L. Labate, C.A. Cecchetti, M. Galimberti, A. Giulietti, D. Giulietti, L.A. Gizzi, P. Tomassini

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


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


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


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


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)


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


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)


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


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


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)


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


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


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


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


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


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


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


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


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


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


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


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)


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


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


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


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).


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

L. Labate, C.A. Cecchetti, M. Galimberti, A. Giulietti, D. Giulietti, L.A. Gizzi, P. Tomassini

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Transcript of L. Labate, C.A. Cecchetti, M. Galimberti, A. Giulietti, D. Giulietti, L.A. Gizzi, P. Tomassini