lecture 13 - university of oxfordreichold/teaching/... · dec 2006, lecture 13 nuclear physics...

Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 1

Lecture 13

Applications of Nuclear PhysicsFission Reactors and Bombs


12.1 Overview12.1 Induced fission

Fissile nucleiTime scales of the fission processCrossections for neutrons on U and PuNeutron economyEnergy balanceA simple bomb

12.2 Fission reactorsReactor basics

ModerationControlThermal stability

Thermal vs. fastLight water vs. heavy waterPressurised vs. Boiling waterEnrichment

12.3 Fission BombsFission bomb fuelsSuspicious behaviour

off syllabus, only in notes at end of slides


12.1 Induced Fission(required energy)

Neutrons

ΔEf =Energy needed to penetrate fission barrier immediately ≈6-8MeV

A=238

Neu

tro

n

Nucleus Potential Energy during fission [MeV]

ΔEsep≈6MeV per nucleon for heavy nuclei

Very slow n


12.1 Induced Fission(required energy & thermal fission)

Spontaneous fission rates low due to high coulomb barrier (6-8 MeV @ A≈240)Slow neutron releases ΔEsep as excitation into nucleusExcited nucleus has enough energy for immediate fission if Ef - ΔEsep >0We call this “thermal fission” (slow, thermal neutron needed)But due to pairing term …even N nuclei have low ΔEsep for additional nodd N nuclei have high ΔEsep for additional n

Fission yield in n -absorption varies dramatically between odd and even N


12.1 Induced Fission(fast fission & fissile nuclei)

ΔEsep(n,23892U) = 4.78 MeV only

Fission of 238U needs additional kinetic energy from neutron En,kin>Ef-ΔEsep≈1.4 MeVWe call this “fast fission” (fast neutrons needed)Thermally fissile nuclei, En,kin

thermal=0.1eV @ 1160K233

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 madeNote: only 0.72% of natural U is 235U


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

<n-delay>τd=few s

<# delayed n>νd=0.006

<# prompt n>νprompt=2.5


12.1 Induced Fission (the fission process)

Energy balance of 23592U induced thermal fission MeV:

Prompt (t<10-10s):Ekin( fragments) 167Ekin(prompt n) 5 3-12 from X+n Y+γE(prompt γ) 6Subtotal: 178 (good for power production)

Delayed (10-10<t<¶):Ekin(e from β-decays) 8E(γ following β-decay) 7Subtotal: 15 (mostly bad, spent fuel heats up)

Neutrinos: 12 (invisible)

Grand total: 205

8

12.1 Induced Fission(n -induced fission crossections (n,f) )

23892U does nearly no n -induced fission below En,kin≈1.4 MeV

23592U does O(85%) fission starting at very low En,kin

Consistent with SEMF-pairing term of 12MeV/√A≈0.8 MeVbetween

odd-even= 23592U and even-even= 238

92U

unresolved, narrowresonances

unresolved, narrowresonances

238U 235U

n -Energy

Dec 2006, Lecture 13 9

12.1 Induced Fission((n,f) and (n,γ) probabilities in natural Uranium)

23592U(n,f)

23592U(n,γ)

23892U(n,γ) 238

92U(n,f)235

92U(n,f)

23592U(n,γ)

23892U(n,γ)

23892U(n,γ)

ener

gy r

ange

of

prom

pt f

issi

on n

eutr

ons

fastthermal

neut

ron

abso

rbtio

npr

obab

ilit

per

1 μm

“bad-238”

“good238 ”

“bad-235”

“good235 ”


12.1 Induced Fission(a simple bomb)

mean free path for fission n:

235 238(1 )tot tot totc cσ σ σ= + +1 ( ) 3 cmnucl totλ ρ σ= ≈

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)) growsmost probable #collisions before 235U(n,f) = 6 (work it out!)6 random steps of λ=3cm lmp=√6*3cm≈7cm in tmp=10-8 s

Uranium mix235U:238U =c:(1-c)

ρnucl(U)=4.8*1028 nuclei m-3

average n crossection:

mean time between collisions =1.5*10-9 s @ Ekin(n)=2MeV



After 10-8 s 1n is replaced with ν=2.5 n, ν=average prompt neutron yield of this fission processLet probability of new n inducing fission before it is lost = q(others escape or give radiative capture)Each n produces on average (νq-1) new such n in tmp=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

δ

ν

δ ν δ

ν→

−

+ = + − ⋅ ⋅

−⇒ =

=

if νq>1 exponential growths of neutron numberFor 235U, ν=2.5 if q>0.4 you get a bomb



