nuclear physics and technology of tokamakreactors · 4 may 2010 particle physics seminar, oxford...

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


Slide 3 of 40

ITER

4 May 2010


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


Slide 5 of 40

• 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

4 May 2010


Slide 6 of 40


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


Slide 7 of 40

• 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.



Q.RPf =

vNNR ba σ=

4 May 2010


Slide 8 of 40

• 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:



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)

4 May 2010


Slide 9 of 40

• In reality N = N(v), i.e. distribution function of

particle velocities (energies) and so:

• In magnetically confined plasmas, can

assume maxwellian distribution functions:


<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=

4 May 2010


Slide 10 of 40


<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


Slide 11 of 40


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

4 May 2010


Slide 12 of 40

• 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

4 May 2010


Slide 13 of 40

• 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

4 May 2010


Slide 14 of 40

• power from fusion:


• 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


Slide 15 of 40

• alpha power from fusion:


• 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


Slide 16 of 40

viability

systems analysis and balance-of-plant

4 May 2010


Slide 17 of 40

• 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


Slide 18 of 40

neutron transport

4 May 2010


Slide 19 of 40

neutron transport

4 May 2010


Slide 20 of 40

scattering

neutron transport

14.1 MeV

4 May 2010


Slide 21 of 40

absorption (and transmutation): n,γ

neutron transport

4 May 2010


Slide 22 of 40

neutron transport

absorption (and transmutation): n,α

4 May 2010


Slide 23 of 40

neutron transport

absorption (and transmutation): n,t

4 May 2010


Slide 24 of 40

absorption (and transmutation): n,p

neutron transport

4 May 2010


Slide 25 of 40

neutron transport

absorption (and transmutation): n,2n

4 May 2010


Slide 26 of 40

• 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

4 May 2010


Slide 27 of 40

neutron transport

implications

4 May 2010


Slide 28 of 40

neutron transport

implications

4 May 2010


Slide 29 of 40

• 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

4 May 2010


Slide 30 of 40

transmutation products

activated material

4 May 2010


Slide 31 of 40

half-life

activated material

4 May 2010


Slide 32 of 40

-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


Slide 33 of 40

• 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


Slide 34 of 40

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


Slide 35 of 40

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


Slide 36 of 40

• 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


Slide 37 of 40

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


Slide 38 of 40

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


Slide 39 of 40

blanket technology

European HCLL and HCPB TBMs in ITER

4 May 2010


Slide 40 of 40

• 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

nuclear physics and technology of tokamakreactors · 4 may 2010 particle physics seminar, oxford...

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