IAEA International Atomic Energy Agency

Atomic Processes in 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 26 March 2015

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Outline

• Motivation • High Energy Density Physics

• Collisional-Radiative Modeling • FLYCHK model

• Spectroscopic Analysis • Long-pulse laser experiment – Gold • Short-pulse laser experiment – Copper • Pulsed-power Z-pinch experiment – Iron • Xray Free Electron Laser experiment –Neon • Radiation loss rates - Krypton

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HIGH ENERGY DENSITY PHYSICS

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High Energy Density Physics (HEDP) is a rapidly growing research area • High energy density physics (for example, pressure

conditions exceeding 1 Mbar) : exciting research opportunities of high intellectual challenge.

• A new generation of sophisticated laboratory facilities and diagnostic instruments exist or are planned that create and measure properties of matter under extreme conditions.

• Laboratory exploration of basic high energy density physics studies, materials research, understanding astrophysical processes, commercial applications (e.g., EUV lithography), inertial confinement fusion, and nuclear weapons research.

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The field spans a wide range of areas

• High-energy-density astrophysics • Laser-plasma interactions • Beam-plasma interactions • Beam-laser interactions • Free electron laser interactions • High-current discharges • Equation-of-state physics • Atomic physics of highly stripped atoms • Theory and advanced computations • Inertial confinement fusion • Radiation-matter interaction • Hydrodynamics and shock physics

Rocky Silicate

Mantle

Iron/Nickel Core

Central Pressure: 360 GPa Central Temperature: 6000 K

Earth

Inertial confinement fusion: High density: 106 air density High temperature ~ 10 keV

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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), LMJ

Hotter and denser matter Transient states of matter

Warm dense matter Astronomical X-ray applications

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Advances in plasma generation access new regimes of matter

XFEL

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Modeling capabilities essential for high energy density physics • Radiation-Hydrodynamics simulations are required to understand transient,

non-uniform plasma evolution • Fluid treatment of plasma physics

- Mass, momentum and energy equations solved • Plasma thermodynamic properties (Ne, Te, Ti, Tr, Vr, Vi .. ) • LTE (Local Thermodynamic Equilibrium)

• PIC simulations provide non-equilibrium electron energy distributions

• Particle treatment of plasma physics - Boltzmann transport and Maxwell equations solved

• Electron energy distribution function (fe ..) • Simple ionization model

• Non-LTE kinetics models provide spectroscopic observables

• Atomic processes in plasmas - Rate equations are solved for a given electron energy distributions (fe)

• Atomic level population distributions • Plasma conditions (Ne, Te)

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Integrated simulations are often required: Rad-Hydro, Electron transport, and NLTE Kinetics

Hydro Code

LSP

PIC NLTE-Kinetics

Code

Predicted Spectrum

Provides estimate of pre-plasma to PIC

PIC sends back hot electron estimates to Hydro.

Hydro provides estimate of background electron temperature to NLTE-kinetics codes

Determines charge state distribution

Experimental USP Laser

Target conditions

Rad. Transport

Feedback?

(S. Wilks)

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COLLISIONAL-RADIATIVE POPULATION KINETIC MODELS

Level population distribution determined by rate equations for non-local thermodynamic equilibrium (NLTE) state plasmas

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Collisional-Radiative Model maxmax N

ijjij

N

ijiji

i WnWndtdn

ijeijijeijijij nCnJBW ijeDRji

RRjiejiejijiijji nnDnJBAW 2)(

Aij Spontaneous emission

Bij Stimulated absorption or emission (I > j)

Cij Collisional excitation

Dij Collisional deexcitation

ijDR Dielectronic recombination

ijRR Radiative recombination

ijRR Photoionization+stimulated recombination

ij Collisional ionization

ij Collisional recombination

The key is to figure out how to manage the infinite set of levels and transitions of atoms and ions into a model with a tractable set of levels and transitions that represents a physical reality! IAEA

Dielectronic recombination (DR) and excitation autoionization (EA) modeling are crucial • 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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Treatment of excited states crucial for ionization and recombination modeling

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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Partial LTE limit for a class of levels as collisional processes dominate

• For some levels, relative population distributions of intermediate density ranges can be represented by Saha-Boltzmann statistics.