If object dimensions << lmp=7 cmmost n escape through surfaceνq << 1

If Rsphere(235U) ≥ 8.7cm ⇔ M(235U) ≥ 52 kgνq = 1explosion in < tp=10-8 slittle time for sphere to blow apartsignificant fraction of 235U will do fission

The problem is how to assemble such a sphere in less than 10-8 seconds

13

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

elastic 238U scatter (slide 8)Fission of 238U (5%)rest is negligible

as Eneutron decreases via elastic scattering σ(238

92U(n,γ)) increases and becomes resonantσ(238

92U(n,f)) decreases rapidly and vanishes below ~1 MeVonly remaining chance for fission is σ(235

92U(n,f)) which is much smaller then σ(238

92U(n,γ)) Conclusion: piling up natural U won’t make a reactor because n get “eaten” by (n,γ) resonances. I said it is not SO simple

23592U(n,f)

23592U(n,γ)

23892U(n,γ) 238

92U(n,f)235

92U(n,f)

23592U(n,γ)

23892U(n,γ)

23892U(n,γ)


12.2 Fission Reactors(two ways out)

Way 1: Thermal Reactorsbring neutrons to thermal energies without absorbing them = moderate themuse low mass nuclei with low n-capture crossection as moderator. (Why low mass?)sandwich fuel rods with moderator and coolant layerswhen n returns from moderator its energy is so low that it will predominantly cause fission in 235U


12.2 Fission Reactors(two ways out)

Way 2: Fast ReactorsUse fast neutrons for fissionUse higher fraction of fissile material, typically 20% of 239Pu + 80% 238UThis is self refuelling (fast breeding) via:

23892U+n 239

92U + γ239

93Np + e- + νe239

94Pu + e¯ + νe

Details about fast reactors later

16

12.2 Fission Reactors (Pu fuel)

239Pu fission crossection slightly “better” then 235UChemically separable from 238U (no centrifuges)More prompt neutrons ν(239Pu)=2.96Fewer delayed n & higher n-absorbtion, more later


12.2 Fission Reactors (Reactor control)

For bomb we found:“boom” if: νq > 1 where ν was number of prompt nwe don’t want “boom” need to get rid of most prompt n

Reactors use control rods with large n-capture crossection σnc like B or Cd to regulate qLifetime of prompt n:

O(10-8 s) in pure 235UO(10-3 s) in thermal reactor (“long” time in moderator)

not “long” enough Far too fast to control… but there are also delayed neutrons

18


Fission products all n -rich all β- activeSome β- decays have excited states as daughtersThese 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 ntypical lifetimes τ≈O(1 sec)Fraction νd ≈ 0.6%

Ener

gy

off

sylla

bus



Since fuel rods “hopefully” remain in reactor longer then 10-2 s must include delayed nfraction νd into our calculationsNew control problem:

keep (ν+νd)q = 1

to accuracy of < 0.6%at time scale of a few seconds

Doable with mechanical systems but not easy


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:

okleaks very passi.3rd bestmildgasHe

difficult

cheap

cheap

rare

cheap

other

very react.

passive

reactive

reactive

reactive

chemistry

excellentmediumsmallliquidNa

okmediummildgasCO2press.

mediummediummildsolidC

good2nd bestnoneliquidD2O

goodbestsmallliquidH2O

coolantreduce Enσn-absStateMaterial

off

sylla

bus


12.2 Fission Reactors (Thermal Stability)

Want dq/dT < 0Many mechanical influences via thermal expansionChange in n-energy spectrumDoppler broadening of 238U(n,γ) resonances large negative contribution to dq/dT due to increased n -absorbtion in broadened spectrumDoppler broadening of 239Pu(n,f) in fast reactors gives positive contribution to dq/dtChernobyl No 4. had dq/dT >0 at low power… which proved that you really want dq/dT < 0


12.3 Fission Bombs (fission fuel properties)

ideal bomb fuel = pure 239Pua. By Alpha-decay, except Pu-241, which is by Beta-decay to Am-241.

1141.2100430Am-241

0.11.7x103100376,000Pu-242

4.249x10-31014.4Pu-241

6.80.91x103406,560Pu-240

1.922x10-31024,100Pu-239

5602.6x1031087.7Pu-238

watts kg-1(gm-sec)-1kg, Alpha-phase

years

Decay heatSpontaneousfission neutrons

Bare critical mass

Half-lifeaIsotope


12.3 Fission Bombs (drawbacks of various Pu isotopes)

241Pu : decays to 241Am which gives very high energy γ-rays shielding problem

240Pu : lots of n from spontaneous fission238Pu : α-decays quickly (τ1/2 = 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 handReactor grade Pu mix has “drawbacks” but could be made into a bomb.


