1

P.A. Lobodaa, S.V. Gagarina, M.V. Kobel’kovaa, S.V.

Koltchugina, S.V.

Morozova, V.V. Popovaa, A.A. Shadrina, I. Yu. Silantievaa,

I.V.

Solominaa, I.A. Vaninaa, M.A. Vorobyovaa, A.Ya. Faenovb, A.I.

Magunovb, T.A. Pikuzb, I.Yu. Skobelevb, I.L. Beigmanc,

F.F.

Goryaevc, A.M. Urnovc, I.Yu. Tolstikhinac, L.A.

Vainshteinc

CALCULATIONS OF MULTIELECTRON-ION ATOMIC DATA, THERMODYNAMICS, AND OPACITIES OF HOT DENSE PLASMAS AND RELEVANT DATABASE DEVELOPMENTS

a)

Russian Federal Nuclear Center –

All-Russian Institute of Technical Physicsb)

Joint Institute for High Temperatures of Russian Academy of Sciencesc)

P.N. Lebedev

Physical Institute of Russian Academy of Sciences

2

Scope of activities

Development of the chemical-picture-based models to consistently simulate EOS & opacities / emissivities

of dense multielectron-ion

plasmas utilizing both the superconfiguration

& detailed description of the LTE ionization balance along with the bound-

bound & bound-free

spectral distributions.

Atomic-data calculations for multielectron

ions.

Development & maintenance of atomic-data & opacity databases.

Application of the developed models and generated atomic data to the modeling of EOS & opacities / emissivities

of warm & hot

dense matter, targeted at the laboratory-plasma diagnostics, modeling of laser-plasma x-ray sources,

etc; filling of the relevant

databases.

3

Chemical

model of dense

LTE 

plasmas

of multielectron

ions

A

A+ + e Ze

e

rcA

iA+

A+

i

V.K. Gryaznov, I.L. Iosilevsky. PNP-13, Chernogolovka

(2009)

(0) ( 1)

( 1) ( 2)

( ( 1)) ( )

,,

.Z Z

A A eA A e

A A e

In

chemical

model,

plasmas

are treated as thermodynamically equilibrium

mixture

of various ions with internal

degrees of freedom (excited states)

and free electrons.

Helmholtz free energy:

( ) ( ) ( )

0, ,

Zid bound id

Q Q eQ

F T F F F F

N

, , 1 /Q e BN N k T N

― ionic ideal-gas contribution; ( ) 3ln 1idQ B Q QF k TN N

( ― modified internal partition function of a Q-electron ion = contribution of bound-electron states perturbed by the plasma environment;QU

― contribution

due to ions with Q

bound electrons;( ) lnboundQQ B QF k TN U

F F(ρ,

T, N)

― interparticle-interaction contribution;

― (partially) degenerate free-electron ideal-gas contribution; ( )1 2 3 23

4 23

ide e e B e

e

F I k T I

4

Interpolation

between

the Debye-Hückel

limit and Monte-

Carlo OCP-calculated data

i = Eкул / Eкин

0.01 0.1 1 10 100- f

ii

0.001

0.01

0.1

1

10

100

0.001

0.01

0.1

1

10

100

приближение Дебая-Хюккелямодель ионной сферыаппроксимация Потехина-Шабриэ

910IS if

3/232DH if

G. Chabrier, A. Potekhin, Phys. Rev. E, 58, 4941 (1998);

G. Chabrier, A. Potekhin, Phys. Rev. E, 62, 8554 (2000).N.F. Carnahan, K.E. Starling, J. Chem. Phys., 51, 635 (1969).

Coulomb

interaction of charged species (generalization of the Z‐charged  OCP calculated data for a partially ionized plasmas

with

<Z>

=

Z)

, , B ii iec eeF Nk T f fT f N

2

24 3, , , packing fraction.1

ionsHS B

plasma

VF T Nk TV

N

finite-ion-volume

effects

(OCP of hard-sphere classical ions generalized for multi- ionic mixture by using the packing fraction):

