Radiative Properties of Krypton Plasma & Emission of ... · PDF file2013 International...
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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
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
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%.
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
0.1
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KrVIIweighted strength (gf)normalized
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KrIXweighted strength (gf)normalized
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KrVIIIweighted strength (gf)normalized
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KrXweighted strength (gf)normalized
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KrXIweighted strength (gf)normalized
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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
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
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KrXIIIweighted strength (gf)normalized
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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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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
Line strengths of Kr ions computed with Flexible atomic code
Krypton line strengths in water-window region
[Ar] 3d2 [Ar] 3d1
Wavelength, nm Wavelength, nm
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
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KrXIXweighted strength (gf)normalized
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KrXXweighted strength (gf)normalized
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KrXXIweighted strength (gf)normalized
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KrXXIIweighted strength (gf)normalized
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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
Line strengths of Kr ions computed with Flexible atomic code
Wavelength, nm
Wavelength, nm
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
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
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
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.
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
Krypton Non-equilibrium Plasma
1e-3
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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
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Plasma temperature, eV Plasma temperature, eV
XI XII XIII XIV XV XVI XVII
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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
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
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Krypton line emission spectra
110 eV120 eV130 eV140 eV
Krypton Plasma Radiance
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Krypton line emission spectra
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Krypton line emission in water-window range
Rad
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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
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
Krypton plasma emission efficiency
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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)
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Plasma temperature, eV
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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
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
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)
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
Krypton Soft X-ray Source: Z* modelingCapillary discharge: Z* modeling results
R(cm)
Z(cm
)
-0.2 0 0.2
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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
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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
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
Krypton Soft X-ray Source: Z* modelingCapillary discharge: Z* modeling results
R(cm)
Z(cm
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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
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* cod
e
R(cm)
Z(cm
)
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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
2013 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 2013, Dublin, Ireland
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