
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.3 Fission Bombs (fission fuel properties)
ideal bomb fuel = pure 239Pu
Isotope Half-lifea Bare critical mass
Spontaneousfission neutrons
Decay heat
yearskg, Alpha-phase
(gm-sec)-1 watts kg-1
Pu-238 87.7 10 2.6x103 560
Pu-239 24,100 10 22x10-3 1.9
Pu-240 6,560 40 0.91x103 6.8
Pu-241 14.4 10 49x10-3 4.2
Pu-242 376,000 100 1.7x103 0.1
Am-241 430 100 1.2 114
a. By Alpha-decay, except Pu-241, which is by Beta-decay to Am-241.
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.3 Fission Bombs (where to get Pu from? Sainsbury’s?)
Grade Isotope
Pu-238 Pu-239 Pu-240 Pu-241a Pu-242
Super-grade - .98 .02 - -
Weapons-gradeb .00012 .938 .058 .0035 .00022
Reactor-gradec .013 .603 .243 .091 .050
MOX-graded .019 .404 .321 .178 .078
FBR blankete - .96 .04 - -
c. Plutonium recovered from low-enriched uranium pressurized-water reactor fuel that has released 33 megawatt-days/kg fission energy and has been stored for ten years prior to reprocessing (Plutonium Fuel: An Assessment (Paris:OECD/NEA, 1989) Table 12A).
a. Pu-241 plus Am-241.
d. Plutonium recovered from 3.64% fissile plutonium MOX fuel produced from reactor-grade plutonium and which has released 33 MWd/kg fission energy and has been stored for ten years prior to reprocessing (Plutonium Fuel: An Assessment(Paris:OECD/NEA, 1989) Table 12A).
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.3 Fission Bombs (drawbacks of various Pu isotopes)
241Pu : decays to 241Am which gives very high energy -rays shielding problem
240Pu : lots of n from spontaneous fission 238Pu : -decays quickly (= 88 years) lots of heat
conventional ignition explosives don’t like that! in pure 239Pu bomb, the nuclear ignition is timed
optimally during compression using a burst of external n maximum explosion yield
… but using reactor grade Pu, n from 240Pu decays can ignite bomb prematurely lower explosion yield but still very bad if you are holding it in your hand
Reactor grade Pu mix has “drawbacks” but can “readily” be made into a bomb.
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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Plutonium isotope composition as a function of fuel exposure in a pressurized-water reactor, upon discharge.
12.3 Fission Bombs (suspicious behaviour)
Early removal of fission fuel rods need control of reactor fuel changing cycle!
Building fast breaders if you have no fuel recycling plants
Large high-E sources from 241Am outside a reactor
large n fluxes from 240Pu outside reactors very penetrating easy to spot over long range
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 26
End of Lecture 12
even more energetic fusion can be found in Dr. Weidberg’s notes…
2 Dec 2005, Lecture 12 27
en
erg
y r
ange o
f fi
ssio
n n
eutr
on
s
12.1 Induced Fission ((n,f) and (n,) probabilities in natural Uranium)
23592U(n,f)
23592U(n,)
23892U(n,) 238
92U(n,f)235
92U(n,f)
23592U(n,)
23892U(n,)
23892U(n,)
fastthermal
neutr
on a
bso
rbti
on p
robabili
t p
er
1
m
“bad-238”
“good 238 ”
“bad-235”
“good 235 ”
reprinted to show high E end of better
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 28
Appendix to lecture 12
More on various reactors Uranium enrichment
Off Syllabus
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (Thermal vs. Fast)
Fast reactors need very high 239Pu concentration Bombs very compact core hard to cool need high
Cp coolant like liq.Na or liq. NaK-mix don’t like water & air & must keep coolant circuit molten & high activation of Na
High coolant temperature (550C) good thermal efficiency
Low pressure in vessel better safety can utilise all 238U via breeding 141 times more
fuel High fuel concentration + breading Can
operate for long time without rod changes Designs for 4th generation molten Pb or gas cooled
fast reactors exist. Could overcome the Na problems
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2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (Thermal vs. Fast)
Thermal Reactors Many different types exist
BWR = Boiling Water Reactor PWR = Pressure Water Reactor BWP/PWR exist as
LWR = Light Water Reactors (H2O) HWR = Heavy Water Reactors (D2O)
(HT)GCR = (High Temperature) Gas Cooled Reactor exist as
PBR = Pebble Bed Reactor other more conventional geometries
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (Thermal vs. Fast)
Thermal Reactors (general features) If moderated with D2O (low n-capture)
can burn natural U now need for enrichment (saves lots of energy!)
Larger reactor cores needed more activation
If natural U used small burn-up time often need continuous fuel exchange hard to control
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (Light vs. Heavy water thermal reactors)
Light Water it is cheap very well understood chemistry compatible with steam part of plant can not use natural uranium (too much n-
capture) must have enrichment plant bombs
need larger moderator volume larger core with more activation
enriched U has bigger n-margin easier to control
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (Light vs. Heavy water thermal reactors)
Heavy Water it is expensive allows use of natural U natural U has smaller n-margin harder to
control smaller moderator volume less
activation CANDU PWR designs (pressure tube reactors)
allow D2O moderation with different coolants to save D2O
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (PWR = most common power reactor)
Avoid boiling better control of moderation Higher coolant temperature higher thermal efficiency If pressure fails (140 bar) risk of cooling failure via boiling Steam raised in secondary
circuit no activity in turbine and generator
Usually used with H2O need enriched U
Difficult fuel access long fuel cycle (1yr) need highly enriched U
Large fuel reactivity variation over life cycle need variale “n-poison” dose in coolant
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (BWR = second most common power reactor)
lower pressure then PWR (70 bar) safer pressure vessel simpler design of vessel and heat steam circuit primary water enters turbine activation of tubine no
access during operation (½(16N)=7s, main contaminant) lower temperature lower efficiency
if steam fraction too large (norm. 18%) Boiling crisis =loss of cooling
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (“cool” reactors)
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (“cool” reactors)
• no boiling crisis• no steam handling• high efficiency 44%• compact core• low coolant mass
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors (enrichment)
Two main techniques to separate 235U from 238U in gas form UF6 @ T>56C, P=1bar centrifugal separation
high separation power per centrifugal step low volume capacity per centrifuge total 10-20 stages to get to O(4%) enrichment energy requirement: 5GWh to supply a 1GW reactor with 1
year of fuel diffusive separation
low separation power per diffusion step high volume capacity per diffusion element total 1400 stages to get O(4%) enrichment energy requirement: 240GWh = 10 GWdays to supply a
1GW reactor with 1 year of fuel
2 Dec 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold
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15-20 cm
1-2
m
O(70,000) rpm Vmax≈1,800 km/h = supersonic! & gmax=106g difficult to build!
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12.2 Fission Reactors (enrichment)