Transcript Tokyo Institute of Technology

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
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:
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. Ka 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 Ions
Experimental:
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
Code Centre Network Meeting, 27 September 2010 IAEA, Vienna
Mean 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.
Code Centre Network Meeting, 27 September 2010 IAEA, Vienna
Identification of the M1 Lines for W26+
Correlation Models
Active Space:
AS1={4f,5s,5p,5d,5f,5g},
AS2=AS1+{6s,6p,6d,6f,6g}
Valence-Valence Correlation:
5SD: 4d104f2 4d10(AS1)2 6SD: 4d104f2 4d10(AS2)2
Core-Valence Correlation:
4p_5SD: 4s24p64d104f2 4s24p54d104f1(AS1)2
The wavelength (in nm) of the transition [4f-2]4
[[4f-]5/2[4f]7/2]5
DF
5SD
VV
6SD
Wavelength
3962
3948
3944
3943
3944
3940
3937
No. of CSF
13
131
408
844
14730
52079
112267
Models
7SD
VV+CV
4pd_5SD 4pd_6SD
4pd_7SD
Obs.
3894
Code Centre Network Meeting, 27 September 2010 IAEA, Vienna
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)
CoBIT experiments
gAr distribution
W26+ (4f25/2)J=4 – (4f5/24f7/2)J=5
Komatsu et al. (2010)
HCI 2010 @ Shanghai
l = 3894.1 (experiment)
l = 3937 (GRASP2K)
l = 4029 (HULLAC)
CR model
Energy Levels of the ground state of W26+
LS
Energy(cm-1)
Configuration Component
3H4
0.00
96% (4f_)24
3F2
19323.19
86% (4f_)22 + 12% [(4f_)5/2( 4f)7/2]2
3H5
52084.83
99% [(4f_)5/2( 4f)7/2]5
1G4
68564.31
96% [(4f_)5/2( 4f)7/2]4
3F3
68599.82
99% [(4f_)5/2( 4f)7/2]3
3H6
77400.42
64%(4f_)26 +35%[(4f_)5/2( 4f)7/2]6
3F4
98302.06
99% (4f)24
1D2
102031.11
76% [(4f_)5/2( 4f)7/2]2 + 14%(4f_)22
1S0
105385.15
81% (4f_)20+ 18%(4f)20
3P1
116790.74
99% [(4f_)5/2( 4f)7/2]1
1I6
119023.48
64%[(4f_)5/2( 4f)7/2]6 +35%(4f_)26
3P2
3P0
136212.13
185305.97
89% (4f)22+ 10%[(4f_)5/2( 4f)7/2]2
81% (4f)20+18%(4f_)20
Collisional-radiative model for W ions
I.Murakami, D. Kato, H. A. Sakaue, N. Yamamoto, C. Suzuki
NIFS
Measurement and atomic calculations
MCDF calculations
W 33+
Berlin
EBIT
W 34+
W 35+
W 36+
ASDEX
W39+ - W45+
P¨utterich et al.(2005)
W 37+
Rhee and Kwon (2008)
Rate equations
• Rate equation of excited level p in steady–state is described as
dn(p)/dt = Γin – Γout =0
in   C e (q, p)ne n(q)   C p (q, p)n p n(q)  {F e (q, p)ne  F p (q, p)n p  A(q, p)}n(q)  { ( p)  a ( p)ne }ne ni
q p
q p
q p
Excitation by electron & proton impact
Deexcitation by electron & proton
impact and radiative decay
recombination
out  [ S ( p)ne   C e ( p, q)ne   C p ( p, q)n p   F e ( p, q)ne   F p ( p, q)n p  A( p, q)]n( p)
q p
q p
Ionization Excitatiob by electron &
proton impact
q p
q p
Deexcitation by electron &
proton impact
radiative decay
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 ∝ni(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.
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
Electron density effect on the calculated spectra for W35+
CR model calculations
Atomic data : HULLAC code
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)
2020/4/24
gA=5.068x1011
13
Code development for single electron
capture by H nucleus from metal
surface
• Daiji Kato
• NIFS
2020/4/24
IAEA CCN Meeting 2010
Features of theoretical method
implemented 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 timedependent 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.
