Use of Use of -Ray-Generating Reactions for -Ray-Generating Reactions for Diagnostics of Energetic Diagnostics of Energetic Particles in Burning Plasma and Relevant Nuclear DataParticles in Burning Plasma and Relevant Nuclear Data

Y. Nakao Department of Applied Quantum Physics and Nuclear Engineering,Kyushu

University,Japan

Collaborators: H. Matsuura, N. Senmyo, K. Tsukida (Kyushu Univ.); M. Nakamura (Univ. of

Tokyo) T. Johzaki (Osaka Univ.); V.T. Voronchev (Moscow State Univ.)

2010 Symposium on Nuclear Data (Fukuoka, Nov. 25-

26, 2010)1/20

Diagnostics of - Knock-on ions in Magnetically- confined burning plasma - Degenerate electrons in Laser- imploded fuel

Proposal & Analysis from theoretical side

1. Energetic Particle Diagnostics---Background

2/20

Energetic particles in fusion plasmas at burning stage

- Products of fusion reactions - Injected beam particles - Ions accelerated by electromagnetic waves - Knock-on ions scattered by these particles Heat bulk electron and ion fluids, and Can trigger many wave-particle interactions and instabilities

Diagnosing the properties of energetic particles confined in burning plasma is one of the key issues in NF research aiming at ITER.

These energetic particles should be diagnosed while they are in

the plasma; Measurements inside the plasma are hardly possible.

Use of reaction-produced neutrals freely escaping from the

plasma core Neutrons, Gamma-rays

3/20

Energetic Particle Diagnostics Based on Energetic Particle Diagnostics Based on -Ray -Ray Measurement Measurement

0.981 (4.44) MeV -raysDT fusion plasma with a small amount of 6Li (9Be)

Information on energetic triton population (α- particle confinement)

Used for energetic particle diagnostics at JET experiments

Kiptilyj et al., NF (2002), PRL (2004), NF (2005)

Use of the D(, )6Li reaction proposed by JAERI group

Ochiai et al., RSI (2006)

Use of the 6Li(t,p)8Li* reaction proposed by our group Voronchev, Kukulin, Nakao, PRE (2001). Nakamura, Nakao, Voronchev et al., JPSJ (2006), NIMA (2007), FST (2008), JPFR (2007).

4/20

Gamma-Ray-Generating Gamma-Ray-Generating 66Li (Li (t,pt,p))88LiLi** Reaction Reaction

1) The reaction threshold is 181 keV in the centre-of-mass system

2) The excited state has a short lifetime of 12 fs.

One can expect that the rate of the 0.981-MeV -ray emission is

sensitive to the population of energetic tritons.

102 10310-9

10-7

10-5

10-3

10-1

101

6Li(t,p)8Li*

Cro

ss s

ection (b)

Centre-of-mass energy (keV)

D(t,n)

181 keV

E > 2MeV : Experimental data available

E < 2MeV : Cluster folding model

calculation Voronchev, Kukulin, Nakao PRE (2001)

6Li + t → 8Li* [0.981 MeV] + p

12fs

8Li [gr. st.] + γ

5/20

Objective of the WorkObjective of the Work

Our early speculation

One could obtain information on the energy distributions of energetic tritons and -particles by comparing the 0.981-MeV -ray measurement with kinetic model prediction incorporating the knock-on effect.

The objective

Analyze theoretically diagnostic information carried by the 0.981-MeV -rays.

Nakamura, Nakao, Voronchev et al., JPSJ (2006)

Teff and n eff of knock-on tritons Confinement property of -particles

6Li (t, p) 8Li*

8Li + γ

α

knock-on t

6/20

Kinetic Model for Energetic Ion PopulationsKinetic Model for Energetic Ion Populations

Alpha-particles & DD burn-up tritons Gaussian formBeam-injected deuterons delta-function-like formKnock-on ions knocking-up from the background

vSvfvQvv kkk

2

1

Fokker-Planck equation for energetic ions

Source terms

.2

,d

d8 2

k

ik

vkkkk

ii m

mmdvvfv

v

nvS

Ryutov, Phys. Scr. (1992); Helander, Lisak, Ryutov, PPCF (1993)

The source of 0.981-MeV -ray Energetic tritons

Alpha knock-on tritons D-beam knock-on tritons DD (burn-up) tritons

.2

,exp2

erf4

ln 2

0

422

jjj jk

jjjkk

mT

vxxxx

mm

neZZvQ

where

7/20

Energetic Triton PopulationsEnergetic Triton Populations

0 1000 2000 3000 40001010

1011

1012

1013

1014

1015

1016

ft,bulk

fbkt

fDDt

fakt

nd = n

t = 0.5x1020m- 3

T = 20keV E

NBI = 1MeV

PNBI

= 50MW

Vplasma

= 815m3

f t (m

-3ke

V-1

)

Et (keV)

Energy distribution functions of α knock-on tritons (akt), D-beam knock-on tritons (bkt) and DD burn-up tritons (DDt)

fakt > fbkt, fDDt at MeV energy range.

