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Particle Physics Seminar, Oxford University
CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority
4 May 2010
Nuclear Physics and Technology
of Tokamak Reactors
Raul PampinCCFE Neutronics and Nuclear Data Group
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
Slide 2 of 40
CCFE neutronics and nuclear data group
JET
MAST
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
Slide 3 of 40
ITER
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
Slide 4 of 40
• The tokamak plasma
fuels and power
viability
• The neutrons
neutron transport
activated material
tritium breeding
blanket technology
• Summary
overview
Work funded by the UK EPSRC and by the European Communities under the contract of association between EURATOM and CCFE. Views and opinions expressed herein do not necessarily reflect those of the European Commission.
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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• Fusion reactions exothermic up to 56Fe
due to positive binding energy change.
• Accurate binding energy (B) formulation
from liquid-drop nuclear model:
• Larger changes in lighter nuclides.
• Excess (Q) released as kinetic energy
of products.
fuels and power production
1. volume term,2. surface term,3. coulomb term,4. asymmetry term,5. paring term (a,b,c,d > 0).
∆±−
−−−=−2
2
3/4
23/1 )(
/A
ZNd
A
ZcbAaAB
1 2 3 4 5
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Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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fuels and power production
fusion reaction rates (1/3)
~1
0.6
0.5
0.9
0.2
5
0.1
~10-20~10-20~10-24
σmaxbarn
~10,000
6,000
5,000
250
1,000
94
1,250
EmaxkeV
23.94He + 2γD + D (*)
1.4D + e+ + νp + p (*)
5.53He + γp + D (*)
59%12.14He + n + pT + 3He
100%11.34He + n + nT + T
100%18.54He + pD + 3He
100%12.94He + p + p3He + 3He
41%14.34He + D
100%17.64He + nD + T
50%3.33He + n
50%4.1T + pD + D
branch
ratio
Q
MeV
productsreactants
(*) electromagnetic, as opposed to strong, interactions.
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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• Fusion power product of reaction rate and
energy release:
• R depends on:
reaction likelyhood (i.e. cross section σ), reactant density,
reactant temperature (i.e. energy, i.e. v).
• Q similar, but R (i.e. σ) can vary orders of magnitude depending on reaction and
reactant temperature and density…
• … hence importance of heating and
confinement (i.e. plasma physics).
• For a given density, DT yields higher rate and
at lower temperatures.
fuels and power production
fusion reaction rates (2/3)
Q.RPf =
vNNR ba σ=
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• Cross section energy dependence reflects
quantum and nuclear physics phenomena:
• S(E) very weak function of energy except for “resonant” reactions.
• Excited intermediate nuclear state implies S(E)
very peaked function at the resonance energy:
fuels and power production
fusion reaction rates (3/3)
Nuclear separation
Potential energy
mr
e
0
2
4πε
rm
E
E’
−=2/1
G
E
Eexp
E
)E(S)E(σ
pHe*LiHeD
nHe*HeTD
+→→+
+→→+453
45
r
2
b
2
aG AZZ~E
E
1/E
exp(-EG/E)
σσσσ(E)resonant
S(E)
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• In reality N = N(v), i.e. distribution function of
particle velocities (energies) and so:
• In magnetically confined plasmas, can
assume maxwellian distribution functions:
fuels and power production
<σv> parameter (a.k.a. reactivity)
∫∞
=0
vdv)v()v(N)v(NR ba σ
−kT
mvvEp
2exp~)(
22
QRPf .=
)(.)( vpNvN ii =
vNNR ba σ=
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fuels and power production
<σv> parameter (a.k.a. reactivity)
∫∞
=0
vdv)v()v(N)v(NR ba σ
−kT
mvvvp
2exp~)(
22
∫∞
>=<0
vdv)v()v(pv σσ
><= vNNR ba σ
)(.)( vpNvN ii =
p(v)
σ(v)v
<σσσσv>
v
4 May 2010
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fuels and power production
emission profiles
• Even more realistically, in
a magnetically confined
plasma N = N(v,x,y,z).
• Hence, in a tokamak,
power (and DT neutron)
emission intensity follows
T and N profiles (i.e.
magnetic contours):
PF
pa
aII
−=
2
0 1
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0 .4 0.6 0.8 1
a/ap
emission intensity (relative to core)
PF=0.05
PF=0.5
PF=1
PF=1.5
PF=5
3.34
4.06
4.78
5.50
6.22
6.94
7.66
8.38
radial distance from
3.34
4.06
4.78
5.50
6.22
6.94
7.66
8.38
radial distance from
3.34
4.24
5.14
6.04
6.94
7.84
emission
density
19-2018-1917-1816-1715-1614-1513-1412-1311-1210-119-108-97-86-75-64-53-42-31-20-1
(1017 n/m2s)
PF=0.5 PF=1.5 PF=5
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• Energy systems viability requires output larger than input.
• For physicists: fusion output > power required to maintain plasma:
breakeven: Pf > power required to maintain plasma temperature;
ignition: Pf > radiated power (self-sustained plasma).