2020/4/24
IAEA CCN Meeting 2010
Semi-classical method for single electron capture by
translating projectile ion outward from metal surface
Electronic transition is treated by quantum mechanics
Ion motion is represented by classical trajectories
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）
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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IAEA CCN Meeting 2010
Classical picture of H atom-metal surface
interaction
electron image
electron
VeI
VCoul
VpI
D
nuclear image
nucleus
ρ= (x2 + y2)1/2
solid
2020/4/24
surface
IAEA CCN Meeting 2010
vacuum
z
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.
2020/4/24
Hydrogen atoms translating
outward from Mo surface with
angle of 60 degree to the surface
normal.
IAEA CCN Meeting 2010
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.
2020/4/24
IAEA CCN Meeting 2010
Ka radiation from low charge chlorine heated by an ion beam
for plasma diagnostics
Toru Kawamura, Kazuhiko Horioka
Department of Energy Sciences, Tokyo Institute of Technology
Fumihiro Koike
Physics Laboratory, School of Medicine, Kitasato University
grasp, grasp92
calculation
Many Ka lines is distributed over photon energy
according to the ionization state.
Tokyo Institute of Technology
Cl(8+m)+:1s2l(8-m) : (1 ≤ m ≤ 7 )
Cln+:1s2s22p63l(8-n): (1 ≤ n ≤ 8)
with open L-shell
radiative decay rate
( x 1014 sec-1)
with open M-shell
1.2
1.0
0.8
0.6
0.4
0.2
0
2.6
9+
11+
Cl
Cl
10+
1+ ~ 8+
Cl
Cl
12+
Cl
13+
Cl
1s2
2.65
2.7
2.75
photon energy (keV)
2.8
Ka photon energies show the characteristic charge state of plasmas ,
and Ka with M-shell electrons may be useful for lower temperature.
grasp92
calculation
Cold Ka is mainly composed of the lines from Cl+ ~ 6+,
and may be a good candidate for cold plasma diagnostics.
Tokyo Institute of Technology
radiative decay rate ( x 1013 s-1)
~10 eV
6
4
2
0
6
4
2
0
6
4
Cl+
Cl2+
Ka1
Ka2
Cl3+
Cl4+
Cl5+ Cl7+
Cl6+ Cl8+
2
0
2610
2615 2620 2625 2630
photon energy (eV)
National Astronomical Observatory :
http: //www.nao.ac.jp/
Ka1 : 2622.3 eV
Ka2 : 2620.7 eV
Blue-shift of Ka lines by outer-shell
ionization is very small.
Accuracy of the order of a 1 eV
is necessary for cold plasma
diagnostics.
Calculated by GRASP92 and RATIP:
F. A. Parpia et al., CPC, 94, p.249, 1996
S. Fritzsche et al., Phys. Scr. T100, p.37, 2002
2635
Auger
calculation
Many Auger channels compete with radiative processes,
and are indispensable to estimate Ka yield.
Tokyo Institute of Technology
Ground states of 1s-vacant Ions
(1s2l2l’ and 1s2l3l’ are estimated for Cl14+.)
1017
1
KLL Auger
KLM Auger
KMM Auger
1016
1s2
0.75
1015
0.5
1014
KLL Auger is the most predominant
over the competition with Ka transition.
Fluorescence Yield
Fluorescence yield of low charge state
( Cl+~Cl13+ ) Ka are :
0.05 ~ 0.1
T. Kawamura et al., PRE, 66, p.016402, 2002
1013
Total Auger Rate(1/sec)
1012
0
5
10
Charge State
0.25
0
15
Calculated by Auger-code:
S. Fritzsche et al., Phys. Scr. T41, p.45, 1992
modeling of
population kinetics
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.
bulk ions
•
•
recombination & ionization
Inner-shell
ionization by
an ion beam
•
•
1s-vacant ions
Cl3+ : 1s 2s22p63s23p3
Cl2+ : 1s22s22p63s23p3
recombination & ionization
radiative & auger decays
Cl4+ : 1s 2s22p63s23p2
Cl3+ : 1s22s22p63s23p2
radiative & auger decays
recombination & ionization
Cl5+ : 1s 2s22p63s23p
Cl4+ : 1s22s22p63s23p
•
Population
Tokyo Institute of Technology
Pbulk
dielectronic
capture
>>
radiative & auger decays
•
P1s-vacant
Code Availability
1.