12.3 Fission Bombs(where to get Pu from? Sainsbury’s?)

--.04.96-FBR blankete

.078.178.321.404.019MOX-graded

.050.091.243.603.013Reactor-gradec

.00022.0035.058.938.00012Weapons-gradeb

--.02.98-Super-grade

Pu-242

Pu-241a

Pu-240

Pu-239

Pu-238

IsotopeGrade

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).


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 plantsLarge high-E γ sources from 241Am outside a reactor large n fluxes from 240Pu outside reactors very penetrating easy to spot over long range


End of Lecture 13

even more energetic fusion and radioactive dating can be found in Dr.

Weidberg’s notes for lecture 14


ener

gy r

ange

of

fissi

on n

eutr

ons

12.1 Induced Fission ((n,f) and (n,γ) probabilities in natural Uranium)

23592U(n,f)

23592U(n,γ)

23892U(n,γ) 238

92U(n,f)235

92U(n,f)

23592U(n,γ)

23892U(n,γ)

23892U(n,γ)

fastthermal

neut

ron

abso

rbtio

npr

obab

ilit

per

1 μm

“bad-238”

“good238 ”

“bad-235”

“good235 ”

reprinted to show high E end of better


Appendix to lecture 13

More on various reactorsUranium enrichment

Off Syllabus


12.2 Fission Reactors (Thermal vs. Fast)

Fast reactorsneed very high 239Pu concentration Bombsvery compact core hard to cool need high Cpcoolant like liq.Na or liq. NaK-mix don’t like water & air & must keep coolant circuit molten & high activation of NaHigh coolant temperature (550C) ☺ good thermal efficiencyLow pressure in vessel ☺ better safetycan utilise all 238U via breeding ☺ 141 times more fuelHigh fuel concentration + breading ☺ Can operate for long time without rod changesDesigns for 4th generation molten Pb or gas cooled fast reactors exist. Could overcome the Na problems




Thermal ReactorsMany different types exist

BWR = Boiling Water ReactorPWR = 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 Reactorother more conventional geometries



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 activationIf natural U used small burn-up time often need continuous fuel exchange hard to control


12.2 Fission Reactors (Light vs. Heavy water thermal reactors)

Light Water ☺ it is cheap ☺ very well understood chemistry☺ compatible with steam part of plantcan not use natural uranium (too much n-capture)

must have enrichment plant bombsneed larger moderator volume larger core with more activationenriched U has bigger n-margin ☺ easier to control


12.2 Fission Reactors (Light vs. Heavy water thermal reactors)

Heavy Waterit is expensive

☺ allows use of natural U natural U has smaller n-margin harder to controlsmaller moderator volume ☺ less activationCANDU PWR designs (pressure tube reactors) allow D2O moderation with different coolants to save D2O


12.2 Fission Reactors (PWR = most common power reactor)

Avoid boiling ☺ better control of moderationHigher coolant temperature ☺ higher thermal efficiencyIf 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 ULarge fuel reactivity variation over life cycle

need variale “n-poison”dose in coolant


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 circuitprimary water enters turbine activation of tubine no access during operation (τ½(16N)=7s, main contaminant)

lower temperature lower efficiencyif steam fraction too large (norm. 18%)

Boiling crisis =loss of cooling


12.2 Fission Reactors (“cool” reactors)


12.2 Fission Reactors (“cool” reactors)

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


12.2 Fission Reactors (enrichment)

Two main techniques to separate 235U from 238U in gas form UF6 @ T>56C, P=1bar

centrifugal separationhigh separation power per centrifugal steplow volume capacity per centrifugetotal 10-20 stages to get to O(4%) enrichmentenergy requirement: 5GWh to supply a 1GW reactor with 1 year of fuel

diffusive separationlow separation power per diffusion stephigh volume capacity per diffusion elementtotal 1400 stages to get O(4%) enrichmentenergy requirement: 240GWh = 10 GWdays to supply a 1GW reactor with 1 year of fuel


15-20 cm

1-2

m

O(70,000) rpm Vmax≈1,800 km/h = supersonic! & gmax=106g difficult to build!


12.2 Fission Reactors (enrichment)

lecture 13 - university of oxfordreichold/teaching/... · dec 2006, lecture 13 nuclear physics...

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