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Effetti di non stazionarietà nella dinamica di ionizzazione di un plasma prodotto da impulsi laser ai ns. L. Labate, C.A. Cecchetti, M. Galimberti, A. Giulietti, D. Giulietti, L.A. Gizzi, P. Tomassini. IV Congresso italiano di fisica del plasma Arcetri (FI), 12-14 Gennaio 2004. - PowerPoint PPT Presentation
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Effetti di non stazionarietà nella dinamica di ionizzazione di un plasma prodotto da impulsi laser ai ns
L. Labate, C.A. Cecchetti, M. Galimberti, A. Giulietti, D. Giulietti, L.A. Gizzi, P. Tomassini
IV Congresso italiano di fisica del plasmaArcetri (FI), 12-14 Gennaio 2004
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
X-ray spectroscopy of laser-plasmas [1]
X-ray spectroscopy is a powerful diagnostic tool of electron temperature and density in laser-produced plasmas
Wavelength (Å)
Inte
nsit
y (A
.U.)
In order to extract information about the plasma parameters, experimental intensity ratios are compared to numerical simulations accounting for the ion charge state distribution inside the plasma
Spectrum by an Al plasma produced by a 3ns FWHM laser
pulse @ I=1e15 W/cm2
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
X-ray spectroscopy of laser-plasmas [2]: the methods
In general, Bragg crystal are used as dispersive element of the spectrometers:
Spectrum by an Al plasma produced by a 3ns FWHM laser
pulse @ I=1e15 W/cm2,,
obtained using a spherically bent
mica crystal
spectral resolution ()
flat crystals
bent crystals
vertical dispersion configuration crystals
(both flat and bent)
up to 5x102
up to 103
up to 5x103
Ly doublet
Li-like satellites to He
He line
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
X-ray spectroscopy of laser-plasmas [3]: spatial resolution
Spatially or temporally resolving the spectra provides informations about selected regions or times of plasma emitting regions
Spatially resolved spectrum by an Al plasma produced by a 3ns FWHM laser pulse @ I=1e15 W/cm2,,
obtained using a spherically bent mica crystal
Spatial resolution can be obtained either by using a slit between the plasma and the crystal or by using bent crystal or Vertical Dispersing Crystals
Space
Wav
elen
gth
Longitudinal profile of the
He emission
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Modelling X-ray spectra from laser-plasmas [1]
Analysis of X-ray spectra from laser-plasmas requires the capability to accurately predict the atomic level populations
Since ionization and recombination processes depend upon the hydrodynamic variables of the plasma, in order to do this a full, both hydrodynamic and atomic, treatment is required:
The radiative transfer should be included in some way in the calculations
Without some simplifying assumptions, this task is not affordable
Hydrodynamic equations Rate equations between all the ion levels and different charge state populations
should be solved self-consistenly as a function of space and time
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Modelling X-ray spectra from laser-plasmas [2]
The general method of X-ray spectra modelling:separating the plasma simulation into a hydrodynamic part and an atomic-physics/radiative part
Hydrodynamic simulationswith a simplified model of ionization equilibrium
ne(x,t), Te(x,t), eventually u(x,t)
An estimate of the energy involved in the ionization processes, which do not provide detailed population informations useful to interpret X-ray spectra, is made
Atomic physics/radiative simulations
Examples:MEDUSA [1] (1D, Lagrangian)POLLUX [2] (2D, Eulerian)
[1] Christiansen et al., Comput. Phys. Commun. 7, 271 (1974)[2] Pert G.J., J. Comput. Phys. 43, 111 (1981)
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Modelling X-ray spectra [3]: post-processing hydrodynamic data
In order to obtain the detailed charge state and level distribution, the rate equations in collisional-radiative equilibrium must be solved using ne(t) and Te(t) provided by the hydrodynamic simulations:
