code centre network meeting, 27 september 2010 iaea, vienna atomic structure and dynamics...
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Code Centre Network Meeting, 27 September 2010 IAEA, Vienna
Atomic structure and dynamics calculations using the GRASP family of codes, and an
introduction of some activities in NIFS
Atomic structure and dynamics calculations using the GRASP family of codes, and an
introduction of some activities in NIFS
Fumihiro Koike, Kitasato University and NIFS
Collaborators:Izumi Murakami, NIFS (National Institute of Fusion Science)Daiji Kato, NIFS (National Institute of Fusion Science)Xiaobin Ding, NIFS (National Institute for Fusion Science)Tohru Kawamura, TITECH (Tokyo Institute of Technology)
Code Centre Network Meeting, 27 September 2010 IAEA, Vienna
Outline:Outline:
1. Analysis of Visible M1 Lines in Tungsten Ions
2. Collisional-radiative model for W ions
3. Code development for single electron capture by H nucleus from metal surface
4. K radiation from low charge chlorine heated by an ion beam for plasma diagnostics
5. Code Availability
6. Summary
Code Centre Network Meeting, 27 September 2010 IAEA, Vienna
Analysis of Visible M1 Lines in Tungsten IonsExperimental:
Analysis of Visible M1 Lines in Tungsten IonsExperimental:
Komatsu et al, Proceedings of HCI@Shanghai (2010) submitted
Code Centre Network Meeting, 27 September 2010 IAEA, Vienna
Magnetic dipole transitions between the W26+ ground state multiplets using
GRASP2K MCDF wavefunctions
Magnetic dipole transitions between the W26+ ground state multiplets using
GRASP2K MCDF wavefunctions
Code Centre Network Meeting, 27 September 2010 IAEA, Vienna
Mean radius of 4l orbital in Cd-like ionsMean radius of 4l orbital in Cd-like ions
Ground state:[Kr]4d104f2
For W26+ ions<r4f> < <r4p>
Strong correlations between 4p,4d, and
4f orbitals are expected.
Ground state:[Kr]4d104f2
For W26+ ions<r4f> < <r4p>
Strong correlations between 4p,4d, and
4f orbitals are expected.
Code Centre Network Meeting, 27 September 2010 IAEA, Vienna
Identification of the M1 Lines for W26+Identification of the M1 Lines for W26+
Correlation ModelsActive Space:
AS1={4f,5s,5p,5d,5f,5g}, AS2=AS1+{6s,6p,6d,6f,6g}
Valence-Valence Correlation:5SD: 4d104f24d10(AS1)2 6SD: 4d104f24d10(AS2)2
Core-Valence Correlation:4p_5SD: 4s24p64d104f24s24p54d104f1(AS1)2
Correlation ModelsActive Space:
AS1={4f,5s,5p,5d,5f,5g}, AS2=AS1+{6s,6p,6d,6f,6g}
Valence-Valence Correlation:5SD: 4d104f24d10(AS1)2 6SD: 4d104f24d10(AS2)2
Core-Valence Correlation:4p_5SD: 4s24p64d104f24s24p54d104f1(AS1)2
The wavelength (in nm) of the transition [4f-2]4 [[4f-]5/2[4f]7/2]5The wavelength (in nm) of the transition [4f-2]4 [[4f-]5/2[4f]7/2]5
14730 52079
Code Centre Network Meeting, 27 September 2010 IAEA, Vienna
Collaboration with theoretical group, LHD and EBIT experimental groups
Collaboration with theoretical group, LHD and EBIT experimental groups
• EBIT/CoBIT measurements of visible spectra for Wq+ (q=12~30)• GRASP calculation for atomic structure.• CR model with atomic data from HULLAC code.• EUV and visible spectroscopy for LHD plasma. (C. Suzuki)
W26+ (4f25/2)J=4 – (4f5/24f7/2)J=5
= 3894.1 (experiment) = 3937 (GRASP2K)= 4029 (HULLAC)
CoBIT experiments
Komatsu et al. (2010)HCI 2010 @ Shanghai
CR modelgAr distribution
Energy Levels of the ground state of W26+
99% [(4f_)5/2( 4f)7/2]3
76% [(4f_)5/2( 4f)7/2]2 + 14%(4f_)22
64%[(4f_)5/2( 4f)7/2]6 +35%(4f_)26
Collisional-radiative model for W ions
I.Murakami, D. Kato, H. A. Sakaue, N. Yamamoto, C. SuzukiNIFS
Measurement and atomic calculations
Rhee and Kwon (2008)
BerlinEBIT
ASDEX
W 37+
W 36+
W 35+
W 34+
W 33+
W39+ - W45+
MCDF calculations
P¨utterich et al.(2005)
Rate equations• Rate equation of excited level p in steady–state is described as
dn(p)/dt = Γin – Γout =0
Population density of level p is then obtained as : n(p)=n0(p)+n1(p)=R0(p)neni+R1(p)nen(1) where n0(p): recombining plasma component n∝ i(FeXXII) n1(p): ionizing plasma component n(1)(FeXXI)∝The plasma considered here is headed by the neutral beam injection (NBI) and the ionizing plasma component is dominant.