2.
3.
4.
5.
GRASP and GRASP2
GRASP92 + RATIP
GRASP2K
CR-Model Code based on HULLAC
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+
CR model
• We have tried to construct a collisionalradiative 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, electronimpact 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
temperature 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,
such 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.
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
in   C e (q, p)ne n(q)   C p (q, p)n p n(q)  {F e (q, p)ne  F p (q, p)n p  A(q, p)}n(q)  { ( p)  a ( p)ne }ne ni
q p
q p
q p
Excitation by electron & proton impact
Deexcitation by electron & proton
impact and radiative decay
recombination
out  [ S ( p)ne   C e ( p, q)ne   C p ( p, q)n p   F e ( p, q)ne   F p ( p, q)n p  A( p, q)]n( p)
q p
Ionization
q p
q p
q p
Deexcitation by electron &
proton impact
radiative decay
• 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 ∝ni(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)
41
gA and calculated spectrum: W37+
4d -4f transitions:
Effect of excitation
processes
Fournier (1998)
(⊿λ/λ=0.005 assumed)
1 10
14
8 10
13
6 10
13
4 10
13
2 10
13
W37+
0
40 45 50 55 60 65 70 75 80
Wavelength (A)
Intensity
1.2 10
14
gA
1.4 10
14
3.5 10
-9
3 10
-9
2.5 10
-9
2 10
-9
1.5 10
-9
1 10
-9
5 10
W37+
100ev
251ev
1000ev
-10
0
40
50
60
70
Wavelength (A)
80
90
gA and calculated spectrum:
W36+
14
3 10
14
2 10
14
1 10
14
Intensity
4 10
gA
5 10
14
W36+
2.5 10
-9
2 10
-9
1.5 10
-9
1 10
-9
5 10
W36+
100eV
251eV
1000eV
-10
0
40 45 50 55 60 65 70 75 80
0
40 45 50 55 60 65 70 75 80
Wavelength (A)
Wavelength (A)
7 10
14
6 10
14
5 10
14
4 10
14
3 10
14
2 10
14
1 10
14
0
40
W35+
Intensity
gA
gA and calculated spectrum:
W35+
2.5 10
-9
2 10
-9
1.5 10
-9
1 10
5 10
50
60
70
Wavelength (A)
80
90
W35+
100eV
251eV
1000eV
-9
-10
0
40 45 50 55 60 65 70 75 80
Wavelength (A)
7 10
-9
6 10
-9
5 10
-9
4 10
-9
3 10
-9
2 10
-9
1 10
W35+ (ne=1010cm-3)
1 10
100eV
251ev
1000eV
-9
0
40 45 50 55 60 65 70 75 80
Wavelength (A)
Intensity
Intensity
Electron density effect on the calculated spectra for W35+
-9
8 10
-10
6 10
-10
4 10
-10
2 10
-10
0
40
W35+ (ne=1020cm-3)
100eV
251eV
1000eV
50
60
70
80
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
90
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.
Effective potential energy of electron above surface
p 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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IAEA CCN Meeting 2010
47
Surface potential well of jellium model
Semi-empirical formula proposed by Jennings et al.,


l  z  z0 

1 e
2 z  z0 , z  z0
1
I
Ve ( z )  
 B  z  z 0  1
2  2V0 1  Ae
, otherwise,
A  4V0 l  1,


B  4V0 A
• z0 is position of image plane. It is given by empirical formula
of Ossicini et al. or fitting to potentials of elaborate firstprinciple calculations.
• V0 is given by the sum of Fermi energy and work function.
• λrepresents electric field strength of surface dipole. ～1
for many elements.
2020/4/24
IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
48
Static linear density response of
electron gas
Electron density fluctuation:

 

ne (r )   d 3r K 0 (r , r )VSC (r ) ,
where K 0 is response function of Kohn-Sham states without
external perturbation. Self-consistent potential:
VpI



1
3 ne ( r )
VSC (r )       d r     VXC (r ) ,
r  r
r  rp


VXC (r )  VXC [n  ne (r )]  VXC [n ] 

dVXC
ne (r ) ,
dn n
where n  n  is bulk electron density n  k F3 / 3 2  .
