SIMULATION STUDIES OF ATOMIC PHYSICS
IN CAPILLARY DISCHARGES

 

 

J. Limpouch, L. Kocbach

Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Brehová 7, 115 19 Prague, Czech Republic

E. M. Ivanov, G. A. Vergunova

P.N. Lebedev Physical Institute of RAS, Leninskyi pr. 53, Moscow, Russia

 

 

 

 

 

 

 

 

Acknowledgements: This research was supported by INGO Copernicus grant LA 055 "Research center of dense magnetized plasmas" and by the grant LN00A100 "Laser plasma research centre", supported by the Ministry of Education, Youth and Sports of the Czech Republic.

 

 

 



Slide 2

 

Aim:   - Analysis, comparison and development of atomic physics codes
- Estimation of viable spectroscopic diagnostics
- Interpretation of spectroscopic measurements
- Search of viable regimes for gain at relatively short wavelength

 

Methodology: Post-processing of results of MHD simulations
Code FLY
Newly developed collisional-radiative code

 

 

ABSTRACT

Fast capillary discharges are widely studied as a prospective medium for lasing in soft x-ray region. Detailed knowledge of kinetics of ionization and excitation states is needed both for diagnostics and application of capillary discharges.

Here, the results of simulations of discharge dynamics in an initially evacuated capillary are post-processed using detailed atomic physics models. Temporally resolved line x-ray spectra are computed using FLY code, that is designed for K-shell spectroscopy and it includes a detailed scheme of excited levels for H-, He- and Li-like ions only. This code is also applied in order to find optimum discharge parameters for recombination pumping scheme of suitable K-shell transitions.

The results are also presented of detailed study of plasma atomic physics including excitation states of all ionization states of light ions, implemented presently in the steady-state approximation assuming optically thin plasmas. Such a model is particularly important for relatively low discharge energies and for the spectroscopic diagnostics in visible and near UV region, where the atomic model of FLY code is insufficient.

The temporal dependent simulations using FLY code show that for the assumed capillary discharge histories the populations of the basic and excited levels for low ionization states correspond well to the steady state values for instant temperatures and plasma densities. However, time dependent solutions of the rate equations are essential.

 

 

 

 



Slide 3

 

Code FLY

 

 

·        standard package by R. W. Lee for K-shell spectroscopy of materials with atomic number Z = 3 – 26 (0 dimensional)

·        0 dimensional time-dependent code including an approximate description of optical depth effects

·        populations of excitation levels – for H-, He- and Li-like ions only

·        detailed line spectra for H-like Lyman and Balmer series, He-like transitions to basic state, Li-like to 2s and 2p states

·        recombination emission for the mentioned series only

 

 

 

Newly developed collisional-radiative code

 

 

·        optical thin populations of excitation levels for all ionization states

·        better treatment of mixtures

·        line and recombination spectra in full spectral range

·        presently stationary version, non-stationary is being developed

 

 

 

 

 

 



Slide 4

 

Carbon ionization in polyacetal plasma

 

Post-processing of MHD simulations by FLY code - comparison of time dynamics and steady state

 

 

-         Time dependent solution (evolution) includes optical depth effect due to finite radius of capillary discharge

-         Steady solution for instant electron temperature and density is plotted for optical thin populations

-         Figure shows that for carbon - shortly after electron temperature peak - mean ion charge Z can be calculated in steady state optical thin approximation

 

 

 



Slide 5

 

Oxygen ionization in polyacetal plasma

 

Post-processing of MHD simulations by FLY code - comparison of time dynamics and steady state

 

 

-         Time dependent solution (evolution) includes optical depth effect due to finite radius of capillary discharge

-         Steady solution for instant electron temperature and density is plotted for optical thin populations

-         Figure shows that for oxygen – with exception of short initial phase - mean ion charge Z can be calculated in steady state optical thin approximation

-         The assumed temperatures are too low to ionize oxygen above He-like state

 

 

 



Slide 6

FLY code results - populations of
carbon Li-like states and basic He-like state

(effects of time dependence and of optical thickness)

Electron temperature, electron density and discharge radius 0.5 - 0.1 mm taken from MHD simulations (Te, ne plotted above)

Full lines – time dependent solutions including finite optical thickness

Dotted lines – stationary populations for optically thin plasma and instantaneous plasma parameters