Excitatiob by electron & proton impact
pq
ieepq
pp
ee
pqp
pe
ein nnnppqnpqAnpqFnpqFqnnpqCqnnpqC })()({)()},(),(),({)(),()(),(
)()],(),(),(),(),()([ pnqpAnqpFnqpFnqpCnqpCnpSpq
pp
pqe
e
pqp
p
pqe
eeout
Excitation by electron & proton impact Deexcitation by electron & proton impact and radiative decay
Ionization
recombination
Deexcitation by electron & proton impact
radiative decay
W ions considered here:
• W 37+ (194 levels) 4s2 4p6 4d, 4s2 4p6 4f, 4s2 4p6 5l (l=s~g), 4s2 4p5 4d2, 4s2 4p5 4d 4f, 4s2 4p5 4d 5s
• W 36+ (213 levels) 4s2 4p6 4d2, 4s2 4p6 4d 4f, 4s2 4p6 4d 5l (l=s~g), 4s2 4p5 4d3
• W 35+ (296 levels) 4s2 4p6 4d3, 4s2 4p6 4d2 4f, 4s2 4p6 4d2 5s, 4s2 4p5 4d4
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Electron density effect on the calculated spectra for W35+
Atomic data : HULLAC code45.12A: 4p54d4 (J=5/2) – 4p64d3 (J=7/2) (45.12A) gA=3.538x1012 4p54d4 (J=9/2) – 4p64d3 (J=7/2) (45.13A) gA=3.33x101252.16A: 4p64d24d (J=5/2) – 4p64d3 (J=3/2) (52.11A) gA=1.506x1013 4p64d24f (J=7/2) – 4p64d3 (J=5/2) (52.17A) gA=1.372x101353A: 4p64d24f(J=3/2) – 4p64d3 (J=3/2) (52.96A) gA=1.011x1013 4p64d34f (J=5/2) – 4p64d3 (J=3/2) (53.00A) gA=2.493x1011 4p54d4 (J=5/2) – 4p64d3 (J=3/2) (53.02A) gA=5.068x1011
CR model calculations
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Code development for single electron capture by H nucleus from metal
surface• Daiji Kato• NIFS
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Features of theoretical methodimplemented with the code
• Semi-classical treatment of H nucleus-metal surface collision.• Target surface electrons are represented by degenerate free
electron gas in the jellium model.• Static linear density response of target electron gas induced by
external nuclear charge (calculated by means of Kohn-Sham DFT in local density approximation).
• Direct numerical solution (split-operator-spectral method) of time-dependent Schrödinger equation of electron wave-function.
• Adiabatic expansion of wave-function, and B-spline method and discrete-variable-representation of adiabatic state function.
• Density matrix formulation of level population.
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Semi-classical method for single electron capture by translating projectile ion outward from metal surface
De Broglie wavelength of ion << atomic scale
( = proton kinetic energy ≥ 1eV )
For electrostatic dielectric response of solids,
Ion velocity ≤ 10-8 cm × plasma frequency ( 1016 s-1 for ne=1023 cm-3 )
( = proton kinetic energy ≤ 25 keV )
Electronic transition is treated by quantum mechanics
Ion motion is represented by classical trajectories
Constant velocity classical trajectory
Electron gas in surface potential well (jellium model)
Dielectric response of the electron gas ( Static linear density response theory )
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z
ρ= (x2 + y2)1/2
nucleus
electron
VCoulVeI
VpI
Dnuclear image
electron image
surface vacuumsolid
Classical picture of H atom-metal surface interaction
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Effective potential energy of electron near Mo surface Hydrogen nucleus is located at the origin, 10 a.u. above from Mo surface. Cylindrical
coordinates are used. 1 au length = 1 Bohr radius. 1 au energy = 27.21 eV.
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Level population created by electron capture from Mo surface
Hydrogen atoms translating outward from Mo surface to the surface normal direction. Fermi velocity of Mo = 1.19 au = 2.61 x 108 cm/s.
Hydrogen atoms translating outward from Mo surface with angle of 60 degree to the surface normal.
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Status of the code development
• The code can be improved substantially (e.g. more realistic target description, beyond jellium model)
• Validation of theoretical methods implemented in the code requires more comparison with experimental results.
• This code is not ready to open for public.
Toru Kawamura, Kazuhiko Horioka
Department of Energy Sciences, Tokyo Institute of Technology
Fumihiro Koike
Physics Laboratory, School of Medicine, Kitasato University
K radiation from low charge chlorine heated by an ion beam for plasma diagnostics
Tokyo Institute of Technology
Many Klines is distributed over photon energy according to the ionization state.
K photon energies show the characteristic charge state of plasmas , and K with M-shell electrons may be useful for lower temperature.
0
0.2
0.4
0.6
0.8
1.0
1.2
2.6 2.65 2.7 2.75 2.8photon energy (keV)
rad
iati
ve
de
cay
rat
e(
x 1
014 s
ec-1
)
Cl9+
Cl1+ ~ 8+
Cl13+Cl
10+
Cl11+
Cl12+
1s2
��������������
with open M-shell
Cln+:1s2s22p63(8-n): (1 ≤ n ≤ 8)
with open L-shell
Cl(8+m)+:1s2(8-m) : (1 ≤ m ≤ 7 )
grasp, grasp92calculation
Cl5+
Cl6+Cl7+
Cl8+
Tokyo Institute of Technology
Cold Ka is mainly composed of the lines from Cl+ ~ 6+,and may be a good candidate for cold plasma diagnostics.
K1 : 2622.3 eVK2 : 2620.7 eV
National Astronomical Observatory :http: //www.nao.ac.jp/
Cl2+ K2
K1Cl+
Cl3+
Cl4+
2610 2615 2620 2625 2630 2635photon energy (eV)
rad
iati
ve d
ecay
rat
e (
x 10
13 s
-1) 6
4
2
6
4
2
6
4
2
0
~10 eV
Blue-shift of Klines by outer-shell ionization is very small.
Accuracy of the order of a 1 eV is necessary for cold plasma
diagnostics.0
0
grasp92calculation
Calculated by GRASP92 and RATIP:F. A. Parpia et al., CPC, 94, p.249, 1996S. Fritzsche et al., Phys. Scr. T100, p.37, 2002
1012
1013
1014
1015
1016
1017
0
0.25
0.5
0.75
1
0 5 10 15
Fluorescence Yield
Charge State
Total Auger Rate(1/sec)
KLL AugerKLM AugerKMM Auger 1s2
��������������
Many Auger channels compete with radiative processes, and are indispensable to estimate K yield.