5

1 2 3 4 8

1 2 3

1 2 3 4

1 2 2 3 3 3 4 4 4 4 8 8

1 2 2 3 3 3 4 4 4 4 8

1 2 2 3 3 3 4 4 4 4 8

Q Q Q Q Q

Q Q Q

Q Q Q Q

s s p s p d s p d f s k

s s p s p d s p d f k

s s p s p d s p d f k

In

the

SC-approximation, sets

of

ionic

configurations

of

a Q-electron

ion

close

in

energy

are

gathered

into

superconfigurations

defined

as

collections

of

supershells

{σ} —

groups

of

energetically

adjacent

ionic

subshells

populated

in

all

possible

ways

consistent

with

the

Pauli

exclusion

principle

А. Bar-Shalom, et al., Phys. Rev. A, 40, 3183 (1989); J. Oreg, A. Bar-Shalom, M. Klapisch,

Phys. Rev. E, 55, 5874 (1997).F.

Gilleron, J.C.

Pain. Stable

method

for

the

calculation

of partition

functions

in

the

SC approach.

Phys. Rev. E, 69, 056117 (2004).

Superconfiguration

(SC) approach to calculate partition functions

.Q CC

U T U U

Some examples of SCs

:

supershellsSupershell

occupancies Q

=

Q

(0) (0) (0)

(0) (0)

, ,

, , , .s s

ss

C C C s s C Cs C

s qEQ s s

sq Q s

E E E где E q E E E

gU U U e U U U X X e

q

6

Modified

partition functions

on the base of the 

SC

approach

Truncation

of plasma-microfield-perturbed spectra of bound electrons by using the occupation probability formalism (introduced by Hummer & Mihalas

in 1988

for H-like ions: Solar interiors):

( )

0

, , ( , )cr

s

sw T P d N

–

occupation probability of an one-electron state including the effect of plasma microfields

defined as the probability

that the microfield

does not exceed the value of critical electric field

–

microfield

distribution function.( , )P

, , ,QU T U

N

, ., ,s s

ss

qs s

sQs

s

q s

gwhere U U X X e

qw T

N

D.G. Hummer, D. Mihalas. Astrophys. J., 331, 794 (1988);

A. Nayfonov, W. Dappen, D. Hummer, D. Mihalas,

Ap. J., 526, 451 (1999).F.

Gilleron, J.C.

Pain. Stable

method

for

the

calculation

of partition

functions

in

the

SC approach.

Phys. Rev. E, 69, 056117 (2004).

* min( , )[ ({ }) ] ( )

; ; 1 0;00

, , 0 , , 1.s

s Q s s

s

s

t gq Q q

Q t sQ t q sq

U U e где U U e t Q s U

Recursive relations to calculate partition functions:

7

Ionization‐balance equations

1 23

1 1

·exp

( ) ,

,

4 ,

1.

Q Qe Q

Q Q

Q

e

QQ Q

e

c Uc U

Z Q c Z

ZN

c

I

(0) ( 1)

( 1) ( 2)

( ( 1)) ( )

,,

.Z Z

A A eA A e

A A e

1 1

ln

.

,

, ,

Q B QQQ Q e Q Q

c

e

HS

F k T

F T

UN N N N N N

F F

N

min[F(ρ,T,N)] ionization balance @ LTE

conditions N

[{NQ

}, Ne

]:

Л.Д.

Ландау, Е.М.

Лифшиц. Теоретическая

физика, т. V. Статистическая

физика. М: НАУКА

(1964).Я.Б.

Зельдович, Ю.П.

Райзер. Физика

ударных

волн

и

высокотемпературных

гидродинамических

явлений. М.: НАУКА

(1966).

8

( ) ( )

,

2 ( ) ( )

,

, , ,

, , .

id idi e b

T

id idi e ioniz b

V

FР T Р Р Р РV

FE T T E E E Е ET T

N

N

N

N

223 / 2 3 31

4

3

22

23

12, ( ) ( ) ,

3 1,

4 2 4 2, .1 1

cc B Q z OCPc OC

Q

HS

P

B HS B

A BA BP cV BE E Nk T where

P Nk T E NkT

A

T

B

Dense‐plasmas

EOS

3 23/2( ) ( ) ( ) ( )3 3

8 3 4, , , .23

eeid id id idi B e B i B e B

e e

IIР Nk T Р k T E Nk T E k T

“Ideal-gas”

contributions:

Ionization energy relative to g.s. of a neutral atom @ T=0:

Contribution due to bound electrons:

2ln ln, .Q Qb B Q b B Q

Q Q

U UР k T N Е k T NV T

Coulomb-interaction and finite-volume effects:

1

,0, 1

(1 ) .Z Q

ioniz Q Q Z kQ k Q Z

E N I

9

Electronic specfic

heat of copper plasma

Te, eV

10-1 100 101 102 103 104

Cv(e

)

10

20

30

40

50

ТФПКVASPFP-LMTOданная работа

( ) , ,13 / 2

iev

B

E T E TC

Nk T

Н.Н.

Калиткин, Л.В.

Кузьмина. Таблицы

термодинамических

функций

вещества

при

высокой

концентрации

энергии.

Препринт

ИПМ

АН

СССР, № 35 (1975); В.П.

Копышев. О

термодинамике

ядер

одноатомного

вещества.

ЧММСС, 8,54–7 (1977).Z. Lin, L.V. Zhigilei. Phys.

Rev.

B,

77, 075133 (2008).FP-LMTO: Г.В. Синько, Н. А. Смирнов, РФЯЦ-ВНИИТФ. Расчет

методом

FP-LMTO (частное

сообщение, 2009).

10

Modeling of opacities of multicharged-ion dense plasmas

Superconfigurations comprise occupied atomic shells

:

Transition arrays between superconfigurations are modeled by effective spectral distributions corresponding to

single-electron

transitions:

Ion populations are found from modified Saha

equations allowing for plasma- nonideality & electron-degeneracy effects or given by the chemical-picture-based

EOS model utilizing the full-scale superconfiguration

appoach

allowing for

plasma-nonideality & electron-degeneracy effects.

A variant of STA (Super Transition Arrays)

model currently implemented in the SPECTR code to calculate monochromatic opacities

1 21 2

kqq qkn n n

n l j n l j

11

The SPECTR-STA model to calculate monochromatic opacities

Gaussian or Voigt effective line shapes for transition arrays include statistical energy dispersion and Doppler broadening or Doppler + homogeneous (radiative + electron-collisional) broadening.

Single-

& two-

electron atomic data, as well as configuration

properties are calculated by using RCN36 program being the principal constituent of the well-known Cowan’s suite of atomic codes (to be replaced by the FAC-code data in a new full-scale version of SPECTR-STA).

12

Comparison of the LTE iron-transmission spectra

0.1 0.15 0.2 0.25 0.30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

, keV

T (

)

1 : Experiment, R = 4400 600 cm2/g2: SPECT R-ST A, nm ax=8, R = 4503 cm2/g3: ST A, LLN L, R = 4630 cm 2/g4: M CUT A, LLN L, R = 4525 cm2/g

2

1

3

4

LTE-transmission spectra of the Fe-component

in the 300

m-long plasma layer of Fe:NaF

mixture at a density = 0.0113 g/cm3

and temperature

T = 59 eV compared to experimental and calculated (STA, MCUTA)

spectra of P.T. Springer et. al (PRL 69, 3735--3738 (1992))

0( ) exptransT I I L

13

Rosseland means of the Be(99.1%):Cu(0.9%) mixture

SPECTR-STA opacities: P.A. Loboda

et. al, J.

Phys.

A., 39, 4781--4786 (2006)

Promising targets for ISKRA-6: N.G. Karlykhanov

et al. JETP Lett., 79, 25--27 (2004)

14

SPECTR-STA

monochromatic partial opacities for heavy- element fractions of Solar

mixture

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

10-2

10-1

100

101

102

103

, keV

[1

/cm

]Fe = 0.001389 g/cc, T=0.1719 keV

OPCD, lR=31.15

Spectr-STA, lR=28.86

15

SPECTR-STA

monochromatic partial opacities for heavy-element fractions of Solar

mixture

1 2 3 4 5 6 7 8 9100

101

102

103

104

105

106

, keV

[1

/cm

]Cr = 1.1859343 g/cc, T=1.217285 keV

OPCD, lR=0.2204

Spectr-STA, lR=0.241

16

Monochromatic partial opacities for heavy-

element fractions of Solar-mixture: Sunbase

17

A numerical model Spectr-DTA

based on detailed description

of bound-bound and bound-free radiation /

absorption spectra (Detailed Term Accounting: DTA- approach) is developed to calculate radiative properties

(spectral emissivities

& opacities) of multicharged-ion plasmas

to analyze & model radiation/absorption spectra of dense plasmas being measured in laser-plasma experiments;

to benchmark approximate statistic methods for simulating radiative properties of dense plasmas.

