IAEA International Atomic Energy Agency

Spectroscopy of Dense Plasmas

H.-K. Chung Atomic and Molecular Data Unit Nuclear Data Section

Joint ICTP-IAEA Advanced School on Modern Methods in Plasma Spectroscopy

Trieste, Italy 19 March 2015

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Plasmas occur over a vast range of conditions

Temperature

10-6K – 100 keV (109K)

Density

105 – 1024 cm-3

Astrophysical observations CHANDRA/XMM

Plasma processing Fusion research

ICF (Inertial confinement fusion) Laser-produced plasma Beam-produced plasma Z-pinch plasmas

MCF (Magnetic confinement fusion) Tokamak plasma

Ultracold plasmas

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Advances in plasma generation access new regimes of matter

USP: Ultra short pulse laser (RAL, LULI, Titan, Texas)

XFEL: X-ray free electron lasers (SLAC, European XFEL, SACLA)

Pulse Power: X-Pinches, Z-Pinches... (Sandia, Cornell, UNR)

NIF (National Ignition Facility)

Hotter and denser matter Transient states of matter

Warm dense matter Astronomical X-ray applications IAEA

A new state of matter achieved experimentally requires new theories and modeling capabilities

• the strong coupling parameter is ratio of the interaction energy to the kinetic energy

• μ is the degeneracy parameter

HDM occurs in: • Supernova, stellar interiors,

accretion disks

• Plasma devices : laser, ion beam and Z-pinches

• Directly driven inertial fusion plasmas

WDM occurs in: • Cores of large planet

• Systems that start solid and end as a plasma

• X-ray driven implosion

Hydrogen phase diagram

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DENSITY EFFECTS ON POPULATION KINETICS

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Population Kinetics Models

Coronal plasmas (low Ne) Rate formalism Charage state distributions are determined by rates of collisional ionization and excitation-autoionization (EA) & radiative recombination and dielectronic recombination (DR) originating from the ground states

LTE plasmas (high Ne) Statistical distributions Collisional processes are dominant and the population distribution is governed by Boltzmann relations and Saha equation. Collisional-radiative plasmas (intermediate Ne) Rate equation model A population distribution is determined by rate equations considering collisional and radiative processes at a given temperature and density. The results should converge to coronal or the LTE limit at low and high Ne limits, respectively.

Mean ionization states, Charge state distributions, Spectral intensity, Emissivity, Opacity, Equation of state, Electrical conductivity require population distributions of ions in the plasma.

Aut

oion

izin

g st

ates

B

ound

Recombined ion

ground state

Bou

nd s

tate

s of

reco

mbi

ning

ion

DR

EA

n=1

n=2

n=3

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Non-LTE plasmas have well documented problems for experiment and theory

Au M-shell emission Glenzer et al. PRL (2001)

1st Non-LTE workshop (1996) documented large differences between codes for Au

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DR and EA treatments are the main sources of discrepancy Mean ion charges for Ar case, ne = 1012 cm-3 agree very well among different codes if Dielectronic Recombination (DR) and Excitation Autoionization (EA) processes are turned off.

NLTE Workshops, HEDP 9, 645 (2013)

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DR and EA treatments are the main sources of discrepancy Mean ion charges for Gold case, ne = 1021 cm-3 agree very well if Dielectronic Recombination (DR) and Excitation Autoionization (EA) processes are turned off

Without DR

With DR

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Processes of dielectronic recombination (DR) and excitation autoionization (EA)

• DR is a two-step process: An electron is captured leaving the recombined ion at autoionizing (Ai) states. Subsequently, the states stabilize either to the bound states completing recombination process or back to the ion by Auger process

• Electron capture (EC) can enhance resonant collisional excitation (CE) when the state autoionizes to the excited state of the recombining ion

• EA process is a reverse process to DR and an electron is excited to Ai states which subsequently ionize by Auger processes

Aut

oion

izin

g st

ates

(Ai)

Boun

d

Recombined ion

ground state Bou

nd s

tate

s of

reco

mbi

ning

ion

CE

EC

EA

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Stepwise Ionization: Excited states contribute to ionization and recombination processes

24

26

28

30

32

34

1 1.5 2 2.5 3 3.5 4 4.5 5

Ne=1E16Ne=1E18Ne=1E20Ne=1E22Ne=1E24

Aver

age

char

ge s

tate

s

Te[keV]

coronal

Ne-like Kr

He-like Kr Continuum

Ground state of ion Z

Con

Grou staund s

nti

uu

Con

Grouun of ion Zoff ion Z

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Highly excited states are in Saha equilibrium with the continuum at high densities

• At Equilibrium, the collisional recombination rate coefficient is given by the detailed balance with collisional ionization rate coefficient

• Recombination rates to high lying hydrogenic levels are proportional to n4 and inversely proportional to T2.