Tokyo Institute of Technology
Calculated by Auger-code:S. Fritzsche et al., Phys. Scr. T41, p.45, 1992
Ground states of 1s-vacant Ions(1s22’ and 1s23’ are estimated for
Cl14+.)
T. Kawamura et al., PRE, 66, p.016402, 2002
Fluorescence yield of low charge state ( Cl+~Cl13+ ) K are :
0.05 ~ 0.1
KLL Auger is the most predominant over the competition with K transition.
Augercalculation
1s-vacant ions are created by inner-shell ionization at low Te .Average Z total is determined by bulk ions due to small population of 1s-vacant ions.
Inner-shell ionization byan ion beam
Tokyo Institute of Technology
Pbulk P1s-vacant>>Population
••
Cl3+ : 1s22s22p63s23p2
Cl4+ : 1s22s22p63s23p
Cl2+ : 1s22s22p63s23p3
Cl4+ : 1s 2s22p63s23p2
Cl5+ : 1s 2s22p63s23p
Cl3+ : 1s 2s22p63s23p3
recombination & ionization
recombination & ionization
recombination & ionization
dielectronic capture• •
••
radiative & auger decays
radiative & auger decays
radiative & auger decays
bulk ions 1s-vacant ions
modeling ofpopulation kinetics
Code Availability
1. GRASP and GRASP2
2. GRASP92 + RATIP
3. GRASP2K
4. CR-Model Code based on HULLAC
5. Code for single electron capture by H nucleus from metal surface
GRASP Family of Codes
1. GRASP and GRASP2-- Very convenient for simple calculation with batch mode user interface
2. GRASP92 + RATIP-- Interactive user interface that is convenient for sophisticated types of calculations.-- In combination to RATIP code package, several types of transitions such as Auger processes may be calculated
3. GRASP2K -- Gives wide range of applicability.
RATIP Package
Others:
4. CR-Model Code based on HULLAC-- Still under development.-- To make this code open, an agreement for the use of HULLAC is necessary.
5. Code for single electron capture by H nucleus from metal surface -- Still under development.-- Will be available in not very future.
Summary
1. Several use and development of the codes have been introduced.
2. GRASP family of codes can be installed in a on line access server.
3. CR-Model code, and proton-surface charge transfer code may be available in not very future.
Thank You
Introduction
• There are strong needs for atomic and spectroscopic data on Tungsten ions for fusion plasma diagnostics, since Tungsten will be used as a wall material in ITER.
• EBIT measurements (NIST, Berlin, LLNL, & Tokyo EBITs, CoBIT) and spectral measurements of laboratory plasmas (ASDEX, JT-60U, LHD) have been done.
• Atomic calculations (GRASP, MCDF) and spectral model calculations (Hullac & FAC codes) have been tried: e.g. Rhee & Kwon (2008) MCDF calculation for W33+ - W37+
Fournier (1998). CRM for W47+ - W37+ (Hullac code).Ralchenko et al.(2005) CRM for W39+ - W47+ (FAC code)
CR model
• We have tried to construct a collisional-radiative model for W ions with using atomic data calculated by HULLAC code: - Atomic structure: parametric potential method - Electron impact excitation and ionization cross sections: relativistic distorted wave approximation.
• Recombination processes are ignored here.• Rate equations are solved with quasi-steady state
assumption (dn(i)/dt = 0).• Ne=3×1013 cm-3, Te= 100 – 1000eV
(Ne=1x1010, 1x1020 cm-3)
3 . Collisional-Radiative Model
• We constructed a set of collisional-radiative models (CR models) for Fe ions from H-like (Fe XXVI) to Ca-like (Fe VII), in which fine structure levels up to n=5 are considered.
• Population densities of excited levels are calculated by solving rate equations with assumption of steady-state.
• In the rate equations, radiative transitions, electron-impact excitation and deexcitation, proton-impact excitation and deexcitation, electron-impact ionization, radiative recombination, 3-body recombination, and dielectronic recombination processes are considered.
• Most of the atomic data are calculated with HULLAC atomic code.
• Line intensity is obtained as a product of population density and transition probability: n(p)Ar(p,q)
Summary
• gA distribution and spectra calculated with the CR model are quite different by excitation effects.When electron density is large, the calculated spectra look similar to gA distribution.
• Current CR model can include up to 500 levels, which is not enough for W ions. Needs to tune to have more levels, also needs some method to handle more than millions levels.
• Dielectronic recombination rates are needs to obtain to include recombination processes.
5. Discussion• Comparing with the electron temperature distribution, the electron tempe
rature of the emission region is lower than the one for the peak abundance of Fe XXI in ionization equilibrium (Te~1.1keV, for low density limit case).
• It could suggest that the equilibrium temperature for the electron density 1012~1014cm-3 would be different from the low density limit case. Due to the density effect (ionization via excited states), effective ionization rate would be larger and the equilibrium temperature could be lower.
• Or, we could expect Fe XXI ions would not be in ionization equilibrium. • To prove them we need more detailed analysis and model calculations, s
uch as time dependent evolution of Fe ion densities after the pellet injections with including the effect of diffusion.
• To check the CR model, (1) we need independent information of proton density, electron density, and electron temperature for Fe XXI emitting region; and (2) spatial distribution of Fe XXI emitting region will be able to obtain by 2D measurements of EUV spectra in near future, which can be compared with this current method.
41
3 . Collisional-Radiative Model
• We constructed a set of collisional-radiative models (CR models) for Fe ions from H-like (Fe XXVI) to Ca-like (Fe VII), in which fine structure levels up to n=5 are considered.
• Population densities of excited levels are calculated by solving rate equations with assumption of steady-state: dn(p)/dt = Γin – Γout =0
• Population density of level p is then obtained as : n(p)=n0(p)+n1(p)=R0(p)neni+R1(p)nen(1) where n0(p): recombining plasma component n∝ i(FeXXII) n1(p): ionizing plasma component n(1)(FeXXI)∝
• The plasma considered here is headed by the neutral beam injection (NBI) and the ionizing plasma component is dominant.