Numerical modeling of radiative properties of multicharged-ion plasmas

using DTA-approach

18

Spectr-DTA model to calculate spectral opacities

Ionization balance & ion-state populations are found from•

superconfiguration

ionization balance models + Boltzmann

distribution over detailed terms (LTE);•

calculations with other collisional-radiative models (NLTE).

Spectr-DTA

uses pre-calculated atomic data for bound-bound (atomic-state properties, multipole

transition matrix elements) &

bound-free radiative transitions (photoionization cross-sections for ground + excited levels, if necessary) contributing to the spectral range of interest.

Voigt lineshapes

for transitions include Doppler and homogeneous (autoionization, radiative, & electron-collisional) broadening.

Detailed Stark-broadened lineshapes

may also be employed, if necessary & reasonable (more expensive).

19

Spectr-DTA model to calculate spectral opacities

Generalized theoretical model LineDM

for calculating local line radiation/ absorption spectra for arbitrary multielectron ions in plasmas [P.A.

Loboda et al. LPB 18, 275 (2000) ]:

•

consistent implementation of the density-matrix approach;•

arbitrary bound-bound transitions;

•

most important line-broadening mechanisms: ion quasi-static & electron Stark broadening, natural, autoionization, and Doppler broadening;

•

enables to describe the effects of plasma microfield and radiation field on the population kinetics of ionic states (individual

calculations).

20

K-shell

emission spectra

of simple Al ions to model short-pulse sources

of narrowband x-ray radiation

Al: Ne = 1023

cm-3, Te = 600 eV

J. Limpouch et al. Proc. SPIE, 5228, 584--593 (2003)

21

LLNL experimental data for near-LTE Al transmission at T=584 eV,

= 0.020.007 g/cm3

vs. DTA-model

calculations

Ion Fraction Lines

[Li] 12% 470

[Be] 16% 10646

[B] 42% 58558

[C] 31% 141911

[N] 8% 115144

0

=

0.05 m

=0

0

/=67.5 m

T.S. Perry, et al. Phys. Rev. Lett., 67, 3784–3787 (1991)

1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.610

20

30

40

50

60

70

80

90

100

110

, keV

trans

mis

sion

T(

) = e

xp[-

()

]

T( ) A l, 0=50 nm, T=58 eV, =0.02 g/cm 3

ExperimentSpectr DTALANL (T4 group)

Convolved with Gaussianinstrumental function,FW HM=0.6 eV

22

Iskra-5 experiments for near-LTE Al transmission at RFNC-VNIIEF

One-sided x-ray irradiation experiments with Al samples 0

=0.9 & 0.1 m

Dy

x-ray backlighter,delay time~

(0.7-1) ns

pinhole

X-ray drive:

–

two laser-driven

“illuminator”

hohlraum-type

targets

(d=L=1 mm )

Laser drive: 4 Iskra-5 laser beams (2ω) E~250

J, 0,5

~ 0.5

ns.

