Emission Properties of Non-equilibrium Zirconium Plasma in ...report the radiance and emission...
Transcript of Emission Properties of Non-equilibrium Zirconium Plasma in ...report the radiance and emission...
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
Emission Properties of Non-equilibrium Zirconium Plasma
in Soft X-ray Region
EPPRA sas, Courtaboeuf, France
Vasily Zakharov, Sergey Zakharov
in collaboration with Keldysh Institute of Applied Mathematics, Russia
Marie CurieAction
also with NRC Kurchatov Institute, Moscow, Russiaand with JIHT RAS and SRC RF TRINITI, Moscow, Russia
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
Emission properties of non-eq Zr plasmaAbstract
Zirconium-based plasmas are considered as 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 non-thermal electron distribution, self-absorption etc. leading to changes in ionization states, state populations, emission intensity and spectrum. In the report the radiance and emission properties of non-equilibrium zirconium plasma is examined and the optimal emission conditions for soft X-ray emission in water window region are explored. Kinetic parameters for non-equilibrium plasma including major inelastic ion interaction processes with non-thermal electrons and radiation, emission and absorption data are obtained in the approach based on Hartree-Fock-Slater (HFS) quantum-statistical model and distorted waves approximation. Modeling of plasma properties and emission is performed by using atomic, kinetic, radiation transport and RMHD Z* code.
Authors kindly thanks Prof. Gerry O’Sullivan for the idea of current work
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XI
Zirconium XI – XVI Lines
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XII
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XIII
Zirconium Line strengths in Water Window region
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XIV
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XV
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XVI
Line strengths of Zr XI – Zr XVI computed with Flexible atomic code
4f-3d, 5p-3d transitions in Zr XI – Zr XX intensively emit in water window (WW) region
[Ar] 3d10 4s2 [Ar] 3d10 4s
[Ar] 3d10 [Ar] 3d9
[Ar] 3d8 [Ar] 3d7
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
Zirconium XVII – XXII Lines
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XVII
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XVIII
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XIX
Zirconium Line strengths in Water Window region
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XX
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XXI
0.1
1
10
100
1 2 3 4 5 6 7 8 9
gf
Zr XXII
Line strength of Zr XVI – Zr XXII computed with Flexible atomic code
Most intensive 4p-3d transitions start to contribute into WW region beginning from Zr XV up to Zr XXI
[Ar] 3d6 [Ar] 3d5
[Ar] 3d4 [Ar] 3d3
[Ar] 3d2 [Ar] 3d1
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
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
FTNNndt
dn
ei
ei
αν→μ and αμ→ν - total rates of the processes leading to increase and decrease of the level μ population nμ, 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
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
Zirconium Non-equilibrium Plasma
0.001
0.01
0.1
1
40 60 80 100 120 140
Rel
ativ
e po
rtio
n
Temperature, eV
Zirconium ion fractions for 1x10**19 1/ccm electron density
6+7+8+9+
10+11+12+13+14+15+16+17+18+19+
Zirconium Ion populations
Electron density
Ne=1019 1/ccm
8
9
10
11
12
13
14
15
16
30 40 50 60 70 80 90 100 110 120
Cha
rge
Temperature, eV
Average ion charge in Zr plasma for 10**19 1/ccm electron density
Average charge
Best conditions for emission in water window are expected at T > 80 eV and higher
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
Zirconium Plasma Radiance at 50–120 eV
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
1 2 3 4 5 6 7 8 9
Rad
ianc
e, a
.u.
Wavelength, nm
Zirconium line emission spectra
50 eV60 eV70 eV80 eV
Zirconium Line emission in Water Window region
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
1 2 3 4 5 6 7 8 9
Rad
ianc
e, a
.u.
Wavelength, nm
Zirconium line emission spectra
90 eV100 eV110 eV120 eV
Spectral Efficiency (SE) reaches its maximum (over 40%) at plasma temperature ~90 eVand decreases slightly after: SE = 2%(50eV) – 33%(70eV) – 40%(90eV) – 38%(110eV)
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
Radiation transfer in plasma
Z
Iω
Ωθ
φ
θϕϕ
θκττ
τκ
θϕ
κ
ω
τττ
ω
ωω
ωω
ωω
ωω
ωωωω
ωωωωω
ctgx zzcosrsinrrx
;dxsin
)z,r()x(
;dej),,z,r(I
);U,T,n,n(j);U,T,n,n(
;dIcU
IkjlIIkjI)(
tI
c
out
out
x
eie
eie
'
⋅+=
+−=
==
=
Ω=
−=∂∂⇒−=∇Ω+
∂∂
∫
∫
∫
−
−
222
0
0
1
1
r
rr
- Quasi-stationary
- Cylindrical symmetry
- Optical depth
- Trajectory
- Intensity
- Spectral radiation energy density
- Opacity
- Emissivity
r
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
ffbfbbωωωω κκκκ ++=
( ) bbss
ss
T/i
bb nnP)e(N eνμμ
νμν
ωω σκ −−= ∑∑− 11
( ) bfT/
ibf )(fn)e(N e
νεν
νω
ω σεκ −−= ∑− 11
( ) ff
'T/
eff )(f)'(f'd)e(N e
εεω
ω σεεεκ −−= ∫− 11
( ))T/)exp((/)(f μεε −+= 11
Absorption coefficientsBound-Bound (bb), Bound-Free (bf) & Free-Free (ff) processes
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
Emissivity ( LTE ): pIj ωωω κ= ; 1
3
−= T/
p
eI ωω
ω
Emissivity ( general nonLTE )
fffbbb jjjj ωωωω ++=
( ) bbss
ssi
bb nnPNj νμννμ
μω σω −= ∑∑ 13
( ) ff
'ieff )'(f)(fdNNj εεω σεεεω −= ∫ 13 ωεε +='
( ) bfei
fb n)'(fNNj νεμ
μω σεω ∑ −= 13
EmissivityEmissivity in LTE and nonLTE cases
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
Zirconium target emission
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9
Emis
sion
inte
nsity
, a.u
.
Wavelength, nm
Zr emission for r=200um spherical target
60 eV70 eV80 eV90 eV
Spectral Modeling for Zirconium spherical target
Electron densityNe=1019 1/ccm
Spherical targetr = 200 µm
Temperature raises → Broadening → Power of emission
Efficiency?
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9
Emis
sion
inte
nsity
, a.u
.
Wavelength, nm
Zr emission for r=200um spherical target
90 eV100 eV110 eV120 eV
2012 International Workshop on EUV and Soft X-ray Sources, University College Dublin, Dublin 4, Ireland, November 8-11, 2012
Remarks
The results were obtained in frame of FP7 FIRE Marie Curie action
Zirconium ions XV – XXI emit intensively in water windowregion: 4p-3d, 4f-3d and 5p-3d transitions
Maximum spectral efficiency for emission in water window region is over 40% for plasma at temperature
of 80eV and hotter
For spherical target of 200um radius and 1019 electron density the spectrum is broadened (absorption
broadening)