• Line intensity is obtained as a product of population density and transition probability: n(p)Ar(p,q)
pq
ieepq
pp
ee
pqp
pe
ein nnnppqnpqAnpqFnpqFqnnpqCqnnpqC })()({)()},(),(),({)(),()(),(
)()],(),(),(),(),()([ pnqpAnqpFnqpFnqpCnqpCnpSpq
pp
pqe
e
pqp
p
pqe
eeout
Excitation by electron & proton impact Deexcitation by electron & proton impact and radiative decay
Ionization
recombination
Deexcitation by electron & proton impact
radiative decay
gA and calculated spectrum: W37+
0
2 1013
4 1013
6 1013
8 1013
1 1014
1.2 1014
1.4 1014
40 45 50 55 60 65 70 75 80
gA
Wavelength (A)
W37+
0
5 10-10
1 10-9
1.5 10-9
2 10-9
2.5 10-9
3 10-9
3.5 10-9
40 50 60 70 80 90
100ev251ev1000ev
Inte
nsity
Wavelength (A)
W37+
4d -4f transitions:Effect of excitation processes( λ/λ=0.005 assumed)⊿
Fournier (1998)
gA and calculated spectrum: W36+
0
1 1014
2 1014
3 1014
4 1014
5 1014
40 45 50 55 60 65 70 75 80
W36+
gA
Wavelength (A)
0
5 10-10
1 10-9
1.5 10-9
2 10-9
2.5 10-9
40 45 50 55 60 65 70 75 80
W36+
100eV251eV1000eVIn
tens
ity
Wavelength (A)
gA and calculated spectrum: W35+
0
1 1014
2 1014
3 1014
4 1014
5 1014
6 1014
7 1014
40 50 60 70 80 90
W35+
gA
Wavelength (A)
0
5 10-10
1 10-9
1.5 10-9
2 10-9
2.5 10-9
40 45 50 55 60 65 70 75 80
W35+
100eV251eV1000eVIn
tens
ity
Wavelength (A)
0
1 10-9
2 10-9
3 10-9
4 10-9
5 10-9
6 10-9
7 10-9
40 45 50 55 60 65 70 75 80
W35+ (ne=1010cm-3)
100eV251ev1000eV
Inte
nsity
Wavelength (A)
Electron density effect on the calculated spectra for W35+
0
2 10-10
4 10-10
6 10-10
8 10-10
1 10-9
40 50 60 70 80 90
W35+ (ne=1020cm-3)
100eV251eV1000eV
Inte
nsity
Wavelength (A)
45.12A: 4p54d4 (J=5/2) – 4p64d3 (J=7/2) (45.12A) gA=3.538x1012
4p54d4 (J=9/2) – 4p64d3 (J=7/2) (45.13A) gA=3.33x1012
52.16A: 4p64d24d (J=5/2) – 4p64d3 (J=3/2) (52.11A) gA=1.506x1013
4p64d24f (J=7/2) – 4p64d3 (J=5/2) (52.17A) gA=1.372x1013
53A: 4p64d24f(J=3/2) – 4p64d3 (J=3/2) (52.96A) gA=1.011x1013
4p64d34f (J=5/2) – 4p64d3 (J=3/2) (53.00A) gA=2.493x1011
4p54d4 (J=5/2) – 4p64d3 (J=3/2) (53.02A) gA= 5.068x1011
4.2 Atomic data and CR model for W ions
• W is one of candidates for plasma wall materials of ITER and a future fusion reactor. But once it is included in a fusion plasma, it will cause large radiation power loss and the accumulation in core plasma and impurity transport is one of big issues to be solved.
• We need to examine W transport problem and spectroscopy is one of good tools to examine it. Large amount of atomic data are necessary.
• Many groups are challenging to produce atomic data and construct CR models.
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Effective potential energy of electron above surfacep Coulomb attractive potential of proton: -1/r,p Induced surface dipole layer and exchange-correlation effect (surface potential well): VeI,p A pile of electron density at surface induced by proton (repulsive potential barrier): VpI.
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Surface potential well of jellium model
AVB
VA
AeV
zzzzezV
zzB
zz
0
0
1
0
00Ie
4
,14
otherwise, ,12
,21
2
1)(
0
0
• z0 is position of image plane. It is given by empirical formula of Ossicini et al. or fitting to potentials of elaborate first-principle calculations. • V0 is given by the sum of Fermi energy and work function.• λrepresents electric field strength of surface dipole. ~1 for many elements.
Semi-empirical formula proposed by Jennings et al.,
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Electron density fluctuation:
)(),()( SC03
e rVrrKrdrn ,
where 0K is response function of Kohn-Sham states without
external perturbation. Self-consistent potential:
)()(1
)( XCe3
SC rVrr
rnrd
rrrV
p
,
)(][)]([)( eXC
XCeXCXC rndn
dVnVrnnVrV
n
,
where nn is bulk electron density 23 3/ Fkn .
Exchange correlation potential (Zangwill and Soven),
ss rrV
4.111ln0666.0
222.1XC .
Static linear density response of electron gas
VpI
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Adiabatic expansion to describe electron wave-functions in the rest frame of a moving nucleus, assuming nucleus translation velocities along surface normal is smaller than Fermi velocity of target metals.
Adiabatic state functions are solutions for eigen-value problem of adiabatic Hamiltonian at each nucleus-surface distance (D).
Adiabatic expansion of electron wave-function in sector
50)(;,),( )()( DDmD mi
m
rr
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Eigen-value curves of single electron above Mo surface. Figure plots results for m=0 state only. Dotted curves are classical image potentials, 1/4D, merging into asymptote for isolated hydrogenic levels.
