Transcript LiCAS - University of Oxford

Lecture 6
Applications of Nuclear Physics
Fission Reactors and Bombs
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
1
6.1 Overview

6.1 Induced fission
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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
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Reactor basics
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Thermal vs. fast
Light water vs. heavy water
Pressurised vs. Boiling water
Enrichment
6.3 Fission Bombs
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19 Nov 2004, Lecture 6
Moderation
Control
Thermal stability
Fission bomb fuels
Suspicious behaviour
Nuclear Physics Lectures, Dr. Armin Reichold
2
6.1 Induced Fission
(required energy)
DEsep≈6MeV per nucleon for heavy nuclei
Nucleus Potential Energy [MeV]
Very slow n
A=
238
Neutron
DEf=Energy needed
to penetrate fission
barrier immediately
≈6-8MeV
Neutrons
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.1 Induced Fission
(required energy)
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Spontaneous fission rates low due to high
coulomb barrier (6-8 MeV @ A≈240)
Slow neutron releases DEsep as excitation into
nucleus
Excited nucleus has enough energy for
immediate fission if Ef - DEsep >0
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
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.1 Induced Fission
(fissile nuclei)
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DEsep(n,238U) = 4.78MeV only 
Fission of 238U needs En>Ef-DEsep≈1.4 MeV
Must be provided by n-kinetic energy
Call this fast fission
Thermally fissile nuclei, Enthermal=0.1eV @ 1160K
233 U, 235 U, 239 Pu, 241 Pu

92
92
94
94
Fast fissile nuclei En=O(MeV)
232 Th, 238 U, 240 Pu, 242 Pu

90
92
94
94
Note: all Pu isotopes on earth are man made
Note: only 0.72% of natural U is 235U
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.1 Induced Fission
(Reminder: stages of the process)
t=0
<# prompt n>
n=2.5
t≈10-14 s
t>10-10 s
<n-delay>
td=few s
19 Nov 2004, Lecture 6
<# delayed n>
nd=0.006
6
6.1 Induced Fission
(the fission process)
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Energy balance in MeV:
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Prompt:
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167
5
 3-12 from X+nY+g
6
178 (good for power production)
Delayed

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Ekin(fragments)
Ekin(prompt n’s)
E(prompt g)
Subtotal:
Ekin(e from b-decays)
E(g following b-decay)
Subtotal:
Neutrinos
Grand total
19 Nov 2004, Lecture 6
8
7
15 (bad, spent fuel heats up)
12 (invisible)
205
Nuclear Physics Lectures, Dr. Armin Reichold
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6.1 Induced Fission
(fission crossections)
235 U
92
 23892U


does O(85%) fission starting at very low En
does nearly no fission below En≈1.4MeV
Consistent with SEMF-pairing term of
12MeV/√A≈0.8MeV between

odd-even=
235
92U
238
92U
unresolved, narrow
resonances
unresolved, narrow
resonances
238U
and even-even=
235U
8
6.1 Induced Fission
238
238
235
energy range of
fission neutrons
absorbtion probabilit per 1 mm
(fission probabilities in natural Uranium)
92U(n,g)
92U(n,g)
235 U(n,f)
92
238
92U(n,g)
238
92U(n,f)
92U(n,g)
235
235
92U(n,f)
92U(n,g)
thermal
fast
9
6.1 Induced Fission
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Uranium mix
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(a simple bomb)
235U:238U
=c:(1-c)
nucl(U)=4.8*1028 nuclei m-3
235
238


c


(1

c
)

average crossection: tot
tot
tot
mean free path: l  1 ( nucl tot )  3 cm
mean time between collisions =1.5*10-9 s @ Ekin(n)=2MeV
Simplify to c=1 (the bomb mixture)
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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
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.1 Induced Fission
(a simple bomb)
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After 10-8 s 1n is replaced with n=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 (nq-1) new n’s in tp=10-8 s
(ignoring delayed n’s as bombs don’t last for seconds!)
n (t   t )  n (t )  (n q  1)  n (t )  ( t t p )
dn (t ) n q  1
lim 