1 m-СН

sandwiched

x-ray heated Al

sample

200m Ta

screen

КАР

crystal

X-ray film

X-ray spectrograph

Line-absorption

x-ray spectra

23

Measured near-LTE transmission of Al radiatively

heated by laser-driven “illuminator”

hohlraum-type targets in 4-beam Iskra-5 experiment (April, 2007) vs. Spectr-DTA

calculations

“Thin”

sample0

= 0.1 m

=0

0

/

Ion Fraction Lines

[Be] 4% 10646

[B] 24% 58558

[C] 43% 141911

[N] 24% 115144

[O] 5% 17136

1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.580.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

, keV

trans

mis

sion

T(

) = e

xp[-

( ,x

)]

T() Al, 0=0.1 m

Convolved with Gaussian instrumentalfunction, FWHM=2 eV

Experiment=0.1g/cm3,T=45eV T=50eV=0.07g/cm3,T=45eV T=50eV

Presented @ ECLIM-2008

24

Input atomic data for Spectr-DTA

Spectroscopic data are calculated for detailed radiative transitions between relativistic ionic terms with •

an improved version of the GRASP2 package

(up to

2500

detailed terms and 3х106

transitions

in a single GRASP2

run)

•

parametric-potential relativistic Flexible Atomic Code (FAC) (somewhat less accurate than GRASP2, but easier to run)

Autoionization widths, photoionization cross-sections are calculated using the distorted-wave approach with the FAC code (if necessary).

A pilot version of the relevant database to accumulate and maintain detailed atomic data is developed and being filled now with consistent spectroscopic data for multielectron

ions.

25

Spectroscopic-data calculations

GRASP

(K.G. Dyall, I.P. Grant, et. al, 1989)

GRASP2

(F. Parpia, I.P. Grant, C.F. Froese-Fischer, 1992)

errors fixed;

convergence of iterations to solve Dirac-Fock equations improved;

algorithm to calculate electron self-energy component of the QED corrections improved;

computation of reduced matrix elements of equivalent nonrelativistic multipole-transition operators included;

special-purpose program to postprocess the calculated data and generate the systematized datasets developed (to fill databases and calculate

emission and

absorption spectra of highly charged multielectron ions).

GRASP-family MCDF packages (General Relativistic Atomic-Structure Package):

GRASP

GRASP2 GRASP92 grasp2K

26

SPECTR-W3: http://spectrhttp://spectr--w3.snz.ruw3.snz.ru

27

Experimental, theoretical, and compiled values of

ionization potentials,

energy levels,

wavelengths,

radiative transition probabilities and oscillator strengths,

statistical weights, radiative & autoionization

widths, satellite intensity factors Qd(recently added fields),

and also

fitting parameters and formulae to analytically approximate collisional cross- sections and electron transition rates in atoms and ions (optional)

in free atoms & ions,

references to the original sources

comments on the methods of the data acquisition, …

etc, where necessary and available

Factual

atomic

database SPECTR-W3

450000 recordsCurrently:

64000

visits

to spectr-w3.snz.ru

since November

2, 2002

28

Data

sources

journal papers published in the leading physical journals;

datasets submitted by the authors (collaborators);

high-resolution experimental and reliable theoretical data obtained by the project participants

A technique of retrieving the atomic data from electronic and printed publications was developed on the base of the up-to-date text recognition software FineReader.

About 200 new spectroscopic

datasets were

converted into HTML

format & incorporated

in

the

SPECTR-W3

database.

29

Data obtained by the authors

Satellite lines due to radiative transitions from Rydberg autoionizing states of Li-like Mg were first identified and high-resolution measurements of wavelengths performed at /

≤

10-4 (LPP) new reference lines to

study complex spectra of multielectron ions;

High-resolution data on the wavelengths of Ne-like Cu & Zn in LPP identify 2p-nd

& 2s-np

Rydberg-series transitions + measure ionization

potentials;

High-resolution data on the wavelengths of N-, O-, and F-like Zn. Most of the lines were identified for the first time.

Consistent spectroscopic datasets were generated with the GRASP2

& FAC codes that involved the states with all possible J

and P & dipole radiative

transitions between them for a nr. of F-, Ne-, Na-like ions with Z~20–50 (n

≤

4, n

≤

5, n

≤

4, respectively), all ions of Al. The datasets

are being

incorporated into the SPECTR-W3

database.

Electron-collision excitation rates for some transitions in H-, He-, Li-, and N-like C, Ar, and Fe, Cu-, …Pd-like Sn

were calculated using the ATOM

& FAC parametric-potential codes.

30

Previous 2-year ISTC project # 1785 (2001–2003)

Fully functional CD variant of the SPECTR-W3 atomic database ―

SPECTR-CD for the off-line

use on PCs under Windows supplied with the automatic setup program has also been created.