Eigen-energy curves of Mo (jellium)-H
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Split-operator-spectral (by sector) method
⇒ Electron translation phase factorInitial condition
52)(;,;,)( )(11
)(i
miii
m DDmDmD
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Density matrix formulation of level population
Transition amplitudes for hydrogen states (nlm) are projection of coefficients for the adiabatic expansion at large distances,
Density matrix is obtained by averaging the amplitudes over the adiabatic states,
Diagonal element of the density matrix gives population of each atomic level.
53)(;, )()( DDmnlma mnlm
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0.1 10.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1s 2s 2p
0
2p1
Popu
lation
Translation velocity (au)
Velocity dependence of level population created by electron capture from Mo surface
Hydrogen atoms translating outward from Mo surface with angle of 60 degree to the surface normal.
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Example of results with this code•Dα emission of reflected neutrals of D ion beam at Mo surface was observed experimentally (incident ion energies of 5-25 keV).
•Dα emission yield per incident ion and Doppler profile (peak shift and width) were measured as a function of incident energy.
•With the aid of Monte-Carlo simulation of kinetic energy distribution of reflected neutrals, present code gives consistent results for Dα emission yield and Doppler peak variation with incident ion beam energy.
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Dα emission intensity is nearly proportional to reflection coefficient of Mo for E > 1 keV.
About 2 % of reflected particles emit Dα photons.
T. Tanabe et al.; J. Nucl. Mater. 220-222 (1995) 841.
Dα (656.1 nm) emission from neutrals of a deuteron beam reflected at Mo surfaces
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Kinetic energy distribution of reflected D atomsIncident angle of 60 degree to the surface normal.Monte-Carlo simulation by means of ACAT code.
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T. Tanabe et al.; J. Nucl. Mater. 220-222 (1995) 841.
Associated energy distribution for 3d2 state and comparison with measured Doppler shift of Dα
lineD atoms reflected specularly:60 degree to the surface normal.
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Doppler peaks of Dα are calculated, consistent with experiments. experiment
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Occupation probability of excited levels of D atoms reflected at Mo surface
D atoms reflected specularly: 60 degree to the surface normal.
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0.1 10.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1s 2s 2p
0
2p1
Popu
lation
Translation velocity (au)
Velocity dependence of level population created by electron capture from Mo surface
Hydrogen atoms translating outward from Mo surface with angle of 60 degree to the surface normal.
IAEA CCN Meeting 2010
23/04/21 IAEA CCN Meeting 2010
Example of results with this code•Dα emission of reflected neutrals of D ion beam at Mo surface was observed experimentally (incident ion energies of 5-25 keV).
•Dα emission yield per incident ion and Doppler profile (peak shift and width) were measured as a function of incident energy.
•With the aid of Monte-Carlo simulation of kinetic energy distribution of reflected neutrals, present code gives consistent results for Dα emission yield and Doppler peak variation with incident ion beam energy.
61IAEA CCN Meeting 2010
23/04/21 IAEA CCN Meeting 2010
Dα emission intensity is nearly proportional to reflection coefficient of Mo for E > 1 keV.
About 2 % of reflected particles emit Dα photons.
T. Tanabe et al.; J. Nucl. Mater. 220-222 (1995) 841.
Dα (656.1 nm) emission from neutrals of a deuteron beam reflected at Mo surfaces
IAEA CCN Meeting 2010 62
23/04/21 IAEA CCN Meeting 2010
Kinetic energy distribution of reflected D atomsIncident angle of 60 degree to the surface normal.Monte-Carlo simulation by means of ACAT code.
IAEA CCN Meeting 2010 63
23/04/21 IAEA CCN Meeting 2010
T. Tanabe et al.; J. Nucl. Mater. 220-222 (1995) 841.
Associated energy distribution for 3d2 state and comparison with measured Doppler shift of Dα
lineD atoms reflected specularly:60 degree to the surface normal.
IAEA CCN Meeting 2010 64
Doppler peaks of Dα are calculated, consistent with experiments. experiment
23/04/21 IAEA CCN Meeting 2010
Occupation probability of excited levels of D atoms reflected at Mo surface
D atoms reflected specularly: 60 degree to the surface normal.
IAEA CCN Meeting 2010 65
Tokyo Institute of Technology
Kradiation from partially ionized atoms is one of good candidates for temperature plasma diagnostics.
Introduction & motivation
Blue-shift of K lines are clearly seen according to the ionization state.
Kwith Z ≥ 9 is available for hot plasma diagnostics.
T. Kawamura et al., LPB, 24, p.261, 2006
previous work
0
0.2
0.4
0.6
0.8
1.0
1.2
2.6 2.65 2.7 2.75 2.8photon energy (keV)
rad
iati
ve d
ecay
rat
e(
x 10
14 s
ec-1) Cl
9+
Cl1+ ~ 8+
Cl13+Cl
10+
Cl11+
Cl12+
1s2
��������������
Temperature highlow
With intensity ratio of K-radiations from different charge states, plasma temperature can be deduced.(T. Kawamura et al., Laser and Particle Beams, 24, p.261, 2006)
Tokyo Institute of Technology
10-2
10-1
100
101
102
He2+
--> Cl
Cl9+
/Cl1+ ~ 8+
Cl10+
/Cl1+ ~ 8+
Cl11+
/Cl1+~8+
Current : 1kA/cm2
Energy : 25 MeV(
40 50 60 70 80 90 100
inte
nsi
ty r
atio
electron temperature (eV)
an intensity ratio between cold andshift K is useful to deduce temperature.
For Te > 100 eV,
conventional Li-like satellite and He-like resonance lines work well.
For lower region, Te < 50 eV, cold K from Cl+ ~ 8+ may be a candidate for plasma diagnostics.
