Transcript LiCAS - University of Oxford

Lecture 12
Applications of Nuclear Physics
Fission Reactors and Bombs
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
1
12.1 Overview

12.1 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
12.2 Fission reactors

Reactor basics
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Thermal vs. fast
Light water vs. heavy water
Pressurised vs. Boiling water
Enrichment
off syllabus,
only in notes at end of slides
12.3 Fission Bombs


2 Dec 2005, Lecture 12
Moderation
Control
Thermal stability
Fission bomb fuels
Suspicious behaviour
Nuclear Physics Lectures, Dr. Armin Reichold
2
12.1 Induced Fission
(required energy)
DEsep≈6MeV per nucleon for heavy nuclei
Very slow n
Nucleus Potential Energy
during fission [MeV]
A=
238
Neutron
DEf=Energy needed
to penetrate fission
barrier immediately
≈6-8MeV
Neutrons
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
3
12.1 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
We call this “thermal fission” (slow, thermal neutron
needed)
But due to pairing term …
even N nuclei have low DEsep for additional n
odd N nuclei have high DEsep for additional n
 Fission yield in n -absorption varies dramatically
between odd and even N
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
4
12.1 Induced Fission
(fissile nuclei)


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DEsep(n,23892U) = 4.78 MeV only 
Fission of 238U needs additional kinetic energy from
neutron En,kin>Ef-DEsep≈1.4 MeV
We call this “fast fission” (fast neutrons needed)
Thermally fissile nuclei, En,kinthermal=0.1eV @ 1160K


Fast fissile nuclei En,kin=O(MeV)
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233 U, 235 U, 239 Pu, 241 Pu
92
92
94
94
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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
5
12.1 Induced Fission
(Reminder: stages of the process up to a few seconds after fission event)
t=0
<# prompt n>
nprompt=2.5
t≈10-14 s
t>10-10 s
<n-delay>
td=few s
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
<# delayed n>
nd=0.006
6
12.1 Induced Fission
(the fission process)
Energy balance of 23592U induced thermal fission MeV:

Prompt (t<10-10s):

Ekin( fragments)
Ekin(prompt n)
E(prompt g)

Subtotal:
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Delayed (10-10<t<):
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Ekin(e from b-decays)
E(g following b-decay)
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Subtotal:
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167
5
 3-12 from X+nY+g
6
178 (good for power production)
Neutrinos:
Grand total:
2 Dec 2005, Lecture 12
8
7
15 (bad, spent fuel heats up)
12 (invisible)
205
Nuclear Physics Lectures, Dr. Armin Reichold
7
12.1 Induced Fission
(n -induced fission crossections (n,f) )
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
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does nearly no n -induced fission below En,kin≈1.4 MeV
235 U does O(85%) fission starting at very low E
92
n,kin
Consistent with SEMF-pairing term of 12MeV/√A≈0.8 MeV
between
238

92U
odd-even= 23592U and even-even= 23892U
unresolved, narrow
resonances
unresolved, narrow
resonances
238U
n -Energy
235U
8
12.1 Induced Fission
“good
235 ”
238
235
238
92U(n,g)
“bad-238”
92U(n,g)
235 U(n,f)
92
238
92U(n,g)
energy range of
fission neutrons
neutron absorbtion probabilit per 1 mm
((n,f) and (n,g) probabilities in natural Uranium)
238
92U(n,f)
92U(n,g)
235
“bad-235”
235
2 Dec 2005, Lecture 12
“good
238 ”
92U(n,f)
92U(n,g)
thermal
fast
9
12.1 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 n crossection: tot
tot
tot
mean free path for fission n:   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(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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
10
12.1 Induced Fission
(a simple bomb)
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After 10-8 s 1n is replaced with n=2.5 n, 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 (nq-1) new such n in tp=10-8 s
(ignoring delayed n as bombs don’t last for seconds!)
n (t   t )  n (t )  (n q  1)  n (t )  ( t t mp )
dn (t ) n q  1
lim 

n (t )
 t 0
dt
t mp
solved by: n (t )  n (0)e


(n q 1) t
t mp
if nq>1  exponential growths of neutron number
For 235U, n=2.5  if q>0.4 you get a bomb
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
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12.1 Induced Fission
(a simple bomb)
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If object dimensions << lmp=7 cm
 most n 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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 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
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238 U(n,g)
92
238U
Inelastic
scatter (slide 8)
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
235 U(n,g)
92

as Eneutron decreases via inelastic scattering
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(23892U(n,g)) increases and becomes resonant
(23892U(n,f)) decreases rapidly and vanishes below 1.4 MeV
only remaining chance for fission is (23592U(n,f)) which is much smaller then
(23892U(n,g))
Conclusion: piling up natural U won’t make a reactor because
n get “eaten” by (n,g) resonances. I said it is not SO simple
13
12.2 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
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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
14
12.2 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 (fast breeding) via:

238
92U+n
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 23992U + g
 23993Np + e- + ne
 23994Pu + e¯ + ne
Details about fast reactors later
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
15
12.2 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
12.2 Fission Reactors
(Reactor control)
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For bomb we found:
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Reactors use control rods with large n-capture
crossection nc like B or Cd to regulate q
Lifetime of prompt n:
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“boom” if: nq > 1 where n was number of prompt n
we don’t want “boom”  need to get rid of most 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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors
(Reactor control)
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Fission products all n -rich  all b- active
Some b- decays have excited states as daughters
These can directly emit n (see table of nuclides, green at bottom of curve)
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Energy
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several sources of delayed n
typical lifetimes 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
-
off syllabus
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18
12.2 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 into our calculations
New control problem:
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keep (n+nd)q = 1
to accuracy of < 0.6%
at time scale of a few seconds
Doable with mechanical systems but not easy
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
19
12.2 Fission Reactors
(Reactor cooling)
As q rises during control, power produced in reactor
rises 
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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
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
off syllabus
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20
12.2 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 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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
21
12.3 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
2 Dec 2005, Lecture 12
239Pu
Nuclear Physics Lectures, Dr. Armin Reichold
22
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
-
-
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).
2 Dec 2005, Lecture 12
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
23
12.3 Fission Bombs
(drawbacks of various Pu isotopes)
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241Pu
: decays to 241Am which gives very high energy g-rays
 shielding problem
240Pu : lots of n from spontaneous fission
238Pu : a-decays quickly (t
1/2 = 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 hand
Reactor grade Pu mix has “drawbacks” but can “readily” be
made into a bomb.
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
24
12.3 Fission Bombs
(suspicious behaviour)
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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.
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
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End of Lecture 12
even more energetic fusion can be
found in Dr. Weidberg’s notes…
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
26
12.1 Induced Fission
reprinted to show high E end of better
“good
235 ”
238
235
238
92U(n,g)
“bad-238”
92U(n,g)
235 U(n,f)
92
238
92U(n,g)
energy range of
fission neutrons
neutron absorbtion probabilit per 1 mm
((n,f) and (n,g) probabilities in natural Uranium)
238
92U(n,f)
92U(n,g)
235
“bad-235”
235
2 Dec 2005, Lecture 12
“good
238 ”
92U(n,f)
92U(n,g)
thermal
fast
27
Appendix to lecture 12

2 Dec 2005, Lecture 12
More on various reactors
 Uranium enrichment
Off Syllabus
Nuclear Physics Lectures, Dr. Armin Reichold
28
12.2 Fission Reactors
(Thermal vs. Fast)

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 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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
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2 Dec 2005, Lecture 12
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31
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
32
12.2 Fission Reactors
(Thermal vs. Fast)

Thermal Reactors

Many different types exist

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
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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
33
12.2 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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
34
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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
35
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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
36
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”
2 Dec 2005, Lecture 12
Nuclear Physics
dose in coolant

Lectures, Dr. Armin Reichold
37
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 (t½(16N)=7s, main contaminant)
lower temperature   lower efficiency
if steam fraction too large (norm. 18%)
  Boiling crisis =
loss of cooling
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
38
12.2 Fission Reactors
(“cool” reactors)
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
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12.2 Fission Reactors
(“cool” reactors)
•
•
•
•
•
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
no boiling crisis
no steam handling
high efficiency 44%
compact core
low coolant mass
40
12.2 Fission Reactors
(enrichment)

Two main techniques to separate
gas form UF6 @ T>56C, P=1bar

from
238U
in
centrifugal separation





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




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
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
41
1-2 m
15-20 cm
O(70,000) rpm  Vmax≈1,800 km/h = supersonic! & gmax=106g  difficult to build!
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
42
12.2 Fission Reactors
(enrichment)
2 Dec 2005, Lecture 12
Nuclear Physics Lectures, Dr. Armin Reichold
43