Transcript スライド 1

Use of g-Ray-Generating Reactions for Diagnostics of Energetic
Particles in Burning Plasma and Relevant Nuclear Data
Y. Nakao
Department of Applied Quantum Physics and Nuclear Engineering,Kyushu University,Japan
Diagnostics of
- Knock-on ions in Magnetically- confined burning plasma
- Degenerate electrons in Laser-imploded fuel
Proposal & Analysis from theoretical side
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
1. Energetic Particle Diagnostics---Background
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
2/20
Energetic Particle Diagnostics Based on g-Ray Measurement
DT fusion plasma with a small
amount of 6Li (9Be)
0.981 (4.44) MeV g-rays
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(,g )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).
3/20
Gamma-Ray-Generating 6Li (t,p)8Li* Reaction
1
10
+t →
8Li*[0.981
MeV] + p
12fs
8Li
[gr. st.] + γ
1) The reaction threshold is 181 keV
in the centre-of-mass system
2) The excited state has a short
lifetime of 12 fs.
D(t,n)
-1
10
Cross section (b)
6Li
6
-3
10
8
Li(t,p) Li
*
-5
10
-7
10
181 keV
-9
10
2
3
10
10
Centre-of-mass energy (keV)
E > 2MeV : Experimental data available
E < 2MeV : Cluster folding model calculation
Voronchev, Kukulin, Nakao PRE (2001)
One can expect that the rate of the 0.981-MeV g-ray emission is
sensitive to the population of energetic tritons.
4/20
Objective of the Work
Our early speculation
Nakamura, Nakao, Voronchev et al., JPSJ (2006)
One could obtain information on the energy distributions of energetic
tritons and -particles by comparing the 0.981-MeV g-ray measurement
with kinetic model prediction incorporating the  knock-on effect.
α
6Li
(t, p) 8Li*
8Li
+γ
knock-on t
The objective
Analyze theoretically diagnostic information carried by the 0.981-MeV g-rays.
 Teff
and n eff of knock-on tritons
 Confinement property of -particles
5/20
Kinetic Model for Energetic Ion Populations
The source of 0.981-MeV g-ray
 Alpha knock-on tritons
 D-beam knock-on tritons
 DD (burn-up) tritons
 Energetic tritons
Fokker-Planck equation for energetic ions
1 
Qk v  f k v    Sk v 
2
v v
where Qk v  

j
Z k2 Z 2j e 4 n j ln j 
2
2 


e
rf
x

x
e
xp

x
,


40 mk m j 




x
v
.
2T j m j
Source terms
Alpha-particles & DD burn-up tritons
Gaussian form
Beam-injected deuterons
delta-function-like form
Knock-on ions
knocking-up from the background
8g 2 ni
Si v  
v


gv
d


vk f k vk
mk  mi
dvk , g 
.
d
2mk
Ryutov, Phys. Scr. (1992); Helander, Lisak, Ryutov, PPCF (1993)
6/20
Energetic Triton Populations
--- Fokker- Planck calculations under conditions typical of the ITER
tokamak plasma
1016
1015
at MeV energy range.
 The  knock-on tritons (akt )
are distributed up to the
energy of 4 MeV.
ft (m-3keV-1)
 fakt > fbkt, fDDt
10
14
10
13
ft,bulk
fakt
nd = nt = 0.5x1020m-3
T = 20keV
ENBI = 1MeV
PNBI = 50MW
Vplasma = 815m3
1012
1011
1010
fbkt fDDt
0
1000
2000
3000
4000
Et (keV)
Energy distribution functions of α knockon tritons (akt), D-beam knock-on tritons
(bkt) and DD burn-up tritons (DDt)
7/20
Gamma-Ray Yield



f t v t  f Li v Li 
 
   
   v t  v Li  v t  v Li dv t dv Li
 8

2

 v f v  v
t
0




t
t
Li
f Li v Li 
0

v r2 v r dvr  dvt dvLi
v t  v Li

v t  v Li
 The 0.981-MeV g-line reflects the
presence of the  knock-on tritons.
10