For Te = 50 ~ 100 eV,
Introduction & motivation
target : C2H3Cldensity : solid
Tokyo Institute of Technology
Kradiation from Cl+ ~ Cl8+ partially ionized atoms may work well for cold plasma diagnostics.
outline
a ) Blue-shift of K lines of Cl+ ~ Cl8+ is very small.
Discussion is mainly devoted to topics a ) and b ), and to give a suggestion on topics c ) .
Spectral blue-shift by M-shell ionization is examined.
The point at issue :
b ) There are so many satellite lines around K lines.
Probability of the existence of atomic states with an excited electron in the outer-shell is considered.
c ) How is the opacity effect of K radiation with M-shell electrons ?
Highly charged K-radiation is created by K-shell ionization of an incident ion beam at electron temperatures Te < 85 eV .( T. Kawamura et al., Laser and Particle Beams, 24, p.261, 2006 )
He2+ current : 1 kA/cm2, Enegry : 25 MeV (±0.1%)Tokyo Institute of Technology
Cl7+
Cl8+
Cl9+
Cl10+
0 50 100 150 200electron temperature (eV)
104
106
108
1010
1012in
ten
sity
of
K
rad
iati
on
(W
/cc)
dominated by K-shell ionization by He2+ impact
dominated by dielectronic capture
previous work
target : C2H3Cldensity : solid
e- --> Cl
He2+
--> Cl
Ne10+
--> Cl
Ar18+
--> Cl
For chlorine, ion energy of more than few tens MeV is necessary to create vacant K-shell by low Z ion impacts.
ion impact K-shell ionization: ADNDT, 20, p.503, 1977
electron impact ionization: J. Phys. B, 11, p.541, 1978, and related papers.
previouswork
cro
ss s
ecti
on
of
K-s
hel
l io
niz
atio
n (
cm
2 )
10-17
10-18
10-19
10-20
10-21
10-22
10-3 10-2 10-1 100 101 102 103
incident ion energy (MeV)
101 102 102
16
14
12
10
8
6
4
2
ave
rag
e io
niz
ati
on
sta
te Z
to
tal
electron temperature Te (eV)
Tokyo Institute of Technology
Assuming CRE, electron temperature Te with high population for Ztotal ≤ 7 is less than ~ 70 eV, and that for Ztotal ≤ 5 is less than ~ 35 eV.
Te with high population for Z total ≤ 5 is:( Z1s-vacant ≈ Ztotal + 1 ≤ 6 )
less than ~ 35 eV at solid density.
~ 35 eV
~ 70 eVless than ~ 70 eV at solid density.
Te with high population for Z total ≤ 7 is:( Z1s-vacant ≈ Z total + 1 ≤ 8 )
Cold K is dominant at ≤ Te ~ 35 eV.
density : solidtarget : C2H3Cl
averagecharge state
C6+ beamCurrent : 3 kA/cm2, Energy : 30 MeV (± 10 %)
Te = 30 eV
Te = 35 eV
Te = 5 eV
Te = 10 eV
Te = 15 eV
Te = 20 eV
Te = 25 eV
Cl2+ Cl3+
Cl4+ Cl5+
Cl6+ Cl7+
Cl+
Peak of cold K line is shifted to blue-side with increase in electron temperature Te due to outer-shell ionization up to Z 1s-vacant = 6 ~ 7, resulting in ~ 10 eV spectral shift.
Tokyo Institute of Technology
calculation ofspectral shape
6
4
2
02610 2615 2620 2625 2630 2635
photon energy (eV)rad
iati
ve d
ecay
rat
e(
x 10
13 s
-1)
inte
nsi
ty (
a.u
.)
0.6
0.4
0.2
0
0.8
1.0C6+ beamCurrent : 3 kA/cm2, Energy : 30 MeV (± 10 %)
With increase in Te up to 35 eV, blue-shift of K shows ~ 10 eV.
Cold K is available to diagnose cold dense plasma at a few tens electron volts.
Cl+ :1s2s22p63s23p5
Cl2+:1s2s22p63s23p4
Cl+:1s2s22p63s23p43d
Cl3+:1s2s22p63s23p3
Cl2+:1s2s22p63s23p33d
K lines from 1s-vacant states with an excited electron in the outer-shell overlap with those from the next ionization state, showing unresolved satellite-line shape.
Tokyo Institute of Technology
6
4
202610 2615 2620 2625 2630 2635
photon energy (eV)
rad
iati
ve d
ecay
rat
e(
x 10
13 s
-1)
6
4
2
grasp92calculation
- satellite lines -
0
Cl3+:1s2s22p63s23p23d
Cl4+:1s2s22p63s23p2
100
80
60
40
20
050403020100
electron temperature Te (eV)
aver
age
con
tin
uu
m l
ow
erin
g
E (
eV)
average io
nizatio
n en
ergy I
p
for C
l n+
: 1s2s22p
63s23p
(6-n) (eV
)
100
80
60
40
20
0
Cl5+
Cl4+
Cl3+
Cl2+
Cl+
Due to large continuum lowering, 1s-vacant states with an excited electron in the outer-shell may have a small contribution for spectral line shape.
Tokyo Institute of Technology
continuumlowering
(E + Te) is almost comparable to Ip
of 1s-vacant ground state.
Probability of the existence of 1s-vacant ground state is a fraction of an isolated atomic state without E.
1s-vacant state with an excited electron may have less contribution for composite spectral shape.
Opacity effect of Kradiation with M-shell electron is small compared with that of highly charged Kradiation with Z ≥ 9.
Tokyo Institute of Technology
opacityestimation
They are belonging to bulk ions, and the fraction is large.
1.2
0
0.2
0.4
0.6
0.8
1.0
2.6 2.65 2.7 2.75 2.8photon energy (keV)
rad
iati
ve d
ecay
rat
e(
x 10
14 s
ec-1)
Cl9+
Cl1+ ~ 8+
Cl13+Cl
10+
Cl11+
Cl12+
1s2
��������������
Final states associated with K lines with open L-shell is:
Cl9+ ~ 13+ :1s22s22p(5-n) : (1 ≤ n ≤ 5 )
opacity is large.