Continuum

Ground state of ion Z

Co

roundnd tad stnd

onCo

ounndnd

um

te of ion Ze of ion Z

gi n2

Ip 1/n2

For Saha Equilibrium R=(ni/ni+1)Non-LTE/(ni/ni+1)Saha ~ 1

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Average charge states are sensitive to the treatment of high-lying states at High Ne Due to the 3-body recombination processes, the average charge state decreases after reaching the maximum value as Ne increases, then increases again due to the ionization potential depression.

10 eV

100 eV

1 keV

475 eV

10 keV

4 keV Krypton

FLYCHK

Te=0.5 eV-100 keV

Ne=1012-1024 cm-3

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Plasma effects: Ionization potential depression & Rate changes

• Ionization potentials are a function of plasma conditions • High-lying states are no longer bound due to interactions with

neighbouring atoms and ions. (pressure ionization)

Isolated atom continuum

Embedded atom continuum

Ionization potential depression (IPD)

• For a given ne,Te, the IPD , is calculated

using a Stewart-Pyatt type model Where ri and rd are the ion sphere and Debye radii

= 2.16x10-7 zri

1rdri

3 2/ 3

rdri

2

(eV )

Ip

Ipp

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Average charge states are sensitive to the treatment of high-lying states at High Ne Due to the 3-body recombination processes, the average charge state decreases after reaching the maximum value as Ne increases, then increases again due to the ionization potential depression.

10 eV

100 eV

1 keV

475 eV

10 keV

4 keV Krypton

FLYCHK

Te=0.5 eV-100 keV

Ne=1012-1024 cm-3

Pressure Ionization Continuum Lowering Ionization Potential Depression

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max

Z=0 Zmax

=0

Planar geometry

Radiative rates should be modified by self-absorption at high density

( )

( )

η: Emissivity χ: Opacity τ: Optical Depth

I( )

)

Aij BjiJij AijBijJij

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Escape probability reduces the total A rate

Frequency-averaged escape probabilities ( ) : line profile

ij

Escape probability: Modified radiative rates due to optical depth effects

Aij BjiJij AijAJij A BijJij Aij

Λ( ) : Escape Probability

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DENSITY EFFECTS ON PLASMA SPECTROSCOPY

Continuum Lowering, Opacity effects and Opacity broadening

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Line shape and intensity changes with opacity effects for dense plasmas

Opacity broadening due to line-core absorption τ0 = line-center optical depth

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Line Width Analysis of argon plasma influenced by opacity effects • ne diagnostics are derived from Stark broadened line widths • Population kinetics needed for correct optical depths Statistical Fitting Analysis of Opacity- and Stark-Broadened Ar+2 Line Profiles Measured in Ion Beam Transport Experiments H.K. Chung et al, JQSRT, vol. 65, p. 135 (2000)

data

calc

Without Opacity With Opacity

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Boltzmann plot analysis should include opacity effects for correct Te analysis

With Opacity Without Opacity

Pi is the line escape probability

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Line intensity and width analysis should include opacity effects

mean charge state

Without opacity effect

With opacity effect

• Analysis of measured spectra from the initial phase of the ion-beam plasma formation using NLTE populations reveals that IPROP (a PIC/Fluid hybrid code) using simple population model overestimates Te

• Note that IPROP uses a simple breakdown ionization model

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Line intensity analysis with opacity effects and plasma space gradients

Measured ratios between Ly- and He- lines are only possible for very high temperatures, Te > 1 keV for optically thin case.

He-

Ly-

RAL experiments: Strong axial and transverse Te gradients in 0.5 ps 300J irradiation of 0.5 μm Al + 5μm Cu target (2005)

Cu K shell spectrum has 3:1

front :back intensity ratio in He-

Is the rear side hotter?

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Measured ratios between Ly-α and He-α lines increase with opacity effects

Cu Solid, Te=2 keV, Nhot=2% 200keV Spectral intensities are senstive to opacity effects

Ly

He

Sat.

Sat.

Hot Plasma Lyα emission

Cold Plasma Heα emission

Line emission from two different (front & back) regions can’t be used for single Te determination

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Disappearance of Line radiation

Hoarty, PRL 110, 265003 (2013) Short-pulse laser heating and compression by laser driven shocks 1-10 g/cc Al dot (100 μm x 0.15μm) buried in plastic foils or diamond sheet

9 g/cc

5.5 g/cc

1.2 g/cc

2.5 g/cc

4 g/cc

FLYCHK

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XFEL irradiated solid Al experiments: Observed K-edges and IPD models

• Kα line intensities are observed as a function of XFEL photon energy • Observed K-edge shifts from the atomic edge for non-equilibrium solid

density plasmas as a function of temperature and density

Nature 482, 59 (20120 PRL 109, 065002 (2012)

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PRL 109, 065002 (2012) SP model challenged after more than 40 years of extensive uses in astrophysics, cosmology, planetary science and inertial confinement fusion research.

