Radiative Properties of Krypton Plasma & Emission of ... · PDF file2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland Radiative Properties

2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland

Radiative Properties of Krypton Plasma & Emission of Krypton DPP Source in Water-Window Spectral Range

EPPRA, France

[email protected] Zakharov

Keldysh Institute of Applied Mathematics, RussiaNRC Kurchatov Institute, Moscow, Russia


Abstract

Krypton- and zirconium-based plasmas are considered as possible candidates for a source of soft X-ray emission in water window waveband alongside with nitrogen- and bismuth-based radiation plasma sources. Such discharge and laser produced plasmas used in soft X-ray (and EUV) sources are in non-equilibrium state as a rule. This leads to a mismatch between the actual conditions of the plasma and its theoretical/computational estimations because of different effects like self-absorption etc. leading to changes in ionization states, state populations, emission intensity and spectrum. Krypton has a UTA at higher ionization degree than zirconium and thus less preferable but krypton plasma source delivers from debris issues in operation cycle comparing to zirconium and bismuth. Due to wide array of transitions the krypton plasma is less opaque to radiated emission than nitrogen.

In the paper the radiance and emission properties of non-equilibrium krypton plasma is examined and the optimal emission temperature conditions for soft X-ray emission output in water window region are explored. Kinetic parameters for non-equilibrium plasma including major inelastic ion interaction processes, radiation and emission data are obtained in the approach based on Hartree-Fock-Slater (HFS) quantum-statistical model and distorted waves approximation. The emission spectral efficiency for krypton up to 25% is achieved at 130 eV, comparable to the one for zirconium (40% at 90 eV). Results of plasma dynamics modeling in capillary discharge by Z* code are presented. Calculated emission energy up to 300mJ per pulse in water window band corresponds to the conversion efficiency (CE) around 7%.


0.1

1

10

100

1 2 3 4 5 6 7 8 9 10

1e-3

1e-2

gf

norm

aliz

ed

KrVIIweighted strength (gf)normalized

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1

10

100

1 2 3 4 5 6 7 8 9 10

1e-3

1e-2

gf

norm

aliz

ed

KrIXweighted strength (gf)normalized

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1

10

100

1 2 3 4 5 6 7 8 9 10

1e-3

1e-2

gf

norm

aliz

ed

KrVIIIweighted strength (gf)normalized

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1 2 3 4 5 6 7 8 9 10

1e-3

1e-2

gf

norm

aliz

ed

KrXweighted strength (gf)normalized

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1 2 3 4 5 6 7 8 9 10

1e-3

1e-2

gf

norm

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ed

KrXIweighted strength (gf)normalized

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1 2 3 4 5 6 7 8 9 10

1e-3

1e-2

gf

norm

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KrXIIweighted strength (gf)normalized

Krypton VII – XII LinesKrypton line strengths in water-window region

Satellite lines for transitions 4f-3d in Kr IX excited ([Ar]3d94p1) are in water-window range but their strengths and populations of double excited states shouldn’t be enough for meaningful radiation output

[Ar] 3d10 4s2 [Ar] 3d10 4s

[Ar] 3d10 [Ar] 3d9

[Ar] 3d8 [Ar] 3d7

Line strengths of Kr ions computed with Flexible atomic code

Wavelength, nm Wavelength, nm


0.1

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1 2 3 4 5 6 7 8 9 10

1e-3

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KrXIIIweighted strength (gf)normalized

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1 2 3 4 5 6 7 8 9 10

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KrXIVweighted strength (gf)normalized

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KrXVweighted strength (gf)normalized

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KrXVIweighted strength (gf)normalized

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KrXVIIweighted strength (gf)normalized

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1 2 3 4 5 6 7 8 9 10

1e-3

1e-2

gf

norm

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KrXVIIIweighted strength (gf)normalized

Krypton XIII – XVIII Lines

Resonant transitions 4f-3d in Kr XIV (~4.3nm), Kr XV (~4.1nm), Kr XVI (~3.9nm), Kr XVII (~3.7nm) intensively emit into water-window range

[Ar] 3d6 [Ar] 3d5

[Ar] 3d4 [Ar] 3d3


Krypton line strengths in water-window region

[Ar] 3d2 [Ar] 3d1

Wavelength, nm Wavelength, nm


0.1

1

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100

1 2 3 4 5 6 7 8 9 10

1e-3

1e-2

gf

norm

aliz

ed

KrXIXweighted strength (gf)normalized

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1 2 3 4 5 6 7 8 9 10

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gf

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KrXXweighted strength (gf)normalized