knock-on t
1011
DD burn-up t
Yg (m-3s-1)
Yg 
nLi /nt = 1 %
12
1010
109
108
nd = nt = 0.5x1020m-3
ENBI = 1MeV
PNBI = 50MW
D-beam
knock-on t
107
10
thermal t
20
 It may be used to infer Teff and neff
Vplasma = 815m3
30
T (keV)
40
50
of the  knock-on triton population.
Yg 0.981MeV   6.71 1010 m-3s-1
Yg 4.44MeV  ~ 3.5  1010 m-3s-1
Comparable!
• Emitted in the 9Be(,n)12C* reaction
• Used in JET experiments
• n Be /n t = 1%, T = 20 keV
8/20
Gamma-Ray Emission Spectrum 4x10
 The spectral broadening reflects the
8Li*
spectrum.
 The 8Li* spectrum is governed by the
 knock-on triton population.
dYg/dEg (m-3keV-1s-1)
9
nd = nt = 0.5x1020 m-3
T = 20 keV
nLi/nt = 1 %
3x109
2x109
18 keV
1x109
0
950
 dYg /dEg can be fitted to
960
970
980 990 1000 1010
Eg (keV)
104

2
  increases monotonically with
increasing Teff .
(keV )



102
2

 Eg  E 0
 e xp 
dEg


E 0  0.981Me V
dYg
dYg/dEg
fitting
( = 96 keV2)
100
98
96
94
500
600
700
800
Teff (keV)
900
9/20
“Analytical”Representations
3.0x1013
fakt
fslp
Fitting to the slope distribution
 E t  EC
f slp  E t  
e xp 

Teff
Teff

neff




ft (m-3keV-1)
2.5x1013
2.0x1013
1.5x1013
1.0x1013
5.0x1012
0.0
500
 The fitting is successfully done
especially in the energy range of
0.5-2 MeV.



EC
 E t  EC
E t exp 

Teff


  E t  dE t


2000
1000
900
Teff (keV)
Yg 
1500
Et (keV)
 Teff increases monotonically with
increasing T.
2 n Li neff
m t Teff
1000
800
700
600
500
400
10
20
30
40
50
T (keV)
10/20
Diagnostics of the  Knock-on Triton Population



 knock-on triton could be diagnosed.
(keV)
 The effective temperature Teff of the
102


 Eg  E 0
 e xp 
dEg


dYg
104
2
100
experimentally
determined
98
96
Yg 
94
2 nLi neff
m t Teff
 E t  EC

E t e xp 

Teff
EC

I Teff
2

nLi neff
mt
Teff


 

  E t dEt


500
600
700
800
Teff (keV)
900
 Once Teff is determined, the
effective concentration neff
could be assessed from
experimental Yg .
11/20
Diagnostics of the Confinement Property of the FusionBorn -Particles
1000
Is the experimental
(T,Teff ) plot placed onto
the theoretical curve ?
Teff (keV)
YES.
900
NO.
 The confinement property
is classical.
Non-classical
800
700
600
Classical
500
400
10
20
30
T (keV)
40
50
 The confinement is
deteriorated.
12/20
2. Degenerate Plasma Diagnostics---Background
10
Electrons should be in
degenerate state.
Degree of degeneracy :
kTe [ keV ]
Laser-imploded dense plasma
r≧ 1000rs , kTe ≦ 1keV
10
3
burning plasma
burning plasma
MCF
ICF
1
 = 1.0
10
-1


2
3
= Fermi energy
10
-3
Consequence of electron degeneracy :
Reduction in stopping power of plasma
for energetic particles
Range lengthening
r 
0.1
ICF
0.01
imploded plasma
  kTe / EF
2
EF 
3 2 ne
2me
0.5
100 10 5
10
10
10
15
10
20
-3
10
25
10
30
ne [ cm ]
Measurements :
Implosion experiment of CD targets
at Osaka Univ.
 Range of D-D fusion tritons


