Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 1 Lecture 13 Applications of Nuclear Physics Fission Reactors and Bombs

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

Lecture 13

Applications of Nuclear Physics

Fission Reactors and Bombs

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

2

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


3

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


4


(required energy & thermal fission)

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


5

12.1 Induced Fission(fast 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


6

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>d=few s

<# delayed n>d=0.006

<# prompt n>prompt=2.5


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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 (mostly bad, spent fuel heats up)

Neutrinos: 12 (invisible) Grand total: 205

8


(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

Dec 2006, Lecture 13 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

fpro

mpt

fiss

ion n

eutr

ons

fastthermal

neutr

on a

bso

rbti

on p

robabili

t p

er

1

m

“bad-238”

“good 238 ”

“bad-235”

“good 235 ”


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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


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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 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

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


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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

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 (238

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

92U(n,f)) decreases rapidly and vanishes below ~1 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,)


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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


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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


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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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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


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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


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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


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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.


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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 could be made into a bomb.


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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).


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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


End of Lecture 13

even more energetic fusion and radioactive dating can be found in Dr. Weidberg’s notes for lecture 14


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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


Appendix to lecture 13

More on various reactors Uranium enrichment

Off Syllabus


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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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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


35

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


36

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


37

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


38

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


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12.2 Fission Reactors (“cool” reactors)


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12.2 Fission Reactors (“cool” reactors)

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


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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


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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)

Documents

Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 1 Lecture 13 Applications of Nuclear Physics Fission Reactors and Bombs