Exchange correlation potential (Zangwill and Soven),
VXC  
2020/4/24
 11.4 
1.222
 0.0666 ln 1 
.
rs
rs 

IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
49
Adiabatic expansion of electron wave-function in sector
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).
2020/4/24
(m)
2010
 ( m ) (IAEA
r , D ) CCN
  Meeting
r  , m; D
( D)
i 

50
Eigen-energy curves of Mo (jellium)-H
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
2020/4/24
IAEA CCN Meeting 2010
isolated
hydrogenic levels.
IAEA CCN Meeting 2010
51
Split-operator-spectral (by sector) method
Initial condition
⇒Electron translation phase factor
2020/4/24
CCN Meeting
 2010 ( m )
 ( m ) ( DIAEA
i 1 )    , m; Di 1  , m; Di    ( Di )

52
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.
2020/4/24
IAEA CCN Meeting 2010
( )
anlm
 nlm  , m; D  ( m ) ( D )
53
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.
1.0
0.9
0.8
Population
0.7
0.6
0.5
0.4
1s
2s
2p0
2p1
0.3
0.2
0.1
0.0
0.1
1
Translation velocity (au)
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IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
54
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.
2020/4/24
IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
55
Dα (656.1 nm) emission from neutrals of a
deuteron beam reflected at Mo surfaces
T. Tanabe et al.; J. Nucl. Mater. 220-222 (1995) 841.
Dα emission intensity is nearly proportional to reflection coefficient
of Mo for E > 1 keV.
About
2 % of reflected particles
Dα
photons.
2020/4/24
IAEA CCNemit
Meeting
2010
IAEA CCN Meeting 2010
56
Kinetic energy distribution of reflected D atoms
Incident angle of 60 degree to the surface normal.
Monte-Carlo simulation by means of ACAT code.
2020/4/24
IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
57
Associated energy distribution for 3d2 state
and comparison with measured Doppler shift of Dα
D atoms reflected specularly:
line
60 degree to the surface normal.
Doppler peaks of Dα are calculated,
consistent with experiments.
experiment
T. Tanabe et al.; J. Nucl. Mater. 220222 (1995) 841.
2020/4/24
IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
58
Occupation probability of excited levels of D
atoms reflected at Mo surface
D atoms reflected specularly: 60 degree to the surface normal.
2020/4/24
IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
59
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.
1.0
0.9
0.8
Population
0.7
0.6
0.5
0.4
1s
2s
2p0
2p1
0.3
0.2
0.1
0.0
0.1
1
Translation velocity (au)
2020/4/24
IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
60
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.
2020/4/24
IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
61
Dα (656.1 nm) emission from neutrals of a
deuteron beam reflected at Mo surfaces
T. Tanabe et al.; J. Nucl. Mater. 220-222 (1995) 841.
Dα emission intensity is nearly proportional to reflection coefficient
of Mo for E > 1 keV.
About
2 % of reflected particles
Dα
photons.
2020/4/24
IAEA CCNemit
Meeting
2010
IAEA CCN Meeting 2010
62
Kinetic energy distribution of reflected D atoms
Incident angle of 60 degree to the surface normal.
Monte-Carlo simulation by means of ACAT code.
2020/4/24
IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
63
Associated energy distribution for 3d2 state
and comparison with measured Doppler shift of Dα
D atoms reflected specularly:
line
60 degree to the surface normal.
Doppler peaks of Dα are calculated,
consistent with experiments.
experiment
T. Tanabe et al.; J. Nucl. Mater. 220222 (1995) 841.
2020/4/24
IAEA CCN Meeting 2010
IAEA CCN Meeting 2010
64
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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65
Introduction
& motivation
Ka radiation from partially ionized atoms is one of good
candidates for temperature plasma diagnostics.
Tokyo Institute of Technology
previous work
Blue-shift of Ka lines are clearly seen according to the ionization state.
Ka with Z ≥ 9 is available for hot plasma diagnostics.
