19 nov 2004, lecture 6 nuclear physics lectures, dr. armin reichold 1 lecture 6 applications of...

19 Nov 2004, Lecture 6 Nuclear Physics Lectures, Dr. Armin Reichold 1

Lecture 6

Applications of Nuclear Physics

Fission Reactors and Bombs

19 Nov 2004, Lecture 6 Nuclear Physics Lectures, Dr. Armin Reichold

2

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)

Neutrons

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

A=238

Neu

tron

Nucleus Potential Energy [MeV]

Esep≈6MeV per nucleon for heavy nuclei

Very slow n


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6.1 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

But due to pairing term … even N nuclei have low Esep

odd N nuclei have high Esep Fission yield in n-absorption varies

dramatically between odd and even N


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6.1 Induced Fission(fissile nuclei)

Esep(n,238U) = 4.78MeV only Fission of 238U needs En>Ef-Esep≈1.4 MeV Must be provided by n-kinetic energy Call this fast fission Thermally fissile nuclei, En

thermal=0.1eV @ 1160K 233

92U, 23592U, 239

94Pu, 24194Pu

Fast fissile nuclei En=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

19 Nov 2004, Lecture 6 6

6.1 Induced Fission (Reminder: stages of the process)

t=0

t≈10-14 s

t>10-10 s

<# prompt n>=2.5

<n-delay>d=few s

<# delayed n>d=0.006


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6.1 Induced Fission (the fission process)

Energy balance in MeV: Prompt:

Ekin(fragments) 167 Ekin(prompt n’s) 5 3-12 from X+nY+ E(prompt ) 6 Subtotal: 178 (good for power

production) Delayed

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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6.1 Induced Fission(fission crossections)

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

23892U does nearly no fission below En≈1.4MeV

Consistent with SEMF-pairing term of 12MeV/√A≈0.8MeV between odd-even= 235

92U and even-even= 23892U

unre

solv

ed, n

arro

wre

sonance

s

unre

solv

ed, n

arro

wre

sonance

s

238U 235U

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6.1 Induced Fission(fission 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

ab

sorb

tion p

rob

abili

t per

1

m


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6.1 Induced Fission(a simple bomb)

mean free path:

235 238(1 )tot tot totc c 1 ( ) 3 cmnucl totl

Simplify to c=1 (the bomb mixture) prob(235U(npromptf)) @ 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 l=3cm lp=√6*3cm≈7cm in tp=10-8 s

Uranium mix 235U:238U =c:(1-c) nucl(U)=4.8*1028 nuclei m-3

average crossection:

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


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After 10-8 s 1n is replaced with =2.5 n Let probability of new n inducing fission before it is lost = q

(others escape or give radiative capture) Each n produces on average (q-1) new n’s in tp=10-8 s

(ignoring delayed n’s as bombs don’t last for seconds!)

0

( 1)

( ) ( ) ( 1) ( ) ( )

( ) 1lim ( )

solved by: ( ) (0) p

p

tp

tq t

n t t n t q n t t t

dn t qn t

dt t

n t n e

if q>1exponential growths For 235U, =2.5 if q>0.4 you get a bomb


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If object dimensions << 7cm most n’s 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


13

6.2 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 Fission of 238U (5%) rest is negligible

Eneutron decreases (238

92U(n,)) increases and becomes resonant (238

92U(n,f)) dercreases rapidly and vanishes below 1.4 MeV only remaining change for fission is (235

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

92U(n,)) Conclusion: piling up natural U won’t make a reactor. 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,)


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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 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:

23892U+n 239

92U + 239

93Np + e- + e

23994Pu + e¯ + e

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 (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: q > 1 where was number of prompt n

Reactors use control rods with large n-capture (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 n’s

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Fission products all n-rich all - active Daughters of some - decays can directly emit n’s (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’s typical ≈O(1 sec) Fraction d ≈ 0.6%

Energ

y


19


Since fuel rods “hopefully” remain in reactor longer then 10-2 s must include delayed n fraction d

New control problem: keep (+d)q = 1 to accuracy of < 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 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


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6.2 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 Doppler broadening of 239Pu(n,f) in fast

reactors gives positive contribution to dq/dt Chernobyl No 4. had dq/dT >1 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 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 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


23


24


26


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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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 (½(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 @ 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


35

15-20 cm

1-2

m

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


36

6.2 Fission Reactors (enrichment)

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6.3 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.


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6.3 Fission Bombs (where to get Pu from?)

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).


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6.3 Fission Bombs (drawbacks of various Pu isotopes)

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

240Pu: lots of spontaneous fission n 238Pu: decays quickly lots of heat conventional

ignition explosives don’t 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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Plutonium isotope composition as a function of fuel exposure in a pressurized-water reactor, upon discharge.

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 sources from 241Am outside a reactor

large n fluxes from 240Pu outside reactors very penetrating easy to spot over long range

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