SPECTR-W3

homepage was integrated into the family of special-purpose atomic databases on the Web, see http://plasma-gate.weizmann.ac.il/DBfAPP.html

Dissemination of information & Project results evaluation

very good reaction

31

Objectives of the current 3-year ISTC project # 3504 (2007–2010)

In the course of work under the ISTC project # 3504

facilities for direct submission of new author’s atomic data will be created

and put into operation, a technique of supplementing SPECTR-W3

with

those data will be developed and optimized;

export utilities providing the selected data output into XML (eXtensible

Markup

Language) and plain text format will be implemented (HTML is already available);

SPECTR-W3

and its local version SPECTR-CD will be essentially

updated by:

the inclusion of new experimental and theoretical information on

the multicharged-

ion spectra both published in literature and obtained in the participatingorganizations under the previous ISTC Project # 1785;

introduction of the new data type on the autoionization-transition rates;

inclusion of the results of systematic calculations and high-resolution measurementsobtained by the participants as well as presented by the other authors;

selection and inclusion of the most important experimental and theoretical data

published after 2003;

software and equipment of the SPECTR-W3

website will be upgraded;

functionality and informative content of the SPECTR-W3

Web-pages will be extended;

a new version of the SPECTR-CD setup package will be generated

32

Current SPECTR-W3 project-related collaborations

Authors:

Yu. Ralchenko (NIST, USA)

D. Humbert, (IAEA)

R.E.H. Clark (IAEA)

M-L. Dubernet (Université

Pierre et Marie Curie, France)

E. Roueff

(Observatoire

Paris-Meudon, France)

D.R. Schultz (ORNL, USA)Contributors:

P.A. Loboda (RFNC-VNIITF, Russia)

S.V. Gagarin (RFNC-VNIITF, Russia)

N. Moreau (Observatoire

Paris-Meudon, France)

a new versatile

standard for atomic, molecular and particle surface interaction data exchange (AM/PSI) based on XML is being developed under the IAEA support

Presented @ ICAMDATA-2008Yu. Ralchenko et al. AIP Conf. Proc. 1125, 207–216 (2009).

www-amdis.iaea.org/xsams/documents

33

XSAMS = XML Schema for Atoms, Molecules & SolidsCurrent SPECTR-W3 project-related collaborations

34

Current SPECTR-W3 project-related collaborations

Collaborative 3.5-year EC projectVirtual Atomic & Molecular Data

Centre

(VAMDC)has started

VAMDC

aims to build a secure, documented, flexible and interoperable e-science environment

based

interface to the existing A&M data.

The VAMDC

will be built upon the expertise of existing

A&M databases, data producers, and service providers with the specific aim of creating an

infrastructure that is easily

tuned to the requirements of a wide variety of users in academic,

governmental, industrial or public

communities both within and outside the European Research Area (ERA).

The project will cover the building of the core consortium, the development and deployment of the infrastructure and the development of interfaces to the existing A&M databases as well as providing a forum for training potential users and dissemination of expertise across the ERA.

www.vamdc.eu

Project Coordinator: Marie Lise Dubernet, UPMC/CNRS, France

35

Current SPECTR-W3 project-related collaborations

VAMDC participants

1. Centre National de la Recherche Scientifique (CNRS), France: coordinator2. Cambridge University (UCAM), UK3. University College London (UCL), UK4. Open University (OU), UK5. Universität Wien (UW-A), Austria6. Uppsala Universitet (Uppsala), Sweden7. Universität zu Köln (Koln), Germany8. Istituto Nazionale di Astrofisica (INAF-OAC), Italy9. The Queen's University of Belfast (QUB), UK10.Astronomical Observatory of Belgrade (AOB), Serbia11. Institute of Astronomy of RAS (INASAN), Russia12.Russian Federal Nuclear Centre All-Russian Institute of Technical

Physics (RFNC-VNIITF), Russia13. Institute of Atmospheric Optics, SB of RAS (IAO), Russia14.Venezuelan Institute for Scientific Research (IVIC), Venezuela15. Institute for Spectroscopy of RAS (ISAN), Russia