T. Kawamura et al., LPB, 24, p.261, 2006
radiative decay rate
( x 1014 sec-1)
low
1.2
1.0
0.8
0.6
0.4
0.2
0
2.6
Temperature
9+
11+
Cl
Cl
10+
1+ ~ 8+
Cl
Cl
high
12+
Cl
13+
Cl
1s2
2.75
2.7
2.65
photon energy (keV)
2.8
Introduction
& motivation
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
target : C2H3Cl
density : solid
For Te = 50 ~ 100 eV,
102
an intensity ratio between cold and
shift Ka is useful to deduce temperature.
intensity ratio
2+
101
He --> Cl
2
Current : 1kA/cm
Energy : 25 MeV(
9+
100
Cl /Cl
10-1
Cl
10+
For Te > 100 eV,
conventional Li-like satellite and
He-like resonance lines work well.
1+ ~ 8+
/Cl
1+ ~ 8+
For lower region, Te < 50 eV,
11+
Cl
10-2
40
/Cl
1+~8+
50 60 70 80 90 100
electron temperature (eV)
cold Ka from Cl+ ~ 8+ may be a
candidate for plasma diagnostics.
outline
Ka radiation from Cl+ ~ Cl8+ partially ionized atoms may
work well for cold plasma diagnostics.
Tokyo Institute of Technology
The point at issue :
a ) Blue-shift of Ka lines of Cl+ ~ Cl8+ is very small.
Spectral blue-shift by M-shell ionization is examined.
b ) There are so many satellite lines around Ka 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 Ka radiation with M-shell electrons ?
Discussion is mainly devoted to topics a ) and b ),
and to give a suggestion on topics c ) .
previous work
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 )
Tokyo Institute of Technology
target : C2H3Cl
density : solid
intensity of
Ka radiation (W/cc)
He2+ current : 1 kA/cm2, Enegry : 25 MeV
(±0.1%)
dominated by K-shell
ionization by He2+ impact
dominated by
dielectronic capture
Cl
10+
1012
Cl
9+
1010
Cl
108
Cl
8+
7+
106
104
0
50
100
150
200
electron temperature (eV)
previous
work
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
cross section of
K-shell ionization ( cm2 )
electron impact ionization: J. Phys. B, 11, p.541, 1978, and related papers.
10-17
Ar
10-18
Ne
10-19
10-20
He
2+
10+
18+
--> Cl
--> Cl
--> Cl
-
e --> Cl
10-21
10-22
10-3 10-2 10-1 100 101 102 103
incident ion energy (MeV)
average
charge state
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.
average ionization state Z total
Tokyo Institute of Technology
16
14
target : C2H3Cl
density : solid
12
~ 35 eV
10
8
~ 70 eV
6
less than ~ 70 eV at solid density.
Te with high population for Z total ≤ 5 is:
( Z1s-vacant ≈ Ztotal + 1 ≤ 6 )
4
less than ~ 35 eV at solid density.
2
101
C6+ beam
Current : 3 kA/cm2,
Energy : 30 MeV (±
10 %)
Te with high population for Z total ≤ 7 is:
( Z1s-vacant ≈ Z total + 1 ≤ 8 )
102
102
electron temperature Te (eV)
Cold Ka is dominant at ≤ Te ~ 35 eV.
calculation of
spectral shape
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
radiative decay rate
intensity ( a.u.)
( x 1013 s-1)
1.0
0.8
0.6
0.4
Te = 5 eV
Te = 25 eV
Te = 10 eV
Te = 30 eV
Te = 15 eV
Te = 35 eV
With increase in Te up to 35 eV,
blue-shift of Ka shows ~ 10 eV.
Te = 20 eV
0.2
0
6
4
2
Cold Ka is available to diagnose
cold dense plasma at a few tens
electron volts.
Cl+ Cl2+ Cl3+
Cl4+ Cl5+
Cl6+ Cl7+
0
2610
2615 2620 2625 2630
photon energy (eV)
C6+ beam
Current : 3 kA/cm2,
Energy : 30 MeV (±
10 %)
2635
grasp92
calculation
- satellite lines -
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
Cl+:1s2s22p63s23p43d
Cl2+:1s2s22p63s23p33d
radiative decay rate
( x 1013 s-1)
Cl3+:1s2s22p63s23p23d
6
4
2
0
6
Cl+ :1s2s22p63s23p5
Cl2+:1s2s22p63s23p4
4
2
0
2610
Cl3+:1s2s22p63s23p3
Cl4+:1s2s22p63s23p2
2615 2620 2625 2630
photon energy (eV)
2635
continuum
lowering
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
100
Cl5+
80
Cl4+
60
80
60
Cl3+
40
20
0
Cl2+
Cl+
40
20
0
0 10 20 30 40 50
electron temperature Te (eV)
average ionization energy Ip
for Cln+ : 1s2s22p63s23p(6-n) (eV)
average continuum lowering DE (eV)
100
(DE + 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 DE.