n (t )
 t 0
dt
tp
solved by: n (t )  n (0)e


(n q 1) t
tp
if nq>1exponential growths
For 235U, n=2.5  if q>0.4 you get a bomb
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.1 Induced Fission
(a simple bomb)
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If object dimensions << 7cm
 most n’s escape through surface
 nq << 1
If Rsphere(235U)≥8.7cm  M(235U)≥52 kg
 nq = 1
 explosion in < tp=10-8 s
 little time for sphere to blow apart
 significant fraction of 235U will do fission
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(not so simple)
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Q: What happens to a 2 MeV fission neutron in a block of
natural Uranium (c=0.72%)?
A: In order of probability
238 U(n,g)
92
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Inelastic 238U scatter
Fission of 238U (5%)
rest is negligible
238 U(n,g)
92
235 U(n,f)
92
238 U(n,g)
92
238 U(n,f)
92
235 U(n,g)
92
235 U(n,f)
92
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Eneutron decreases
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235 U(n,g)
92
(23892U(n,g)) increases and becomes resonant
(23892U(n,f)) dercreases rapidly and vanishes below 1.4 MeV
only remaining change for fission is (23592U(n,f)) wich is much smaller then
(23892U(n,g))
Conclusion: piling up natural U won’t make a reactor. I said it
is not SO simple
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(two ways out)
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Way 1: Thermal Reactors
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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
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(two ways out)
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Way 2: Fast Reactors
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Use fast neutrons for fission
Use higher fraction of fissile material, typically
20% of 239Pu + 80% 238U
This is self refuelling (breeding) via:
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238
92U+n
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
92U
+g

239
239
93Np +
 239
e- + ne
¯ + n
Pu
+
e
94
e
Details about fast reactors later
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
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(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
16
6.2 Fission Reactors
(Reactor control)
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For bomb we found:
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Reactors use control rods with large n-capture  (B,
Cd) to regulate q
Lifetime of prompt n:
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“boom” if: nq > 1 where n was number 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
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(Reactor control)

Energy

Fission products all n-rich  all b- active
Daughters of some b- decays can directly emit n’s (see table
of nuclides, green at bottom of curve)
 several sources of delayed n’s
 typical t≈O(1 sec)
 Fraction nd ≈ 0.6%
Delayed Neutron Precursor Groups
for Thermal Fission in 235-U
Delayed Average
Half-Life Neutron Energy
Group (sec) Fraction (MeV)
1
55.7 0.00021
0.25
2
22.7 0.00142
0.46
3
6.2 0.00127
0.41
4
2.3 0.0026
0.45
5
0.61 0.00075
0.41
6
0.23 0.00027
Total
0.0065
-
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6.2 Fission Reactors
(Reactor control)
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Since fuel rods “hopefully” remain in reactor
longer then 10-2 s  must include delayed n
fraction nd
New control problem:
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keep (n+nd)q = 1
to accuracy of < 6%
at time scale of few seconds
Doable with mechanical system but not easy
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(Reactor cooling)
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As q rises, power produced in reactor rises 
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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
H2 O
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
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(Thermal Stability)
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Want dq/dT < 0
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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 >1 at low power
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(Thermal vs. Fast)
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Fast reactors
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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
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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25
6.2 Fission Reactors
(Thermal vs. Fast)
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Thermal Reactors
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Many different types exist
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BWR = Boiling Water Reactor
PWR = Pressure Water Reactor
BWP/PWR exist as
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LWR = Light Water Reactors (H2O)
HWR = Heavy Water Reactors (D2O)
(HT)GCR = (High Temperature) Gas Cooled Reactor
exist as
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PBR = Pebble Bed Reactor
other more conventional geometries
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(Thermal vs. Fast)
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Thermal Reactors (general features)
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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
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(Light vs. Heavy water thermal reactors)
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Light Water
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 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
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(Light vs. Heavy water thermal reactors)
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Heavy Water
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 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
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(PWR = most common power reactor)
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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
30
6.2 Fission Reactors
(BWR = second most common power reactor)
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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
31
6.2 Fission Reactors
(“cool” reactors)
32
6.2 Fission Reactors
(“cool” reactors)
•
•
•
•
•
no boiling crisis
no steam handling
high efficiency 44%
compact core
low coolant mass
33
6.2 Fission Reactors
(enrichment)
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Two main techniques to separate
gas form UF6 @ T>56C, P=1bar

from
238U
in
centrifugal separation
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235U
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
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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
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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1-2 m
15-20 cm
O(70,000) rpm  Vmax≈1,800 km/h = supersonic! & gmax=106g  difficult to build!
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.2 Fission Reactors
(enrichment)
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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6.3 Fission Bombs
(fission fuel properties)
Half-lifea
Bare critical
mass
Spontaneous
fission
neutrons
Decay heat
years
kg, Alphaphase
(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
Isotope
a. By Alpha-decay, except Pu-241, which is by Beta-decay to Am-241.

ideal bomb fuel = pure
239Pu
37
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
-
-
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 (Paris:OECD/NEA, 1989) Table
12A).
19 Nov 2004, Lecture 6
d. Plutonium recovered from 3.64% fissile
plutonium MOX fuel produced from reactorgrade 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).
Nuclear Physics Lectures, Dr. Armin Reichold
38
6.3 Fission Bombs
(drawbacks of various Pu isotopes)



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

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 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.
241Pu:
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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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.
19 Nov 2004, Lecture 6
Nuclear Physics Lectures, Dr. Armin Reichold
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