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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 plasma Arcetri (FI), 12-14 Gennaio 2004.

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

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  1. 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

  2. X-ray spectroscopy of laser-plasmas [1] Intensity (A.U.) Wavelength (Å) X-ray spectroscopy is a powerful diagnostic tool of electron temperature and density in laser-produced plasmas Spectrum by an Al plasma produced by a 3ns FWHM laser pulse @ I=1e15 W/cm2 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 IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  3. X-ray spectroscopy of laser-plasmas [2]: the methods spectral resolution (l/dl) up to 5x102 flat crystals bent crystals up to 103 up to 5x103 vertical dispersion configuration crystals (both flat and bent) Li-like satellites to Heb Lya doublet Heb line 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 IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  4. X-ray spectroscopy of laser-plasmas [3]: spatial resolution Space Wavelength Spatially or temporally resolving the spectra provides informations about selected regions or times of plasma emitting regions 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 Longitudinal profile of the Heb emission 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 IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  5. Modelling X-ray spectra from laser-plasmas [1] Rate equations between all the ion levels and different charge state populations Hydrodynamic equations should be solved self-consistenly as a function of space and time 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 IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  6. Modelling X-ray spectra from laser-plasmas [2] Examples: MEDUSA [1] (1D, Lagrangian) POLLUX [2] (2D, Eulerian) The general method of X-ray spectra modelling: separating the plasma simulation into a hydrodynamic part and an atomic-physics/radiative part 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 Hydrodynamic simulations with a simplified model of ionization equilibrium ne(x,t), Te(x,t), eventually u(x,t) Atomic physics/radiative simulations [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

  7. 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: 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

  8. Modelling X-ray spectra [5]: atomic physics codes 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 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] 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

  9. Modelling X-ray spectra [4]: SS vs TD solution When tat << thydr a steady-state (SS) solution can be considered, by solving the rate equations at each time of interest with dNZ/dt = 0 For 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 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

  10. The experimental technique Tight-focus irradiation of a solid Al target in order to have a spherical expansion Focusing lens: f/4 Flat Bragg TlAP crystals have been used as dispersive elements both for time-integrated and time-resolved spectra Spectral resolution: l/dl~102 X-ray spectra has been resolved in time to obtain the temporal evolution of line intensity ratios IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  11. The laser system YLF oscillator, 1053 nm Phosphate amplifiers Equivalent plane monitor of the laser beam 3 ns (FWHM) gaussian temporal profile Single transverse and longitudinal mode High-quality, near diffraction-limited focal spots (beam waist ~ 8µm) IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  12. 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 In particular, X-ray emission has been recorded during the rise-time of the laser-pulse Image provided by the time resolving diagnostics, corrected for the imaging system aberrations, 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

  13. 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 Streak-camera response at different sweep speeds Cross-calibration IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  14. Experimental ratio vs. time Different time-intagrated line intensity ratios have been used to check numerical results Due to experimental reasons, the time-resolved Lya-to-Heb line intensity ratio has been used to study the ionization dynamics during the rise-time of the laser pulse: Lya: 2p -> 1s Heb: 1s21S -> 1s3p 1P The use of the resonance line Lya requires a careful consideration of the reabsorption effects Experimental Lya-to-Heb ratio during the rise-time of the laser-pulse IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  15. 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

  16. 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

  17. Post-processing hydrodynamic data A numerical predictions about the temporal behaviour of the Lya-to-Heb 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

  18. 2D maps of the line emission +20 +20 +10 +10 0 0 -10 -10 -20 -20 Lya line history of line emission in a 3ns interval centered at the pulse peak history of the maximum emission for each line µm Heb line +75 µm -25 0 +50 +25 IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  19. History of the line emission profiles: Lya The instantaneous profile of the Lya 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 Lya emission profile IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  20. History of the line emission profiles: Heb The instantaneous profile of the Heb 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 Heb emission profile IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  21. 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

  22. Atomic physics simulations: SS vs TD solution Simulated history of the Lya-to-Heb 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 Lya-to-Heb ratio IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  23. Atomic physics simulations: plasma opacity [1] 100% (optically thin line) 90% 50% 10% 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 Heb emission profile at the peak of the laser pulse IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  24. Atomic physics simulations: plasma opacity [2] Atomic physics simulations corresponding to these different values for the thickness of the reabsorption region have been performed, both SS and TD 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) 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

  25. 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

  26. 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 Lya Heb The width of these curves allows to consider the plasma as optically thin for both the lines IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

  27. 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

  28. 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 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 Finally the atomic physics code has then been used in order to simulate the time history of Lya-to-Heb line intensity ratio both in SS and TD conditions 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 IV Congresso italiano di fisica del plasma, Arcetri (FI) 12-14 Gennaio 2004

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