1s-vacant state with an excited electron
may have less contribution for
composite spectral shape.
opacity
estimation
Opacity effect of Ka radiation with M-shell electron is small
compared with that of highly charged Ka radiation with Z ≥ 9.
Tokyo Institute of Technology
Final states associated with Ka lines
with open M-shell is:
Final states associated with Ka lines
with open L-shell is:
Cl1+ ~ 7+ :1s22s22p53l(8-n) : (1 ≤ n ≤ 7 )
Cl9+ ~ 13+ :1s22s22p(5-n) : (1 ≤ n ≤ 5 )
radiative decay rate
( x 1014 sec-1)
They are belonging to bulk ions,
They are vacant L-shell states, and
and the fraction is large.
the fraction is small compared with
conventional states.
opacity is large.
opacity is small.
1.2
9+
1.0
0.8
0.6
11+
Cl
Cl
10+
1+ ~ 8+
Cl
Cl
12+
Cl
13+
Cl
1s2
0.4
0.2
0
2.6
2.65
2.7
2.75
photon energy (keV)
2.8
summary
Ka radiation with M-shell electrons is one of good candidates
to diagnose cold dense plasma properties.
Tokyo Institute of Technology
previous study
Ka radiation with open L-shell ( Z ≥ 9 ) is useful at Te < ~ 100 eV.
( T. Kawamura et al., Laser and Particle Beams, 24, pp.261, (2006) )
current & future studies
Ka radiation with open M-shell ( Z ≤ 8 ) is available at Te < ~ 70 eV.
For Te < ~ 35 eV , Ka radiation 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 Ka lines.
This issue will be studied more quantitatively.
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
低価数Ka線による高密度プラズマ中の
高速電子輸送診断
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,
ILE OSAKA
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
Introduction
& motivation
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。
Tokyo Institute of Technology
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Ka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。
質量制限(薄膜)ターゲット
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。
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。
Setup of an
experiment
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。
Tokyo Institute of Technology
Side View
target
type
A
B
C
D
L
50 m
100 m
300 m
1000 m
Front View
S
A
C
B
Laser
L
Type B
C8H8 (Parylene-N) 5 m
Polyvinyl-chloride PVC (C2H3Cl) 5 m (tracer)
C8H8 (Parylene-N) 5 m
parylene
PVC
: 1.11 g/cc
: 1.40 g/cc
Experimental
results
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。
Tokyo Institute of Technology
(A),(B)について
shift-Ka : focalエリア
cold-Ka : focalエリア周辺分
(A) r ~ 50m
(B) r ~ 100m
shifted成分
shifted成分
Cl9~10+ hot plasma
Cl9~10+ hot plasma
Intensity (a.u.)
Intensity (a.u.)
2600
2640
2680
2720
2760
2800
2600
2640
(C) r ~ 300m
Cl9+
cold Ka
Cl1~8+ cold plasma
2640
2720
2760
2800
Hea
(D) r ~ 1mm
shifted成分
Intensity (a.u.)
2600
2680
Photon Energy (eV)
Photon Energy (eV)
Intensity (a.u.)
2680
2720
Photon Energy (eV)
2760
2800
2600
2640
2680
2720
Photon Energy (eV)
2760
2800
Outline of
a talk
Ka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 Tokyo Institute of Technology
1.) 時間空間積分されたKa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Kaスペクトルに現れるはず
2.) cold Ka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
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、Ka放射の価数分布とVDFの相関を検討する
3.) 外殻電子が励起されたcold Ka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 )
GRASP92 &
RATIP
calculation
Cold Ka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。
radiative decay rate
( x 1013 s-1)
6
4
Tokyo Institute of Technology
~10 eV
GRASP92
& RATIP
Cl+ Cl3+ Ka2
Cl2+ Cl4+
National Astronomical Observatory :
http: //www.nao.ac.jp/
Ka1
Ka1 : 2622.3 eV
Ka2 : 2620.7 eV
2
0
6
4
GRASP92
& RATIP Cl5+ Cl7+
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
Cl6+ Cl8+
2
実験スペクトルとの比較から、…
intensity
(a.u.)