Understanding of IPD is critical to explain spectral features

1805 eV

1780 eV

1750 eV

1720 eV

1720 eV

1650 eV

1600 eV

1580 eV

1630 eV

1830 eV

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Model completeness of dense matter with high energy particles (K spectra)

• Generally CR codes use the minimum set of configurations for NLTE plasmas • This may lead to inaccurate K emissivities for dense matter (Te ≥ 100eV)

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0

1x106

2x106

3x106

4x106

5x106

6x106

8000 8050 8100 8150 8200 8250 8300 8350

300 eV <Z>=17.8

Emiss

ivity

[erg

/s/H

z/cm

2 ]

Energy

Model Completeness: the set of configurations should be expanded

FLYCHK <Z> is good; but, emissivities may not be good enough for warm dense matter Analysis with limited configuration sets can give higher Te in K diagnostics

Silver : <Z> and total K emissivities Solid density and Ne= 1024 cm-3 Hot e- of 1020 cm-3 at 1 MeV

FLYCHK (K1L6)M1 (K1L6)

Copper : K spectra

SCFLY (K1L6)M1 (K1L6) + (K1L6)M3

(K1L6)M2N1 (K1L6)M1N2 (K1L6)M2 (K1L6)M1N1

0

5x1034

1x1035

1.5x1035

2x1035

0

5

10

15

20

25

50 100 150 200 250

(Yield) SCFLY(Yield) FLYCHK

<Z> SCFLY

<Z> FLYCHK

Emiss

ivity

[eV/

s/cm

-3]

zbar

Te[eV]

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GENERALIZED POPULATION KINETICS MODEL

FLYCHK

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Need for Generalized CR models

• If PLTE condition exists • If the plasma state is coronal, CR or LTE • If a line is optically thick • If strongly transient plasmas upward or downward • If excitation flow results in different distribution of population

densities • If excitation temperature Texc differs from Te • Survey spectra low spectral resolution • Total line intensities medium spectral resolution • Line profiles high spectral resolution

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Screened Hydrogenic Model

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FLYCHK Model : simple, but complete

• Screened hydrogenic energy levels with relativistic corrections • Dirac Hartree-Slater (DHS) oscillator strengths and photoionization

cross-sections • Fitted collisional cross-section to PWB approximation • Semi-empirical cross-sections for collisional ionization • Detailed counting of autoionization and electron capture processes • Continuum lowering (Stewart-Pyatt)

(n) (nl) (nlj) (detailed-term) FLYCHK HULLAC / FAC / MCDF

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Application to a wide range of Z and experiments: Excitation autoionization (EA) /Dielectronic recombinationa (DR) processes are modeled with doubly-excited and inner-shell (IS) excited states

Promotion of IS electrons can lead to states near the continuum limit and EA/DR process of IS is critical

N-shell Ion 3l18 4lz+1

N-shell Ion 3l184lz

3l174lznl

3l164lz+1nln’l’

3l174lz+1nl

High Z atom

L-shell Ion 1s22lZ+1

L-shell Ion 1s22lZ

1s12lZ+1nl”

Doubly- excited

Inner- Shell

1s22lZ-13l’nl”

Bound

Low Z atom

Promotion of IS electrons leads to states far from continuum limit and rarely matters in CSD

Bound

Doubly- excited

Inner- Shell 3l184lZ-15l’nl”

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Total line emissivity and energy-dependent spectral intensity in the STA formalism

EAB

gi exp( Ei / kTe )AijEiji A: j B

gi exp( Ei / kTe )Aiji A: j B

AAB

gi exp( Ei / kTe )Aiji A: j B

gi exp( Ei / kTe )i A: j B

( ) nAAABEAB ( )nA gi exp( Ei /kTe )AijEij ( )

i A: j B

gi exp( Ei /kTe )i A: j B

Total line emissivity: plots show approximate line emission spectra and provides information on energy range of dominant emission

S nuAulEul /Ne [eVcm3/s/atom]

Spectral emissivity is computed in the STA formalism using configuration-average atomic data generated by the DHS(Dirac-Hartree-Slater) code (M.Chen)

AB2

gi exp( Ei / kTe )AijEij2

i A: j B

gi exp( Ei / kTe )Aiji A: j B

2

EAB2

STA width

[ergs/s/Hz/cm3/ster]

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Screened Hydrogenic Model

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Applications to Plasma Research

• Short-pulse laser-produced plasmas • Arbitrary electron energy distribution function • Time-dependent ionization processes • K- shifts and broadening: diagnostics

• Long-pulse laser-produced plasmas • Average charge states • Spectra from a uniform plasma • Gas bag, Hohlraum (H0), Underdense foam