Final states associated with K lines with open M-shell is:
Cl1+ ~ 7+ :1s22s22p53(8-n) : (1 ≤ n ≤ 7 )
They are vacant L-shell states, and the fraction is small compared with conventional states. opacity is small.
Kradiation with M-shell electrons is one of good candidates to diagnose cold dense plasma properties.
Tokyo Institute of Technology
summary
Kradiation with open L-shell ( Z ≥ 9 ) is useful at Te < ~ 100 eV.( T. Kawamura et al., Laser and Particle Beams, 24, pp.261, (2006) )
previous study
Kradiation with open M-shell ( Z ≤ 8 ) is available at Te < ~ 70 eV.
current & future studies
For Te < ~ 35 eV , Kradiation with Z ≤ 6 is suitable.Satellite lines may have a small contribution to spectral line shape due to large continuum lowering at solid density.
Opacity effect may weak due to the small population compared with that of highly charged K lines.
This issue will be studied more quantitatively.
河 村 徹 東京工業大学大学院総合理工学研究科
共同研究者
理論解析: A) 小池文博 , D)Rohini Mishra, D) 千徳 靖彦 , D)Peter Hakel, D)Roberto Mancini
実験解析: B) 大島慎介 , B) 中村浩隆 , B) 藤岡慎介 ,B) 田辺稔 , C)Mina Veltcheva, C)Tara Desai, C)Dimitri Batani, B) 西村博明
A 北里大学 医学部
B 大阪大学レーザーエネルギー学研究センター
C University of Milano,Bicocca, Italy
D University of Nevada, USA
低価数 K 線による高密度プラズマ中の高速電子輸送診断
ILE OSAKA
日本物理学会 2010 年秋期大会 2010/09/23-26@ 大阪府立大学中百舌鳥キャンパス
サブピコ秒のレーザー生成プラズマ実験では、時間空間分解計測が困難であることに加え、ターゲットとして massive なものを用いたケースが少なくない。
時間空間積分された K スペクトルの価数分布が加熱過程の時間履歴を示しているのか、プラズマ温度の空間勾配を示しているのかが不明。
高速電子が、ターゲット両面に形成されたシースポテンシャルによって閉じ込められる。
Tokyo Institute of Technology
質量制限 ( 薄膜 ) ターゲットを用いると、高速電子のRefluxing によって等温プラズマを生成することができると期待されている。
質量制限 ( 薄膜 ) ターゲット
高速電子の Refluxing による等温プラズマの生成によって、高速電子からプラズマへのエネルギー付与過程の理解を容易にすると期待されている。
Introduction & motivation
Tokyo Institute of Technology
質量制限ターゲットに、強度が 5x1017 ~ 1018 W/cm2 ( パルス幅: ~ 500fs, エネルギー: 10 J )のレーザーパルスを照射した。
C8H8 (Parylene-N) 5 m
Polyvinyl-chloride PVC (C2H3Cl) 5 m (tracer)
Laser
Side View
target type
A B C D
L 50 m 100 m 300 m 1000 m
Type B
Front View
parylene : 1.11 g/ccPVC : 1.40 g/cc
S A B C
L
C8H8 (Parylene-N) 5 m
Setup of an experiment
Tokyo Institute of Technology
低 ~ 高価数の K 線が観測され、温度分布の非一様性または温度履歴の積分情報(その両方?)が観測されている。
Experimentalresults
2600 2640 2680 2720 2760 2800
Intensity (a.u.)
Photon Energy (eV)
(A) r ~ 50m (B) r ~ 100m
(C) r ~ 300m
2600 2640 2680 2720 2760 2800
Intensity (a.u.)
Photon Energy (eV)2600 2640 2680 2720 2760 2800
Intensity (a.u.)
Photon Energy (eV)
(D) r ~ 1mm
2600 2640 2680 2720 2760 2800
Intensity (a.u.)
Photon Energy (eV)
Hecold KCl1~8+ cold plasma
shifted 成分shifted 成分hot plasma hot plasmaCl9~10+ Cl9~10+
shifted 成分Cl9+
(A),(B) についてshift-K: focal エリアcold-K: focal エリア周辺分
Tokyo Institute of Technology
K 線スペクトルによる高速電子のプラズマ加熱ダイナミクスの推定
- ターゲットによって focal エリアの加熱ダイナミクスが異なる理由 -
Outline of a talk
1.) 時間空間積分された K スペクトルの価数分布が加熱過程の時間履歴を示しているのか、プラズマ温度の空間勾配を示しているのかが不明
GRASP92+RATIP による計算結果との比較から、どちらの情報を反映したスペクトルであるかを検討する→加熱過程の時間履歴ならば、加熱開始から終了まで、連続的な価数分布が時間積分 K スペクトルに現れるはず
2.) cold Kおよび shift- 成分が観測される領域の温度推定と高速電子の VDF推定
3.) 外殻電子が励起された cold K 線の分布と、固体密度中における励起イオンの存在確率に関する指針 ( → satellite lines )
高速電子の stopping を考慮して、プラズマ温度の時間プロファイルを評価し、衝突輻射モデルにより、 K放射の価数分布と VDF の相関を検討する
Cl6+
Cl5+ Cl7+
Cl8+
Cl3+
Cl2+
K2K1Cl+
Cl4+
Tokyo Institute of Technology
Cold K 線は、 Cl1+ ~ 6+ の 2620 ~ 2630 eV のラインで形成され、7 ~ 8価のスペクトルへの寄与はマイナーである。
K1 : 2622.3 eVK2 : 2620.7 eV
National Astronomical Observatory :http: //www.nao.ac.jp/
2610 2615 2620 2625 2630 2635photon energy (eV)
rad
iati
ve d
ecay
rat
e(
x 10
13 s
-1)
~10 eV
GRASP92 & RATIP
calculation
Calculated by GRASP92 and RATIP:F. A. Parpia et al., CPC, 94, p.249, 1996S. Fritzsche et al., Phys. Scr. T100, p.37, 2002
6
4
2
06
4
2
0
inte
nsi
ty(a
.u.)