• As collisional processes dominate radiative processes between two levels, a partial equilibrium may be established.

• For levels with small ∆E spacing.

• For Rydberg states close to the continuum limit

• By ion collisions

Continuum

Ground state of ion Z

ion Z+1

Boltzmann

Non-LTE

Saha

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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 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) • Escape probability formalism for self-absorption

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

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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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SPECTROSCOPIC ANALYSIS OF DENSE PLASMAS

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National Ignition Facility (NIF):1.8 MJ-192 beam laser will generate extreme states of matter

• Laser is focused through hole in holhraum • Laser impinges on wall creating a plasma • Wall plasma radiates x-rays • X-rays are absorbed in the pusher part of

sphere • Heated material drives a shock

DT ice

980 μm

Be and Cu

DT vapor

1140 μm

900 μm

Laser beams

hohlraum

ρ-T Track of Be pusher and DT fuel

• DT and Be sample the warm dense matter regime (see yellow bands)

The matter is dense with temperatures less than their Fermi energy

• DT becomes hot dense matter Compression to 103 liquid density with

temperatures at 104 eV (R.W. Lee) IAEA

Gold ionization balance in high temperature hohlraum (HTH) experiments

LASNEX simulation (D. Hinkel)

Ne/Ncr

Te

L-shell gold spectra (K. Widmann)

• Large-scale hohlraum temperatures ~ 2-3 keV

• High-temperature hohlraum reach temperatures: ~ 10 keV

• Spectrum from ne ~ 4x1021 cm-3, Te ~ 7-10 keV measured for first time

Line of sight

Line of sight

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65

60

55

50

45

<Z>

12x10 3 10 8 6 4 2 T e [eV]

FLYCHK at Ne=10 21 cm -3

FLYCHK at Ne=10 22 cm -3

DATA for large-scale HO at 2.5 keV

HTH

Lower Te than the peak simulated Te: <Z> consistent for large and small scale hohlraums

FLYCHK gives an estimate of Gold Charge state distributions and L-shell spectra

FLYCHK Gold ionization balance

FLYCHK gives an estimate of <Z> for a wide range of plasma conditions, which is suitable for experimental design and analysis

Spectroscopic data and calculation

HEDP 4, 78 (2008) IAEA

Ultra-short-pulse laser experiments provide unique opportunities to study high energy density physics(HEDP)

Intense laser-plasma interaction

- Ultrahigh gradient multi-Gev electron accelerators

- Novel light sources from THz to fs x-rays

- High energy focused proton beams

- Fast ignition (Inertial Fusion) Hot e- refluxing

Hot e-

protons laser

laser

Fast Ignitor

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Cu K radiation measured by single hit CCD spectrometer and 2-D imager for Te diagnostics

Total Single Hit CCD K yield is higher than that of 2-D imager for smaller target volumes. 2-D imager collects K yield at 8.048 keV (2 eV bandwidth)

Kα yield (photons/Sr/J)

At 8.048 keV

Target volume ( m )

500x500x30

100x100x20

100x100x5

100x100x1

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Shifts and Broadening of K emission as a function of electron thermal temperature

Target volume ( )

FLYCHK simulations

Average Te(eV) of targets

500x500x30

100x100x20

100x100x5

100x100x1

2d spacing uncertainty

Phys. Plasmas 14, 023102 (2007)

2 eV

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Sandia Z machines mimics X-rays from stars: Non-LTE opacity and radiation transport

Z Accelerator : The machine uses currents of about 26 MA to reach peak X-ray emissions of 350 TW and an X-ray output of 2.7 MJ

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The ionization parameter characterizes X-ray photoionized plasmas

