Applications%20of%20Nuclear%20Physics

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Lecture 6

• Applications of Nuclear Physics
• Fission Reactors and Bombs

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6.1 Overview

• 6.1 Induced fission
• Fissile nuclei
• Time scales of the fission process
• Crossections for neutrons on U and Pu
• Neutron economy
• Energy balance
• A simple bomb
• 6.2 Fission reactors
• Reactor basics
• Moderation
• Control
• Thermal stability
• Thermal vs. fast
• Light water vs. heavy water
• Pressurised vs. Boiling water
• Enrichment
• 6.3 Fission Bombs
• Fission bomb fuels
• Suspicious behaviour

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6.1 Induced Fission(required energy)
Nucleus Potential Energy MeV
A 238
Neutrons
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6.1 Induced Fission(required energy)

• Spontaneous fission rates low due to high coulomb
  barrier (6-8 MeV _at_ A240)
• Slow neutron releases DEsep as excitation into
  nucleus
• Excited nucleus has enough energy for immediate
  fission if Ef - DEsep gt0
• But due to pairing term
• even N nuclei have low DEsep
• odd N nuclei have high DEsep
• ? Fission yield in n-absorption varies
  dramatically between odd and even N

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6.1 Induced Fission(fissile nuclei)

• DEsep(n,238U) 4.78MeV only ?
• Fission of 238U needs EngtEf-DEsep1.4 MeV
• Must be provided by n-kinetic energy
• Call this fast fission
• Thermally fissile nuclei, Enthermal0.1eV _at_ 1160K
• 23392U, 23592U, 23994Pu, 24194Pu
• Fast fissile nuclei EnO(MeV)
• 23290Th, 23892U, 24094Pu, 24294Pu
• Note all Pu isotopes on earth are man made
• Note only 0.72 of natural U is 235U

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6.1 Induced Fission (Reminder stages of the
process)
t0
lt prompt ngt n2.5
t10-14 s
tgt10-10 s
ltn-delaygt tdfew s
lt delayed ngt nd0.006
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6.1 Induced Fission (the fission process)

• Energy balance in MeV
• Prompt
• Ekin(fragments) 167
• Ekin(prompt ns) 5 ? 3-12 from Xn?Yg
• E(prompt g) 6
• Subtotal 178 (good for power production)
• Delayed
• Ekin(e from b-decays) 8
• E(g following b-decay) 7
• Subtotal 15 (bad, spent fuel heats up)
• Neutrinos 12 (invisible)
• Grand total 205

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6.1 Induced Fission(fission crossections)

• 23592U does O(85) fission starting at very low
  En
• 23892U does nearly no fission below En1.4MeV
• Consistent with SEMF-pairing term of
  12MeV/vA0.8MeV between
• odd-even 23592U and even-even 23892U

unresolved, narrow resonances
unresolved, narrow resonances
235U
238U
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6.1 Induced Fission(fission probabilities in
natural Uranium)
absorbtion probabilit per 1 mm
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6.1 Induced Fission(a simple bomb)

• Uranium mix
• 235U238U c(1-c)
• rnucl(U)4.81028 nuclei m-3
• average crossection

• mean free path

• mean time between collisions 1.510-9 s _at_
  Ekin(n)2MeV

• Simplify to c1 (the bomb mixture)
• prob(235U(npromptf)) _at_ 2MeV 18
• rest of n scatter, loosing Ekin ? prob(235U(n,f))
  grows
• most probable collisions before 235U(nf) 6
  (work it out!)
• 6 random steps of l3cm ? lpv63cm7cm in
  tp10-8 s

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6.1 Induced Fission(a simple bomb)

• After 10-8 s 1n is replaced with n2.5 n
• Let probability of new n inducing fission before
  it is lost q
• (others escape or give radiative capture)
• Each n produces on average (nq-1) new ns in
  tp10-8 s (ignoring delayed ns as bombs dont
  last for seconds!)

• if nqgt1?exponential growths
• For 235U, n2.5 ? if qgt0.4 you get a bomb

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6.1 Induced Fission(a simple bomb)

• If object dimensions ltlt 7cm
• ? most ns escape through surface
• ? nq ltlt 1
• If Rsphere(235U)8.7cm ? M(235U)52 kg
• ? nq 1
• ? explosion in lt tp10-8 s
• ? little time for sphere to blow apart
• ? significant fraction of 235U will do fission

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6.2 Fission Reactors(not so simple)

• Q What happens to a 2 MeV fission neutron in a
  block of natural Uranium (c0.72)?
• A In order of probability
• Inelastic 238U scatter
• Fission of 238U (5)
• rest is negligible
• Eneutron decreases
• s(23892U(n,g)) increases and becomes resonant
• s(23892U(n,f)) dercreases rapidly and vanishes
  below 1.4 MeV
• only remaining change for fission is
  s(23592U(n,f)) wich is much smaller then
  s(23892U(n,g))
• Conclusion piling up natural U wont make a
  reactor. I said it is not SO simple