The knock-on tritons

(akt ) are distributed up to the energy of 4 MeV.

--- Fokker- Planck calculations under conditions typical of the ITER tokamak plasma

8/20

Gamma-Ray YieldGamma-Ray Yield

-1-310 sm1071.6981.0 MeV Y

-1-310 sm105.3~44.4 MeV YComparable!

Lit

vv

vvrrr

LiLiLittt

LitLitLit

LiLitt

dvdvdvvv

vfvvfv

vdvdvvvv

vfvfY

Lit

Lit

2

00

28

The 0.981-MeV -line reflects the presence of the knock-on tritons.

• Emitted in the 9Be(,n)12C* reaction• Used in JET experiments

10 20 30 40 50

107

108

109

1010

1011

1012

D- beamknock- on t

thermal t

DD burn- up t

knock- on t

nd = n

t = 0.5x1020m- 3

ENBI

= 1MeV

PNBI

= 50MW

Vplasma

= 815m3

Y (m

-3s-1

)T (keV) It may be used to infer Teff and neff

of the knock-on triton population.

nLi /nt = 1 %

• n Be /n t = 1%, T = 20 keV

9/20

GammaGamma--RayRay EmissionEmission SpectrumSpectrum

950 960 970 980 990 1000 10100

1x109

2x109

3x109

4x109

dY/ dE

fitting

( = 96 keV2)

dY/

dE (m

-3ke

V-1

s-1)

E (keV)

nd = n

t = 0.5x1020 m- 3

T = 20 keVn

Li/ n

t = 1 %

500 600 700 800 90094

96

98

100

102

104

(k

eV2 )

Teff

(keV)

The spectral broadening reflects the 8Li* spectrum.

dY /dE can be fitted to

MeV981.0

exp

0

20

E

EE

dE

dY

increases monotonically with increasing Teff .

The 8Li* spectrum is governed by the knock-on triton population.

18 keV

10/20

““Analytical”Analytical” RepresentationsRepresentations

Fitting to the slope distribution

500 1000 1500 20000.0

5.0x1012

1.0x1013

1.5x1013

2.0x1013

2.5x1013

3.0x1013

fakt

fslp

f t (m

-3ke

V-1

)

Et (keV)

eff

Ct

eff

efftslp T

EE

T

nEf exp

10 20 30 40 50400

500

600

700

800

900

1000

Teff (

keV

)

T (keV)

The fitting is successfully done especially in the energy range of 0.5-2 MeV. Teff increases monotonically with increasing T.

CEtt

eff

Ctt

eff

effLi

t

dEET

EEexpE

T

nn

m

2Y

11/20

2

0expEE

dE

dY

Diagnostics of the Diagnostics of the Knock-on Triton Population Knock-on Triton Population

experimentally determined

The effective temperature Teff of the knock-on triton could be diagnosed.

eff

effeffLi

t

Ett

eff

Ctt

eff

effLi

t

T

TInn

m

dEET

EEE

T

nn

mY

C

2

exp

2

Once Teff is determined, the effective concentration neff could be assessed from experimental Y .

500 600 700 800 90094

96

98

100

102

104

(k

eV)

Teff

(keV)

12/20

Diagnostics of the Confinement Property of the Fusion-Diagnostics of the Confinement Property of the Fusion-Born Born -Particles-Particles

Is the experimental(T,Teff ) plot placed onto the theoretical curve ?

YES.NO.

The confinement property is classical.

The confinement is deteriorated.

10 20 30 40 50400

500

600

700

800

900

1000

Teff

(ke

V)

T (keV)

Classical

Non-classical

1010 1015 1020 1025 103010-3

10-1

101

103

imploded plasma

burning plasma

100 10 5

0.01

0.1

kTe [

keV

]

ne [ cm-3]

= 1.0

0.5MCF ICF

ICF

burning plasmaLaser-imploded dense plasma

2.2. Degenerate Plasma Diagnostics---BackgroundDegenerate Plasma Diagnostics---Background

≧ 1000s , kTe ≦ 1keV

= Fermi energy

Degree of degeneracy :

3

22

2

32 e

eF n

mE

　

Electrons should be in degenerate state.

Fe EkT /

Consequence of electron degeneracy :

Reduction in stopping power of plasma for energetic particles

Range lengthening

Measurements :

Implosion experiment of CD targets at Osaka Univ.