• Z-pinch plasmas: photoionizing plasmas • Proton-heated plasmas: warm dense matter • EBIT: electron beam-produced plasmas • EUVL: Sn plasma ionization distributions • TOKAMAK: High-Z impurities

28eV 36eV 32eV

SiO2-Ti foam exp

Time-dependent Ti K emissivities

Tin charge state distributions

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Available to the community at password-protected NIST website: http://nlte.nist.gov/FLY

Advantages: simplicity and versatility applicability • <Z> for fixed any densities: electron, ion or mass • Mixture-supplied electrons (eg: Argon-doped hydrogen plasmas) • External ionizing sources : a radiation field or an electron beam. • Multiple electron temperatures or arbitrary electron energy distributions • Optical depth effects

Outputs: population kinetics code and spectral synthesis • <Z> and charge state distribution • Radiative Power Loss rates under optically thin assumption • Energy-dependent spectral intensity of uniform plasma with a size

Caveats: simple atomic structures and uniform plasma approximation • Less accurate spectral intensities for non-K-shell lines • Less accurate for low electron densities and for LTE plasmas • When spatial gradients and the radiation transport affect population significantly

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Activities at IAEA AMD Unit : http://www-amdis.iaea.org

• Databases on Atomic and Molecular Data for Fusion. ALADDIN The atomic and molecular, plasma-surface interaction database AMBDAS The bibliographical database GENIE A search engine on different databases on the web OPEN-ADAS A joint development between the ADAS Project and IAEA

• Online Computing Heavy Particles collisions Cross sections for excitation and charge transfer for collisions Los Alamos atomic physics codes An interface to run several Los Alamos atomic physics codes Average Approximation An average approximation cross sections Rate coefficients collisional radiative calculations with the Los Alamos modeling codes to obtain total

radiated power, average ion charge, and relative ionization populations

• Coordinate Research Projects Light Element Atom, Molecule and Radical Behaviour in the Divertor and Edge Plasma Regions Characterization of Size, Composition and Origins of Dust in Fusion Devices Data for Surface Composition Dynamics Relevant to Erosion Processes Spectroscopic and Collisional Data for Tungsten from 1 eV to 20 keV

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885

17

429

90

0

10

20

30

40

50

60

70

80

25020 50 100 150 200

graph

Spectroscopic diagnostics of plasmas: Theoretical plasma spectroscopy

The microscopic response of the atom carried by photons provides information on the macroscopic environment

• Te and ne • Electromagnetic fields • Plasma wave modes

Atoms respond to perturbations of the ensemble of surrounding particles and/or external fields

– Electronic transitions – Photon-atom interactions – Atomic level shifts and broadens

time

energy

Observed photons

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<Z> spread at low Ne decreases at higher Ne due to the reduced DR/EA

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High-n states

Coronal Limits (low densities)

Coronal Model

Continuum

Ground state of ion Z

Ground state

of ion Z+1

Highgh-

Contin

tate o

n stn

nuunnn

d st

-

inn

ta

G

of

GroundG

CI Ne

ates

f i Zt

CI C

AI

Ec Ne

CE Ne AE

• At low densities, 99% of population lies in the ground states. Excited state population densities are so low that they are assumed to be populated from the ground state by collisional excitation CE and depopulated by spontaneous emission AE. Hence the excited population density is proportional to Ne.

• Charge state distributions are determined by rates of collisional ionization (CI) and excitation-autoionization (EA) & radiative recombination (RR) and dielectronic recombination (DR) originating from the ground states. Charge state distribution is independent of Ne

RR

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LTE Limits (high densities) • Collisions dominate population/depopulation and

rates should be in detailed balance.

• 3-body recombination rates are proportional to Ne

2 and n4 of recombined state. Hence high-lying states are important for charge state balance.

• A population distribution is an explicit function of “local” plasma conditions, governed by Boltzmann statistics and Saha equations.

• Ionization potential depression (IPD) important

LTE Model

Continuum

Ground state of ion Z

ion Z+1

Grou of ion Z

Ej gj 2n2

Ip~n-2

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Collisional-Radiative Regime

• Population distribution is obtained by rate equations considering collisional and radiative processes, along with plasma effects

• Excited states are substantially populated and increase the total ionization by step-wise ionization processes while 3-body recombination to these states is proportional to n3 and they significantly enhance the total recombination.

• Plasma effects such as non-local radiation transport, fast particle collisions and density effects should be included in the model.

• For optically thick lines, the self-absorption should be included to reduce the radiative processes.

Collisional-Radiative Model

Continuum

Ground state of ion Z

ion Z+1

Con

Grou staund s

nti

uu

Con

Grouun of ion Zoff iion Z

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Born approximation for collisional excitation

• Born approximation using DHS wave functions and YK Kim’s threshold scaling (JJATOM) gives reasonable cross-sections

Comparison of FAC, HULLAC & JJATOM Comparison of Fit & JJATOM