In-flight T-D reaction rate
,r
13/20
Purpose of the Study
Influence on Ignition & Burn history
of compressed DT targets through
-particle heating
 electron thermal conduction
 electron-ion temperature relaxation
 bremsstrahlung
g-ray generating reaction
D + T →  3.52MeV) + n (14MeV)

 + 9Be → 12C*[2+;0] + n
12C [gr.st.] +
g(4.44 MeV)
How to diagnose the degree of electron
degeneracy in compressed DT fuel
--- A matter of interest
We propose a new method based on
g-ray measurement.
DT fuel admixed with a
small amount of 9Be
14/20
Key Idea of Degeneracy Diagnostics
Suppose the case that
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.
 The fuel would not be ignited, and
P  Be  P  Be ( , kTe )
  kTe / EF
EF 
Most of nuclear reactions occur
around the maximum compression.
P-Be
2


3 2 ne
2me

kTe = 0.4~1.0 keV
2
3

 Reaction products carry information
about compressed
state of fuel.
Experimentally,
P  Be 
T
D
YDTn
Principal reaction

9Be
Yg , 4.44 MeV
n
Secondary reaction
12C
g
If plasma temperatures are
determined in other ways, we can
assess  from PBe- curve by
measuring the g-rays and D-T
neutrons.
n
15/20
Calculated In-flight Reaction Probability
nBe    Be E  (r , E ) dE dV

P  Be 
 nd nt v dV
10
-4
P-Be
10
rR = 1.0 g/cm
2
rR = 0.7 g/cm
2
rR = 0.4 g/cm
2
rR = 0.1 g/cm
kTe = 1.0 keV
nBe / ni = 0.1
2
P-Be
kTe = 0.4 keV
nBe / ni = 0.1
-3
無限大プラズマ
････ infinite plasma
10
-4
10
-5
rR = 1.0 g/cm
2
rR = 0.7 g/cm
2
rR = 0.4 g/cm
2
rR = 0.1 g/cm
2
無限大プラズマ
････ infinite
plasma
-5
10
0.1
1
10
100
= kTe / EF
EF 
2

0.1

3 2 ne
2me

1
2
3
10
100
= kTe / EF
Probability P-Be has clear dependences on degeneracy parameter  and
plasma temperature kTe,i .
16/20
g-Rays from Compressed Finite-Size DT/ 9Be Pellets
We ignore the spatial distributions of temperature and density, and their temporal
evolutions.
nBe /ni = 0.1.
Yield per shot :
rR = 0.4 g/cm2, r= 200 g/cm3
kTe
Ng ,4.44 MeV  P  Be  S V 
400eV
700eV
1keV

0.81
1.42
2.04
S= nD nT< v >DT
P-Be
2.21×10-5
3.26×10-5
4.00×10-5
V
[ps]
38.1
28.8
24.1
Ng,4.44MeV [個/shot]
9.87×104
7.59×106
7.62×107

= plasma volume
= time interval while the high
density state is maintained
≈ R /3Cs
rR = 0.7 g/cm2, r= 200 g/cm3
kTe
The yield depends strongly on the
plasma temperature and it seems
enough for the g-rays to be
detected.
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
Ng,4.44MeV [個/shot]
9.45×105
7.77×107
7.40×108
17/20
Summary (1)
The 0.981-MeV g-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.
If the 0.981-MeV g-rays are detected, we can obtain information on
 Key parameters of  knock-on triton population (Teff , neff ), and
 Confinement property of the fusion-born -particles
by comparing experimental data on the 0.981-MeV g-ray yield and emission
spectrum with the theoretical slowing-down calculations.
18/20
Summary (2) and Future Works
We have proposed use of 9Be (, ng )12C for diagnostics of electron degeneracy in
compressed DT fuel pellets.
- 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
g-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 g-rays
and D-T neutrons can be measured.
- Temporal
evolutions of density-temperature profiles, g-ray and D-T neutron
generation rates should be taken into account.
→
Analysis including implosion dynamics
19/20