Range of D-D fusion tritons In-flight T-D reaction rate

13/20

+ 9Be → 12C*[2+;0] + n

12C [gr.st.] + (4.44

MeV)

Influence on Ignition & Burn history of compressed DT targets through

D + T →3.52MeV) + n (14MeV)

Purpose of the StudyPurpose of the Study

How to diagnose the degree of electron degeneracy in compressed DT fuel --- A matter of interest

We propose a new method based on -ray measurement.

DT fuel admixed with a small amount of 9Be

-ray generating reaction

-particle heating electron thermal conduction electron-ion temperature relaxation bremsstrahlung

14/20

Suppose the case that

The fuel would not be ignited, and Most of nuclear reactions occur around the maximum compression.

Key Idea of Degeneracy DiagnosticsKey Idea of Degeneracy Diagnostics

In-flight reaction probability

DT fuel admixed with a small amount of 9Be is imploded to high densities, but Not subjected to any heating laser pulse.

Reaction products carry information about compressed state of fuel.

kTe = 0.4~1.0 keV

P-Be

),( eBeBe kTPP

DTn

MeVBe Y

YP 44.4,

3

22

2

32 e

eF n

mE

　

Fe EkT /

9Be

DT

n

12C

Principal reaction

Secondary reaction

n

Experimentally,

If plasma temperatures are determined in other ways, we can assess from PBe- curve by measuring the -rays and D-T neutrons.

15/20

Calculated In-flight Reaction ProbabilityCalculated In-flight Reaction Probability

Probability P-Be has clear dependences on degeneracy

parameter and plasma temperature kTe,i .

dV vn n

dV dE E EnP

td

BeBeBe

),(r

16/20

0.1 1 10 100

10-5

10-4

無 限 大 プラズマ

nBe

/ ni = 0.1

= kTe / EF

P-

Be

R = 1.0 g/cm2

R = 0.7 g/cm2

R = 0.4 g/cm2

R = 0.1 g/cm2

kTe = 0.4 keV

3

22

2

32 e

eF n

mE

　

0.1 1 10 10010-5

10-4

10-3

無 限 大 プラズマ

nBe

/ ni = 0.1

kTe = 1.0 keV

= kTe / EF

P-

Be

R = 1.0 g/cm2

R = 0.7 g/cm2

R = 0.4 g/cm2

R = 0.1 g/cm2

････ infinite plasma

････ infinite plasma

We ignore the spatial distributions of temperature and density, and

their temporal evolutions. nBe /ni = 0.1.

VSPN BeMeV44.4,

S= nD nT<v >DT

V = plasma volume

= time interval while the high density state is maintained ≈ R / 3Cs

-Rays from Compressed Finite-Size DT/-Rays from Compressed Finite-Size DT/ 99Be PelletsBe Pellets

Yield per shot :

The yield depends strongly on the plasma temperature and it seems enough for the -rays to be detected.

R = 0.4 g/cm2, = 200 g/cm3

　kTe

400eV 700eV 1keV

0.81 1.42 2.04

P-Be 2.21×10-5 3.26×10-5 4.00×10-5

[ps] 38.1 28.8 24.1

N,4.44MeV [ 個 /shot] 9.87×104 7.59×106 7.62×107

　kTe

400eV 700eV 1keV

0.81 1.42 2.04

P-Be 2.25×10-5 3.35×10-5 4.14×10-5

[ps] 66.6 50.3 42.1

N,4.44MeV [ 個 /shot] 9.45×105 7.77×107 7.40×108

17/20

R = 0.7 g/cm2, = 200 g/cm3

The 0.981-MeV -rays emitted in the 6Li (t, p )8Li* reaction have an important application for diagnostics of the knock-on tritons and the -particles in burning plasmas.

18/20

Summary (1)Summary (1)

If the 0.981-MeV -rays are detected, we can obtain information on Key parameters of knock-on triton population (Teff , neff ), and Confinement property of the fusion-born -particlesby comparing experimental data on the 0.981-MeV -ray yield and emission spectrum with the theoretical slowing-down

calculations.

We have proposed use of 9Be (, n )12C for diagnostics of electron degeneracy in compressed DT fuel pellets.

Summary (2) and Future WorksSummary (2) and Future Works

- Reaction probability P-Be depends strongly on the degeneracy

parameter and plasma temperature kTe,i .

- Experimentally, P-Be would be determined as the ratio of the yield of 4.44-MeV -rays from this reaction to the D-T neutron yield. - It will be possible to diagnose the degree of degeneracy, if the 4.44-MeV -rays and D-T neutrons can be measured.

- Temporal evolutions of density-temperature profiles, -ray and D-T neutron generation rates should be taken into account.

→ Analysis including implosion dynamics

19/20