€
NZ : population of charge state Z
€
ScZ and SR
Z : collisional and photo - ionisation rate from charge state Z
€
3bZ +1 and α RR
Z +1 : three - body and rad. rec. rate from charge state Z +1
In the ideal case, a set of equations has to be solved for each cell provided by he hydrodinamic simulations, taking also into account the radiative transfer
Escape factors approximation: the set of rate equations is solved on a single-cell basis and the emission coefficients are reduced by a factor accounting for the probability for the photon to be reabsorbed inside the plasma
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Modelling X-ray spectra [5]: atomic physics codes
Average ionization of Aluminium as a function of the electron temperature for an
electron density of 1021 cm-3
(the He-like ion population fraction is also shown in the inset)[1]
A simplification of the rate equations can be made by considering detailed levels only for the most populated charge states
A set of test cases has been established in order to sistematically compare non-LTE atomic physics codes
Discrepancies in the results are mainly due to the principal quantum number taken into account for the different charge state
The FLY [2] code has been used for modeling this experiment:• ion stages from neutral down to Be-like: only ground state• Li-like: n=1-10 (6-10 hydrogenic)• He-like: n=1-10 (6-10 hydrogenic)• H-like: n=1-10
[1] Lee R.W. et al., J. Quant. Spectr. Radiat. Transfer 58, 737 (1997)[2] Lee R.W., Larsen J.T., J. Quant. Spectr. Radiat. Transfer 56, 535 (1996)
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Modelling X-ray spectra [4]: SS vs TD solution
When at << hydr a steady-state (SS) solution can be considered, by solving the rate equations at each time of interest with dNZ/dt = 0For an indication of this solution to be acceptable, a simplified system with two charge states can be solved, in order to calculate the relaxation times
10 -12
10 -11
10 -10
10 -9
10 -8
0 200 400 600 800 1000
Be-like to Li like AlLi-like to He like Al
He-like to H like Al
Electron Temperature (eV)
ne=1.0×10 21 cm-3
Relaxation times for an Al plasma at a density
ne=1e21xm-3
These calculations show that relaxation time from He-like to H-like Al at temperatures greater than 100 eV is comparable to the rise-time of nanosecond pulse
In this case a full time-dependent treatment of the atomic physics may be necessary
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
The experimental technique
Tight-focus irradiation of a solid Al target in order to have a spherical expansion
Flat Bragg TlAP crystals have been used as dispersive elements both for time-integrated and time-resolved spectra
TargetLens
Crystal
Filter
CCD
Shield0.7 mm Pb
Laser
x
Spectral resolution: /102
X-ray spectra has been resolved in time to obtain the temporal evolution of line intensity ratios
Focusing lens: f/4
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
The laser system
YLF oscillator, 1053 nm
Phosphate amplifiers
3 ns (FWHM) gaussian temporal profile
Single transverse and longitudinal mode
Equivalent plane monitor of the laser beam
High-quality, near diffraction-limited focal spots (beam waist ~ 8µm)
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Temporal resolution of the spectra
The time evolution of the spectral emission in the spectral range from 6.0 to 8.0 Å has been recorded by means of an X-ray streak-camera coupled to the flat crystal spectrometer
Image provided by the time resolving diagnostics, corrected for the imaging system aberrations, during the rise-time of the laser pulse
In particular, X-ray emission has been recorded during the rise-time of the laser-pulse
Temporal resolution has been estimated to be ~20 ps
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Streak-camera intensity calibration
Streak-camera images have been calibrated by using time-integrated spectra provided by a high-dynamics, linear spectrometer viewing the plasma at the same angle
He--Ly -He -He γ-Ly
.