1 eV のスペクトル計測精度で、低温領域のプラズマ計測が可能
GRASP92 & RATIP
7 ~ 8 価の K 線が殆ど見えない→ cold K優位な領域と shift 成分優位な領域が存在する→ 主に空間的非一様性を反映
実験スペクトルとの比較から、…
(A) 50 m(B)100 m(C)300 m(D)1mm expt.
GRASP92 & RATIP
K 線に係る電離過程のシミュレーションを衝突輻射モデルを用いて実施し、ターゲット形状に依存する K スペクトルの価数分布の解析を行う。
Inner-shell ionization bya fast e- beam
Tokyo Institute of Technology
Pbulk P1s-vacant>>Population
••
Cl3+ : 1s22s22p63s23p2
Cl4+ : 1s22s22p63s23p
Cl2+ : 1s22s22p63s23p3
Cl4+ : 1s 2s22p63s23p2
Cl5+ : 1s 2s22p63s23p
Cl3+ : 1s 2s22p63s23p3
recombination & ionization
recombination & ionization
recombination & ionization
dielectronic capture• •
••
radiative & auger decays
radiative & auger decays
radiative & auger decays
bulk ions 1s-vacant ions
Modeling ofpopulation kinetics
0
0.5
1
0
50
100
150
0 0.5 1 1.5
electron temperature (eV)
Time(ps)
fractional fast electron (%)
C2H
3Cl : solid density
0.5 %
Tz = 200keV, Tr = 20keV
Tz = 200keV, Tr = 200keV
~76 eV
~56 eV
Tokyo Institute of Technology
1
8
12ln
122ln1
2
1ln
22
2
min
4
2mv
en
dx
dE e
free
2/3ln
4 4
2Dp
e
waves
v
mv
en
dx
dE
背景のバルク電子温度を2体衝突とプラズマ波励起を記述する衝突モデルによって計算した。
プラズマ条件 # ターゲット : C2H3Cl # 全イオン密度 : 8.094×1022 cm-3 (~
s )
# Peak of Fraction of Fast e- : 0.5 % (~ nc ) # 高速電子温度 : Tz = 200 keV, Tr 可変 # 背景電子の初期温度 : 5 eV
高速電子の時間プロファイル # Gaussian pulse, Pulse width (FWHM) 0.5 ps
# Peak density : ~ nc (critical density with = 1 m)
高速電子の阻止能 * # free: binary collision between free electrons # waves: excitation of plasma waves
[*] D.Batani, Laser and Particle Beams, 20, pp.321(2002).
Modeling offast e- stopping
Tokyo Institute of Technology
高速電子の VDF の非等方性が大きくなると、背景電子温度が高くなり、 shift-K放射が顕著になる。
Modeling offast e- VDF
ターゲットに依存して変化する高速電子のreflux のダイナミクスが、 focal エリアの高速電子 VDF の非等方性に影響する。例えば、非等方性が大きくなるとき、→ プラズマ電子温度が上昇→ 高電離の shift-K が顕著になる
1.00.5 1.5time (ps)
K
em
issi
on
( x
1022
erg
/sec
/cc
)
Cl+
Cl2+
Cl3+
Cl4+
Cl5+
Cl7+
Cl8+
Cl9+
(shift-K
0.8
0.6
0.4
0.2
0
1.0Tz=Tr=200keV
1.0
Cl+
Cl2+
Cl3+
Cl4+
Cl5+
Cl7+
Cl8+
Cl9+
(shift-K
0.8
0.6
0.4
0.2
0
Tz=200keV Tr=20 keV
0
~ 56 eV
~ 76 eV
charge state
inte
grt
aed
K
( e
rg/c
c )
109
108
1 2 3 4 5 6 7 8 9 10
Tz=200keV
200keV100keV50keV20keV
Cl+ :1s2s22p63s23p5
Cl2+:1s2s22p63s23p4
Cl+:1s2s22p63s23p43d
Cl3+:1s2s22p63s23p3
Cl2+:1s2s22p63s23p33d
外殻電子が励起したイオンからの K 線は、次の価数のラインと重なるが、固体密度では continuum lowering により、その存在確率は小さいと考えられる。 Tokyo Institute of Technology
6
4
202610 2615 2620 2625 2630 2635
photon energy (eV)
rad
iati
ve d
ecay
rat
e(
x 10
13 s
-1)
6
4
2
GRASP92 & RATIPcalculation
- satellite lines -
0
Cl3+:1s2s22p63s23p23d
Cl4+:1s2s22p63s23p2
Tokyo Institute of Technology
Cold Kα 線スペクトルによって、質量制限 ( 薄膜 ) ターゲット中の高速電子輸送ダイナミクスを検討した。
まとめ
Cold K 線スペクトルの低温高密度プラズマ計測への利用の可否を議論した塩素の場合、低温プラズマでは M殻電子を持つ K 線の spectral purityが高い
前回の講演では、
GRASP92+Ratip による解析が有力
実験スペクトル (cold K)が示す温度は、 < ~50 eV@solid density
今回の講演では、
Grasp92+RATIP を用いて、 Cold K の構成要素を調べることにより、実験スペクトルは空間的な非一様性を顕著に示していることを明らかにした
ターゲットの大きさによるスペクトルの違いは、 Reflux する高速電子のダイナミクスの相違が、 focal エリアの高速電子輸送に影響を及ぼしている可能性について議論した→ 高速電子の VDF のモデリングによってスペクトルの相違の説明が可能