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