0
(D)1mm
(C)300 m
(B)100 m
(A) 50 m
2610
7 ~ 8価のKa線が殆ど見えない
→ cold Ka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
expt.
2615 2620 2625 2630
photon energy (eV)
2635
Calculated by GRASP92 and RATIP:
F. A. Parpia et al., CPC, 94, p.249, 1996
S. Fritzsche et al., Phys. Scr. T100, p.37, 2002
Modeling of
population kinetics
Ka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Kaスペクトルの
価数分布の解析を行う。
bulk ions
•
•
recombination & ionization
Inner-shell
ionization by
a fast e- beam
•
•
1s-vacant ions
Cl3+ : 1s 2s22p63s23p3
Cl2+ : 1s22s22p63s23p3
recombination & ionization
radiative & auger decays
Cl4+ : 1s 2s22p63s23p2
Cl3+ : 1s22s22p63s23p2
radiative & auger decays
recombination & ionization
Cl5+ : 1s 2s22p63s23p
Cl4+ : 1s22s22p63s23p
•
Population
Tokyo Institute of Technology
Pbulk
dielectronic
capture
>>
radiative & auger decays
•
P1s-vacant
Modeling of
fast e- stopping
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。
Tokyo Institute of Technology
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 l = 1 m)
高速電子の阻止能 *
1
150
C H Cl : solid density
# free: binary collision between free electrons
# waves: excitation of plasma waves
dE
dx
dE
dx
free
2 ne e
mv 2
4
ln
1
2
min
4
waves
4 ne e
ln
mv 2
プラズマ条件
# ターゲット
# 全イオン密度
s )
1 ln 2
2
2
1
2
1
ln 2
8
2
p
D
3/ 2
~76 eV
0.5 %
0.5
100
~56 eV
50
: C2H3Cl
: 8.094×1022 cm-3 (~
# Peak of Fraction of Fast e- : 0.5 % (~ nc )
# 高速電子温度
Tz = 200keV, Tr = 20keV
Tz = 200keV, Tr = 200keV
1
v
elec
3
: Tz = 200 keV, Tr 可変
# 背景電子の初期温度 : 5 eV
[*] D.Batani, Laser and Particle Beams, 20, pp.321(2002).
fractional fast electron (%)
0
0
0.5
1
Time(ps)
0
1.5
Modeling of
fast e- VDF
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-Ka放射が顕著になる。
Tokyo Institute of Technology
T =T =200keV
2+
z
r
Cl Cl3+
~ 56 eV
4+
Cl
5+
+
Cl Cl7+ Cl8+
Cl
0.8
Ka emission ( x 1022 erg/sec/cc )
integrtaed Ka ( erg/cc )
1.0
0.6
109
0.4
9+
0.2
Cl (shift-K
0
1.0
8+
Cl
+
0.8 Cl
0.6
2+
7+
Cl Cl3+ 4+
Cl
Cl Cl5+
Tz=200keV
Tr=20 keV
~ 76 eV
9+
0.2
0.5
time (ps)
1.0
1
2
3
6 7
4 5
charge state
8
9
10
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-Kaが顕著になる
0.4
0
20keV
50keV
100keV
200keV
108
Cl (shift-K
0
Tz=200keV
1.5
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。
GRASP92 & RATIP
calculation
- satellite lines -
Tokyo Institute of Technology
Cl+:1s2s22p63s23p43d
Cl2+:1s2s22p63s23p33d
radiative decay rate
( x 1013 s-1)
Cl3+:1s2s22p63s23p23d
6
4
2
0
6
Cl+ :1s2s22p63s23p5
Cl2+:1s2s22p63s23p4
4
2
0
2610
Cl3+:1s2s22p63s23p3
Cl4+:1s2s22p63s23p2
2615 2620 2625 2630
photon energy (eV)
2635
まとめ
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。
前回の講演では、
Tokyo Institute of Technology
Cold Ka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Ka線のspectral purityが高い
GRASP92+Ratipによる解析が有力
実験スペクトル(cold Ka)が示す温度は、 < ~50 eV@solid density
今回の講演では、
Grasp92+RATIPを用いて、Cold Ka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