• For engineers (and investors!), need to account for:
systems efficiency,
blanket energy multiplication,
balance-of-plant,
etc…
e.g. Lawson’s criterion (the 1957’s original, not the physicists version!),
more recently: systems analysis.
• Viability measured in terms of triple product NkTτ .
viability
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• power from fusion:
• plasma power loss:
• radiation power loss:
• assume Na=Nb=N/2=Ne/2 and Ta=Tb=Te=T, and impose that
ηPth=η(Pf+Pp+Pr)> Pp+Pr, where η is efficiency of the power conversion:
viability
ababbaf QvNNP ><= σ
++= eebbaap kTNkTNkTNP2
3
2
3
2
31
τ
kTQv1
)kT(3)NkT(
abab
2
Lawson
ασηη
τ−><
−
≥
2/12
r )kT(NP α=
Lawson’s criterion
DT
η = 0.3α = 3.8 10-19 J1/2m3s-1
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• power from fusion:
• plasma power loss:
• assume N=Nb=N/2=Ne/2 and
Ta=Tb=Te=T and impose that Pf > Pp:
viability
ababbaf QvNNP ><= σ
++= eebbaap kTNkTNkTNP2
3
2
3
2
31
τ
abab
breakevenQv
)kT()NkT(
><≥
στ
212
breakeven (a.k.a. “the physicist’s Lawson’s”)
1.E+20
1.E+21
1.E+22
1.E+23
1.E+24
1.E+25
1.E+26
1 10 100 1000
kT (keV)
triple product NkTτb (keV s/m3)
D-T
D+D
1026
1025
1024
1023
1022
1021
1020
not enough fusion power
too much lost power
4 May 2010
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• alpha power from fusion:
• plasma power loss:
• radiation power loss:
• assume Na=Nb=N/2=Ne/2 and
Ta=Tb=Te=T, but this time Pa > Pp+Pr:
viability
ababbaa QvNNP ><= σ5
1
++= eebbaap kTN2
3kTN
2
3kTN
2
31P
τ
abab
2/32
ignitionQv
)kT(N20)kT(60)NkT(
><+
≥σ
τατ
2/12
r )kT(NP α=
ignition
4 May 2010
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viability
systems analysis and balance-of-plant
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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• Boltzmann transport equation:
• or:
• change co-ordinates:
• define flux:
neutron transport
)t,,E,r(n.v)t,,E,r( Ω=ΩΦ
)t,v,r(S)t,v,r(S)t,v,r(ndt
d −+ −=
−+ −=∂∂
+∇+∇ SS)t,v,r(nt
)t,v,r(n.a)t,v,r(n.v v
=ΩΦΩΣ+ΩΦ∇Ω )t,,E,r().t,,E,r()t,,E,r(. t
)t,,E,r(S'd'.dE).t,','E,r().t,',E'E,r('E'
s Ω+ΩΩΦΩ→Ω→Σ= ∫∫Ω
)t,,E,r()t,v,r( Ω→
• assume neutrons and photons (no charge, i.e. no force, i.e. a=0) and steady
state:
streaming
interaction sink
scattering source
other sources (i.e. the plasma!)
4 May 2010
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neutron transport
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neutron transport
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scattering
neutron transport
14.1 MeV
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absorption (and transmutation): n,γ
neutron transport
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neutron transport
absorption (and transmutation): n,α
4 May 2010
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neutron transport
absorption (and transmutation): n,t
4 May 2010
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absorption (and transmutation): n,p
neutron transport
4 May 2010
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neutron transport
absorption (and transmutation): n,2n
4 May 2010
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• Interaction probabilities ~ cross sections.
neutron transport
interactions
−=
E
Eexp
E
)E(S)E( Gσ
log σ
log E
1. scattering
2. resonant reaction (keV-MeV)
3. threshold reaction (> MeV)
1
2
3
=ΩΦΩΣ+ΩΦ∇Ω )t,,E,r().t,,E,r()t,,E,r(. t
)t,,E,r(S'd'.dE).t,','E,r().t,',E'E,r('E'
s Ω+ΩΩΦΩ→Ω→Σ= ∫∫Ω
...2 ++++=
+=
=Σ
npnannna
ast
N
σσσσσ
σσσσ
γ
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neutron transport
implications
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neutron transport
implications
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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• Neutron damage:
high energy collisions and build-up of transmutation products have important
repercussions on systems performance and lifetime.
• Activated material:
needs to be disposed of, and the magnitude and implications of the activation
radiation field need to be assessed during design and operation of a reactor.
• Both damage and activation issues arise mainly from the high neutron energy
(14.1 MeV) triggering threshold reactions such as (n,p) and (n,α).