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KrXXIweighted strength (gf)normalized

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gf

norm

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KrXXIIweighted strength (gf)normalized

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100

1 2 3 4 5 6 7 8 9 10

1e-3

1e-2

gf

norm

aliz

edKrXXIIIweighted strength (gf)

normalized

Krypton XIX – XXIII LinesKrypton line strengths in water-window region

Resonant transitions 4d-3p and 4f-3p in Kr XIX (~2.8nm and ~3.3nm), Kr XX, Kr XXI, Kr XXII and Kr XXIII (~2.5nm and ~2.8nm) contribute in water-window range

[Ar] [Ne] 3s2 3p5

[Ne] 3s2 3p4 [Ne] 3s2 3p3

[Ne] 3s2 3p2


Wavelength, nm

Wavelength, nm


Non-Equilibrium ModelSystem of Kinetic equations

,1=∑μ

μn

To calculate spectrum of emission we need to resolve the system of kinetic equationsto obtain relative populations nµ of levels

,),,,,(

),,,,(

∑

∑

≠→

≠→

−

−=

ν

μννμμ

ν

μνμνν

μ

ρα

ρα

FTNNn

FTNNndtdn

ei

ei

αν→μ and αμ→ν - total rates of the processes leading to increase and decrease the population nμ of level μ, Ni and Ne – number of ions and electrons, T – temperature, ρ – density. Total rates include a different set of processes depending of model, kind of modelling etc.

,00 Z , μμ

μnzNZN ie ∑==Quasi-neutrality:

zμ – charge of the ion of level μ, Z0 - average charge


Non-Equilibrium ModelProcesses included

To process to a correct solution of system of kinetic equations for non-equilibrium plasma the set of impact and radiative processes should be taken into account via rates of the processes.

In general case the rates are calculated from cross-sections of concordant processes (and for given distribution functions of electrons and spectral functions) in the approach based on Hartree-Fock-Slater (HFS) quantum-statistical model and distorted waves approximation. Complete system of kinetic equations is nonlinear and self-consistent.

The processes taken into account leading to increase the population nμ of level μand to decrease the population nν of level ν are following:

• Impact recombination and ionization ν→μ,• Excitation and deexcitation ν→μ,• Dielectronic capture and autoionization ν→μ,• Photorecombination and photoionization ν→μ,• Emission and absorption in lines ν→μ.


Krypton Non-equilibrium Plasma

1e-3

1e-2

0.1

60 80 100 120 140

Kr ion fractions for 10**20 1/ccm electron density

Krypton ionization

Best conditions for emission in water window range are expected at T > 90 eVwhen Kr XIV - Kr XVII ions are dominant in the plasma composition

Rel

ativ

e po

rtio

n

Ave

rage

cha

rge

Plasma temperature, eV Plasma temperature, eV

XI XII XIII XIV XV XVI XVII

0

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25

30

35

0 20 40 60 80 100 120 140

Kr ionization degree for 10**20 1/ccm e-density

Ion populations simulated by authors kinetic code with rates&cross-sections of impact and radiative processes computed in distorted-wave approach and based on self-consistent Hartree-Fock-Slater quantum-statistical model

18 18


0

0.001

0.002

0.003

0.004

0.005

0.006

1 2 3 4 5 6 7 8 9

Krypton line emission spectra

110 eV120 eV130 eV140 eV

Krypton Plasma Radiance

0

0.001

0.002

0.003

0.004

0.005

0.006

1 2 3 4 5 6 7 8 9

Krypton line emission spectra

70 eV80 eV90 eV

100 eV

Krypton line emission in water-window range

Rad

ianc

e, a

.u.

Rad

ianc

e, a

.u.

Wavelength, nm Wavelength, nmResonant lines of Kr XIV-Kr KVII start to contribute in WW range at T >90eV (average charge Z0~13)

and provide maximum output at T~130eV (Z0~15.5): 3.7nm by Kr XVI & 3.9nm by Kr XVIIEmission spectra modelling done by authors kinetic code with rates&cross-sections of impact and radiative processes

computed in distorted-wave approach and based on self-consistent Hartree-Fock-Slater quantum-statistical model


Krypton plasma emission efficiency

0

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30

40

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60 80 100 120 140

Krypton spectral efficiency vs Zirconium

KrZr

Krypton plasma spectral efficiency

Spectral Efficiency (SE) for Kr reaches its maximum (~25%) at plasma temperature T~130 eVMaximum SE for Zirconium is ~40% at T ~90 eV (for Ne = 1019)

Rel

ativ

e po

rtio

n

Plasma temperature, eV

0

0.001

0.002

0.003

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0.005

0.006

0.007

0.008

1 2 3 4 5 6 7 8 9

Krypton line emission spectra vs Zirconium

Kr@130eVZr@90eV

Rad

ianc

e, a

.u.

