code centre network meeting, 27 september 2010 iaea, vienna atomic structure and dynamics...

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)


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


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


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


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.


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


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

23/04/21 13

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

23/04/21 IAEA CCN Meeting 2010

Code development for single electron capture by H nucleus from metal

surface• Daiji Kato• NIFS


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.


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 ）


z

ρ= (x2 + y2)1/2

nucleus

electron

VCoulVeI

VpI

Dnuclear image

electron image

surface vacuumsolid

Classical picture of H atom-metal surface interaction


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.


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.


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+


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.


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


Pbulk P1s-vacant>>Population

••

Cl3+ : 1s22s22p63s23p2

Cl4+ : 1s22s22p63s23p

Cl2+ : 1s22s22p63s23p3

Cl4+ : 1s 2s22p63s23p2

Cl5+ : 1s 2s22p63s23p

Cl3+ : 1s 2s22p63s23p3

recombination & ionization



dielectronic capture• •

••

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)


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)


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.


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.

47IAEA CCN Meeting 2010


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.,



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



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


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



Split-operator-spectral (by sector) method

⇒ Electron translation phase factorInitial condition

52)(;,;,)( )(11

)(i

miii

m DDmDmD


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


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


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.



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 56


Kinetic energy distribution of reflected D atomsIncident angle of 60 degree to the surface normal.Monte-Carlo simulation by means of ACAT code.




Associated energy distribution for 3d2 state and comparison with measured Doppler shift of Dα

lineD atoms reflected specularly:60 degree to the surface normal.


Doppler peaks of Dα are calculated, consistent with experiments. experiment


Occupation probability of excited levels of D atoms reflected at Mo surface

D atoms reflected specularly: 60 degree to the surface normal.



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


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.



Dα emission intensity is nearly proportional to reflection coefficient of Mo for E > 1 keV.

About 2 % of reflected particles emit Dα photons.


Dα (656.1 nm) emission from neutrals of a deuteron beam reflected at Mo surfaces



Kinetic energy distribution of reflected D atomsIncident angle of 60 degree to the surface normal.Monte-Carlo simulation by means of ACAT code.




Associated energy distribution for 3d2 state and comparison with measured Doppler shift of Dα

lineD atoms reflected specularly:60 degree to the surface normal.


Doppler peaks of Dα are calculated, consistent with experiments. experiment


Occupation probability of excited levels of D atoms reflected at Mo surface

D atoms reflected specularly: 60 degree to the surface normal.



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


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)


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,


target : C2H3Cldensity : solid


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)


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.


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.


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.


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.


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


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.


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。


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。



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


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


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+


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


Pbulk P1s-vacant>>Population

••

Cl3+ : 1s22s22p63s23p2

Cl4+ : 1s22s22p63s23p

Cl2+ : 1s22s22p63s23p3

Cl4+ : 1s 2s22p63s23p2

Cl5+ : 1s 2s22p63s23p

Cl3+ : 1s 2s22p63s23p3




dielectronic capture• •

••




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


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


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


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

code centre network meeting, 27 september 2010 iaea, vienna atomic structure and dynamics...

Documents

4p64d3 j

levels 4s2 4p6 4d2

4s2 4p5 4d2

levels 4s2 4p6 4d3

4p64d24d j

4s2 4p5 4d3w

4s2 4p5 4d4

iaea ccn meeting