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

[email protected]

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


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


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


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


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


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


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)


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


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


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


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


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)

emission properties of non-equilibrium zirconium plasma in ...report the radiance and emission...

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