Wavelength, nm

Emission spectra modelling and SE calculations done by authors kinetic code with rates&cross-sections of impact and radiativeprocesses computed in distorted-wave approach and based on self-consistent Hartree-Fock-Slater quantum-statistical model


Soft X-ray emission DPP SourcePulsed power capillary discharge

Pulsed-powerEnergy storage line 5 JLiquid dielectric & coolantVoltage 25 kVCurrent 19 kAPulse ~153 ns

Capillary ∅ 1.6 mmdimensions L = 18 mm

Various electrode geometries

Gas: Kr0.1 - 2 Torr gradients

Experimental set up

Example ofthe central part of

simulated geometry

capillaryEnergy storageline

Soft-X

Capillary discharge dynamics & emission features:E-beam, plasma channelling (ε >> 1)Volumetric MHD compression (skin depth >>plasma diameter) Highly ionized ions (fast electrons)


Krypton Soft X-ray Source: Z* modelingCapillary discharge: Z* modeling results

R(cm)

Z(cm

)

-0.2 0 0.2

25.5

26

26.5

27

Qx(J/ccm)

25002120.861799.211526.351294.871098.49931.898790.569670.674568.961482.674409.473347.374294.692250212.086179.921152.635129.487109.84993.189879.056967.067456.896148.267440.947334.737429.469225

Time integrated

Time integrated ⏐ 31 Oct 2013 ⏐ ZSTAR - code output, cell values

0

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0 5 10 15 20 25 30 35 40 45

Emission power in WW range

Emis

sion

, MW

Time, ns

Maximum emission power @ 22 nsSoft X-ray emission pulse duration ~ 15 ns

Energy emitted in WW range ~ 300 mJ/pulseConversion efficiency (CE) ~ 7%

Plasma dynamics and emission are done by Z* code

Emission energy density

Capillary

Capillary


Krypton Soft X-ray Source: Z* modelingCapillary discharge: Z* modeling results

R(cm)

Z(cm

)

-0.2 0 0.2

25.5

26

26.5

27

Ne(Av)

1.000E-058.483E-067.197E-066.105E-065.179E-064.394E-063.728E-063.162E-062.683E-062.276E-061.931E-061.638E-061.389E-061.179E-061.000E-068.483E-077.197E-076.105E-075.179E-074.394E-073.728E-073.162E-072.683E-072.276E-071.931E-071.638E-071.389E-071.179E-071.000E-07

t = 21.90 ns

Frame ⏐ 31 Oct 2013 ⏐ ZSTAR - code output, cell values

Plas

ma

dyna

mic

s an

d em

issi

on a

re d

one

by Z

* cod

e

R(cm)

Z(cm

)

-0.2 0 0.2

25.5

26

26.5

27

Gx(MW/ccm)

5.119E+054.367E+053.726E+053.179E+052.712E+052.314E+051.974E+051.684E+051.437E+051.226E+051.046E+058.924E+047.614E+046.496E+045.542E+044.728E+044.034E+043.442E+042.936E+042.505E+042.137E+041.824E+041.556E+041.327E+041.132E+049.662E+038.243E+037.033E+036.000E+03

t = 21.90 ns

Frame ⏐ 31 Oct 2013 ⏐ ZSTAR - code output, cell values

Density distribution @ max emission Emission power @ max emission

Capillary

Capillary

Capillary

Capillary


Conclusion

The results were obtained in frame of FP7 FIRE Marie Curie action

Krypton ions XIV - XXII emit intensively in water window range: 4p-3d, 4f-3d and 5p-3d transitions

Maximum spectral efficiency for emission in water window range reaches over 20% for Kr plasma at temperature of 110eV and hotter

Compare to Zirconium, Krypton plasma provides less spectral efficiency and needs to be hotter:SEKr=25%@130eV versus SEZr=40%@90eV

Krypton pulsed-power soft X-ray source based on capillary discharge may produce up to 300 mJ of radiation in water window range and with conversion efficiency ~ 7%

Conclusion

Documents

Radiative Properties of Krypton Plasma & Emission of ... · PDF file2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland Radiative Properties