Shortly after temperature peak at 20 ns – stationary approximation is sufficient for the presented levels; plasma is nearly optically thin

 



Slide 7

FLY code results - populations of
carbon He-like states and basic H-like state

(effects of time dependence and of optical thickness)

 

Electron temperature, electron density and discharge radius 0.5 - 0.1 mm taken from MHD simulations (Te, ne plotted above)

Full lines – time dependent solutions including finite optical thickness

Dotted lines – stationary populations for optically thin plasma and instantaneous plasma parameters

Populations of H-like and of excited He-like states differs substantially from steady state values

 



Slide 8

Code comparison – carbon spectral emissivity

(spectral region 300 – 200 nm)

 

Parameters – Ne = 1019 cm, Te = 20 eV, carbon

 

FLY code  – does not include Stark broadening for transitions between higher excited states

– does not include recombination emission for recombination to higher excited states ® continuum is substantially underestimated

 

Þ FLY is not suitable for low photon energies

 

 

 



Slide 9

 

Code comparison – carbon spectral emissivity

(spectral region of Li-like resonance lines)

 

Parameters – Ne = 1019 cm, Te = 20 eV, carbon

 

Spectral regions – transitions to Li2s and Li2p states

 

FLY code – continuum underestimated in region of Li-like resonance lines and in region of Balmer series (Ba-a line =  68.14 eV)

 

 

 

 



Slide 10

 

FLY code results – time-integrated carbon spectra

comparison of time dynamics and stationary solutions

(spectral region of Li-like resonance line)

 

 

 

Difference is negligible Þ Stationary solution is sufficient in this spectral region

Stationary solution is not sufficient for K-shell spectra

 

 

 



Slide 11

 

Result of newly developed code

Spectral emissivity of polyacetal mixture and pure elements

(spectral region 300 – 200 nm)

Parameters – Ne = 1019 cm, Te = 20 eV, CH2O, C and O

 

Dominant line emission – emission of Li-like carbon
at 4.899 eV (253 nm) – 1s24f - 1s25g transition and
at 4.911 eV (252 nm) – 1s24d - 1s25f transition

In agreement with experiment, where time resolved measurements using small grating monochromator revealed line emission only in spectral region 250-255 nm

 



Slide 12

 

FLY code result

Inversion on carbon Balmer transitions in polyacetal plasma

 

 

Electron temperature, electron density and discharge radius 0.5 - 0.1 mm taken from MHD simulations (Te, ne plotted above)

Inversion between hy2 and hy3 (Ba-a) from 32 to 51 s, between hy2 and hy4 (Ba-b) from 35 to 45 s, no inversion for higher Ba transitions

Negligible gain due to negligible population of fully stripped ions

 

 

 

 



Slide 13

 

FLY code result

Gain on carbon Balmer transitions in polyacetal plasma
(higher parameters than presently in experiment)

 

 

Electron temperature, density taken ad hoc

Gain on Ba-a transition (hy3 ®hy2) > 1 cm-1

Gain on Ba-b and higher transitions small

Maintaining electron temperature > 100 eV for at least 20 ns essential for a sufficient concentration of fully stripped C ions

 

 

 

 



Slide 14

 

Conclusions from code comparison:

 

1.    New code shows - FLY inapplicable for low photon energies (<30 eV) – atomic model insufficient, line broadening not included, recombination continuum practically missing (underestimated even for higher energies)

2.    New code used for interpretation of near UV diagnostics
FLY shows – stationary approximation is applicable for populations of low energy states and for spectra below 200 eV

3.    FLY used for x-ray laser studies – it is applicable for recombination scheme using H-like levels

 

Conclusions from simulations:

 

1.    New code – dominant spectral line in region 200 – 300 nm agrees with experiment, suitable for low ionization states and for spectra at low photon energy.

2.    Simulations of gain in lithium
Discharge with FJFI present parameters can fully strip » 98 % of Li atoms.
Inversion duration on Ly transitions of Li ions is t» 1 ps for ne » 1019 cm-3 - fast cooling essential.
Inversion duration on Ba transitions of Li ions t» 20 ps.

3.    Simulations of gain in carbon
Present discharge parameters insufficient – content of fully stripped carbon ions negligible.
Maintaining electron temperature > 100 eV for at least 20 ns essential – inversion may last for several nanoseconds.

 

Plan: time-dependent version of the new code (rate equations for populations of excitation levels for all ionization stages)