• Tritium breeding:
some transmutation reactions generate tritium, and this can be “encouraged” to
produce the necessary fuel.
neutron transport
implications
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Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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transmutation products
activated material
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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half-life
activated material
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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-B/A A odd
Z
ββββ- ββββ+
-B/A
Z
ββββ- ββββ+
∆±−
+++=−2
2
3/4
23/1 )(
/A
ZNd
A
ZcbAaAB
A even A even-B/A
ββββ-ββββ+
Z
beta decay
activated material
• Nuclei pursue stability by means of
radioactive decay.
• Stability is achieved when mass is
minimum, i.e. B is maximum beta
decay achieves this.
υβ ++→ −pnυβ ++→ +np
2/1
1~T
B∆
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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• Tritium self-sufficiency is a requirement:
atmospheric: ~50 kg (from cosmic-ray);
civil nuclear: ~25 kg (from CANDU);
power plant consumption of: ~1 kg per day.
• Can produce it by fitting the blanket with a breeder, i.e. a material prone to
undergo (n,t) or (n,n’t) reactions – e.g. Li.
• Can improve efficiency by also introducing a multiplier, i.e. a material prone to
undergo (n,2n) reactions – e.g. Be, Pb.
• Can also improve efficiency by enriching natural Li (7.5% 6Li, 92.5% 7Li) in 6Li.
tritium breeding
MeV.HeTnLi 78446 ++→+
MeV.HeT'nnLi 47247 −++→+
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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tritium breeding
Li4SiO4 (15%)
Be (85%)
Li17Pb83(nat.)
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08
energy (eV)
cross-section (b)
Li-6(n,t)He-4
Li-7(n,n't)He-4Be-9(n,t)Li-7
B-10(n,t)Be-8
B-11(n,n't)Be-8N-14(n,t)C-12
O-16(n,t)N-14Al-27(n,t)Mg-25Fe-56(n,t)Mn-54
2m blanket, no structure
w multiplier
w/o multiplier
ceramics
molten metals/salts
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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tritium breeding
• Need tritium breeding ratio (TBR) > 1.
• Extra result is additional energy (energy
multiplication, a.k.a. blanket gain).
• TBR > 1 challenged by engineering, rather than
physics:
structural material;
coolant;
FW coverage area (gaps, ports);
space limitations (particularly inboard).
• Current limitations in nuclear data uncertainties
imply it is not possible to determine TBR with
error < 5-10%.
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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• The blanket (and associated systems) is one of the major differences between
ITER and a fusion power plant:
in ITER it only serves as a shield and heat sink (500 MW!);
in a power plant it must:
shield,
recover and transport high-grade heat for power production,
breed and recover tritium online.
• Test blanket module (TBM) programme in ITER: parties (not UK!) testing
different blanket concepts for tritium generation and feasibility.
blanket technology
(Pb)
(Pb)
Be
Be
(Pb)
multiplier
LiPb
He+LiPb
water
He
He
coolant
steelLi2TiO3JapanWCPB water-cooled pebble bed
steelLiPbEUHCLL He-cooled lithium-lead
steelLi4SiO4EU, ChinaHCPB He-cooled pebble bed
steel+SiCLiPb +Li2TiO3IndiaLLCB LiPb ceramic breeder
steel+SiCLiPbUS, KoreaDCLL dual-coolant lithium-lead
structurebreederpartyconcept
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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blanket technology
HCPB – helium cooled pebble bed
DEMO
(HCPB blanket module)
HCPB blanket module
(breeding zone)
HCPB breeding zone
green=Be
blue=Li4SiO4
• Breeding zone: ~50cm thick, 70%vol Be PB, 10%vol Li4SiO4 (30%at 6Li)
• Achievable TBR: ~1.23 (90% coverage factor)
• Achievable gain: ~1.20
• Coolant Tin / Tout: 450 / 550 oC
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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blanket technology
HCLL – helium cooled lithium-lead
• Breeding zone: ~70cm thick, 80%vol LiPb (90% 6Li)
• Achievable TBR: ~1.15 (90% coverage factor)
• Achievable gain: ~1.16
• Coolant Tin / Tout: 450 / 550 oC
DEMO
(HCLL blanket module)HCLL blanket module HCLL blanket module
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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blanket technology
European HCLL and HCPB TBMs in ITER
4 May 2010
Particle Physics Seminar, Oxford UniversityNuclear Physics and Technology of Tokamak Reactors
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• DT is the only choice for fusion power this century (thanks to a 5He resonance).
• Tokamaks are on the verge of achieving DT physics breakeven (JET, TFTR):
engineering feasibility still to come (ITER).
• DT neutrons damage and activate materials but also generate tritium.
• Damage and activation differ from fission due to high energy of neutrons (14.1
MeV) triggering threshold reactions: (n,p), (n,α).
• Tritium self-sufficiency physically possible with a combination of enriched
lithium and neutron multiplier.
• Tritium self-sufficiency engineering, however, is challenging: calculations show
current blanket concepts only marginally achieve TBR > 1.
• Experimental evidence crucially needed: all but one ITER parties (not UK) to
test this key technology, nuclear data uncertainties need to be resolved.
summary