1
2
3
4
5
Cross-calibration
Streak-camera response at different sweep speeds
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Experimental ratio vs. time
Different time-intagrated line intensity ratios have been used to check numerical results
Due to experimental reasons, the time-resolved Ly-to-He line intensity ratio has been used to study the ionization dynamics during the rise-time of the laser pulse:
Ly: 2p -> 1s He: 1s2 1S -> 1s3p 1P
The use of the resonance line Ly requires a careful consideration of the reabsorption effects
Experimental Ly-to-He ratio during the rise-time of the laser-pulse
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Hydrodynamic simulations: 2D density map
Hydrodynamic simulation shows the expansion, due to the tight-focusing, has a 2D behaviour
2D map of the mass density at the pulse peak
history of electron density profile obtained by considering a full ionization
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Hydrodynamic simulations: 2D temperature map
Temperature also rapidly decreases 50 µm far from the original target surface
2D map of the electron temperature at the pulse peak
history of electron temperature profile
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Post-processing hydrodynamic data
A numerical predictions about the temporal behaviour of the Ly-to-He intensity ratio can be retrieved by post-processing hydrodynamic data using FLY
Since the plasma is strongly inhomogeneous, an estimate of the most emitting regions for each line should be done, in order to get a temperature and density history
This has been done by post-processing the hydrodynamic 2D data cell-by-cell by the code FLY
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
2D maps of the line emission
-20
-10
0
+10
+20
-20
-10
0
+10
+20
µm
µm-25 +250 +50 +75
history of line emission in a 3ns interval centered at the pulse peak
Ly line
He line
history of the maximum emission for each line
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
History of the line emission profiles: Ly
history of the Ly emission profile
The instantaneous profile of the Ly emission exhibits a narrow peak, sitting on a long tail due to the plume of the plasma
The location of the peak moves inward by approximately 10µm during the entire pulse
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
History of the line emission profiles: He
history of the He emission profile
The instantaneous profile of the He emission exhibits a narrow peak, sitting on a long tail due to the plume of the plasma
The location of the peak moves inward by approximately 10µm during the entire pulse
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Atomic physics simulations: electron density and temp. history
Since the emission regions are very peaked, the electron density and temperature corresponding to their peak can be used for the atomic physics simulation
During the rise-time of the laser pulse density and temperature conditions are obtained to which atomic relaxation times of the order of some hundredths of ps are expected
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Atomic physics simulations: SS vs TD solution
Simulated history of the Ly-to-He line intensity ratio both in SS and TD conditions (assuming a thin plasma)
Early during the emission, time dependent and steady-state model show different results. Later on both models give identical values for the Ly-to-He ratio
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Atomic physics simulations: plasma opacity [1]
Line reabsorption effects has been taken into account by allowing for plasma sizes given by the widths of the emission regions
The widths at different height with respect to the maximum have been considered
He emission profile at the peak of the
laser pulse
90%
50%
10%
100% (optically thin line)
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Atomic physics simulations: plasma opacity [2]
comparison between exprimental line ratio and simulated one for
different thickness of the reabsorption region
in TD conditions (similar results hold for the SS
case)
Atomic physics simulations corresponding to these different values for the thickness of the reabsorption region have been performed, both SS and TD
The plasma can be considered as optically thin for the two lines
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Line thicknesses: Doppler decoupling [1]
The small optical depth of the two lines can be explained by considering the decoupling to the Doppler effect
longitudinal profile of the
radial component of the
fluid velocity at the peak of the
pulse
Hydrodynamic simulations show a strong velocity gradient near to the regions of maximum emissivity for the two lines
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Line thicknesses: Doppler decoupling [2]
By taking into account the Doppler emission and absorption profiles in two different points, the probability for a photon to be reabsorbed can be calculated
reabsorption probability due to the Doppler
effect for a photn emitted in the point of
maximum emissivity
The width of these curves allows to consider the plasma as optically thin for both the lines
Ly He
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Evidence of transient ionization
The history of the experimental line ratio can now be compared to the atomic physics predictions both in the SS and TD case
Early during the emission, experimental data agrees well with TD calculations only
L.A.Gizzi et al., Letter on Phys. Plasmas 10, 4601 (2003).
IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004
Summary and conclusions
An experiment has been performed devoted to detect transient effects in the ionization dynamics during the rising of a ns laser pulse
A single longitudinal mode laser beam has been tight-focused on a thick solid Al target in order to obtain a nearly spherical expansion of the produced plasma
Finally the atomic physics code has then been used in order to simulate the time history of Ly-to-He line intensity ratio both in SS and TD conditions
2D maps of the lines emissivity has preliminary been obtained by post-processing hydrodynamic data in order to evaluate the density and temperature of the emitting regions as well as its dimensions
By comparing with the experimental ratio, the plasma has been found to be optically thin for the two lines. An evaluation of the effects of the Doppler decoupling due to the velocity gradient has been performed
The comparison of these histories with the experimental one has shown the existence of transient effects during the rising of the laser pulse, when ionization relaxation times have been found to be comparable with hydrodynamic times