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6.2 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 s as
  moderator material. (Why low mass?)
• sandwich fuel rods with moderator (and coolant)
  layers
• when n return from moderator energy is so low
  that it will predominantly cause fission in 235U

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6.2 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 (breeding) via
• 23892Un ? 23992U g
• ? 23993Np e- ne
• ? 23994Pu e ne
• Details about fast reactors later

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6.2 Fission Reactors (Pu fuel)

• 239Pu fission crossection slightly better then
  235U
• Chemically separable from 238U (no centrifuges)
• More prompt neutrons n(239Pu)2.96
• Fewer delayed n higher n-absorbtion, more later

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6.2 Fission Reactors (Reactor control)

• For bomb we found
• boom if nq gt 1 where n was number of prompt n
• Reactors use control rods with large n-capture s
  (B, 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)
• Far too fast to control
• but there are also delayed ns

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6.2 Fission Reactors (Reactor control)

• Fission products all n-rich ? all b- active
• Daughters of some b- decays can directly emit ns
  (see table of nuclides, green at bottom of curve)

• several sources of delayed ns
• typical tO(1 sec)
• Fraction nd 0.6

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6.2 Fission Reactors (Reactor control)

• Since fuel rods hopefully remain in reactor
  longer then 10-2 s ? must include delayed n
  fraction nd
• New control problem
• keep (nnd)q 1
• to accuracy of lt 6
• at time scale of few seconds
• Doable with mechanical system but not easy

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6.2 Fission Reactors (Reactor cooling)

• As q rises, power produced in reactor rises ?
• cool reactor and drive heat engine with coolant
  
• coolant will also act as moderator
• Coolant/Moderator choices

Material State sn-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
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6.2 Fission Reactors (Thermal Stability)

• Want dq/dT lt 0
• Many mechanical influences via thermal expansion
• Change in n-energy spectrum
• Doppler broadening of 238U(n,g) resonances ?
  large negative contribution to dq/dT
• Doppler broadening of 239Pu(n,f) in fast reactors
  gives positive contribution to dq/dt
• Chernobyl No 4. had dq/dT gt1 at low power

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6.2 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 ? ? dont
  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 time
  more fuel
• High fuel concentration breading ? ? Can
  operate for long time without rod changes
• Designs for 4th generation Pb or gas cooled fast
  reactors exist. Could overcome the Na problems

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6.2 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

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6.2 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

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6.2 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

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6.2 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

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6.2 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

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6.2 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
  (t½(16N)7s, main contaminant)

• lower temperature ? ? lower efficiency

• if steam fraction too large (norm. 18) ? ?
  Boiling crisis
• loss of cooling

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6.2 Fission Reactors (cool reactors)
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6.2 Fission Reactors (cool reactors)

• no boiling crisis
• no steam handling
• high efficiency 44
• compact core
• low coolant mass

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6.2 Fission Reactors (enrichment)

• Two main techniques to separate 235U from 238U in
  gas form UF6 _at_ Tgt56C, P1bar
• 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

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1-2 m
15-20 cm
O(70,000) rpm ? Vmax1,800 km/h supersonic!
gmax106g ? difficult to build!
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6.2 Fission Reactors (enrichment)
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6.3 Fission Bombs (fission fuel properties)
Isotope Half-lifea Bare critical mass Spontaneousfission neutrons Decay heat
years kg, 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. a. By Alpha-decay, except Pu-241, which is by Beta-decay to Am-241. a. By Alpha-decay, except Pu-241, which is by Beta-decay to Am-241. a. By Alpha-decay, except Pu-241, which is by Beta-decay to Am-241. a. By Alpha-decay, except Pu-241, which is by Beta-decay to Am-241.

• ideal bomb fuel pure 239Pu

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6.3 Fission Bombs (where to get Pu from?)
Grade Isotope Isotope Isotope Isotope 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 - -
a. Pu-241 plus Am-241.
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 (ParisOECD/NEA,
1989) Table 12A).
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(ParisOECD/NEA, 1989) Table 12A).
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6.3 Fission Bombs (drawbacks of various Pu
isotopes)

• 241Pu decays to 241Am which gives very high
  energy g-rays ? shielding problem
• 240Pu lots of spontaneous fission n
• 238Pu decays quickly ? lots of heat
  ?conventional ignition explosives dont like
  that!
• in pure 239Pu bomb, ignition timed optimally
  during compression using burst of n ? maximum
  explosion yield
• but using reactor grade Pu, n from 240Pu can
  ignite bomb prematurely ? lower explosion yield
  but still a very bad bomb
• Reactor grade Pu mix has drawbacks but can
  readily be made into a bomb.

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6.3 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 g sources from 241Am outside a
  reactor
• large n fluxes from 240Pu outside reactors ?very
  penetrating ? easy to spot over long range

Plutonium isotope composition as a function of
fuel exposure in a pressurized-water reactor,
upon discharge.