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Application to photoionized plasmas compares well with astrophysical models

The agreement between measured and calculated CSDs is reasonable at Te = 150 eV: • Cloudy: Astrophysics code • Galaxy: NLTE kinetics code • FLYCHK: NLTE kinetics code

=20-25 ergs-cm/s

Z-pinch

PRL 93 055002 (2004) IAEA

X-ray free-electron lasers, XFELs, are well suited to HEDS research

Ultrashort pulses are useful … • to create HED states of matter • to probe the highly transient behavior of HED states High photon energy is required… • to heat the target volumetrically and, thus, minimize gradients • to directly probe the high densities High photon number is useful…

• to make single-shot data feasible

Intense (1012 photons), short pulse (~10 to 350 fs), tunable from 0.8 to 20 keV

(R.W. Lee)

Plasma and Warm Dense Matter Studies Atomic Physics Experiments Structural Studies on Single Particles and Biomolecules Femtochemistry Studies of Nanoscale Dynamics in Condensed Matter Physics

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LCLS XFEL strips neon bare in a single ~100 fs pulse and hollow atoms are observed

• 105 x-rays/Å2 • 80 - 340 fs • 800 - 2000 eV • ~1018 W/cm2

Nature 466, 56 (2010)

Ne K-shell IP: 870.2 eV

A: Auger decay

(1360 eV) (1200 eV)

V: Valence-shell PI

P: K-shell PI

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NLTE simulations give reasonable agreement with measurements including collisional effects

O. Ciricosta et al. HEDP 7, 111 (2011)

P: K-shell PI A: Auger decay

V: L-shell PI

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Time-dependent charge states of XFEL plasmas may depend on Ne and Te

• Collisions change charge state distributions at high densities • The odd-even charge state asymmetry is reduced by collisions.

Ion density

2000 eV

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FLYCHK radiative loss rates give quick estimates over a wide range of conditions

0

1 x 10-7

2 x 10-7

3 x 10-7

4 x 10-7

1 1.5 2 2.5 3 3.5 4 4.5 5

H:1E16H:1E18H:1E20H:1E22H:1E24F:1E16F:1E18F:1E20F:1E22F:1E24

Te(keV)

Radiative cooling rates per Ne Ion HULLAC+DHS FLYCHK 1 3049 45

2 27095 107

3 30078 89

4 404328 140

5 3058002 140

6 5882192 140

7 7808014 140

8 6202123 140

9 5544814 140

10 1050919 131

11 841094 122

sum 30,851,708 1334

Time ~2 days ~mins

# of radiative transitions

Max~30%

Better agreement for higher Ne

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FLYCHK Available to the community at NIST website: http://nlte.nist.gov/FLY

• A time-dependent collisional-radiative model to provide charge state distributions and spectral intensities

• Applications • Long-pulse laser produced plasmas • Short-pulse laser produced plasmas • XFEL laser produced plasmas • Electron beam produced plasmas • Time-dependent plasmas • Tokamak plasmas

• More than 700 registered users • Cited by more than 200 papers since 2005

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∆n=0 Contributions to DR/EA process

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Spectral Accuracies for dense matter

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Model completeness for dense matter with high energy particles

• 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 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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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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Astrophysical Models used for diagnostics can be benchmarked in Laboratory experiments

Understanding laboratory data helps understanding astrophysical objects

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Radiative loss rates are important as an energy loss mechanism of high-Z plasmas

0

1x10-7

2x10-7

3x10-7

4x10-7

1 1.5 2 2.5 3 3.5 4 4.5 5

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

Te(keV)

Calculated Kr radiative cooling rates per Ne [eV/s/atom/cm-3]

coronal Ion HULLAC+DHS

1 3049

2 27095

3 30078

4 404328

5 3058002

6 5882192

7 7808014

8 6202123

9 5544814

10 1050919

11 841094

Sum 30,851,708

# of radiative transitions using HULK code