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), Gennaio 2004

IV Congresso italiano di fisica del plasma, Arcetri (FI) 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) Intensity (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 I=1e15 W/cm 2

IV Congresso italiano di fisica del plasma, Arcetri (FI) 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 I=1e15 W/cm 2,, obtained using a spherically bent mica crystal spectral resolution ( ) flat crystals bent crystals vertical dispersion configuration crystals (both flat and bent) up to 5x10 2 up to 10 3 up to 5x10 3 Ly doublet Li-like satellites to He He line

IV Congresso italiano di fisica del plasma, Arcetri (FI) 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 I=1e15 W/cm 2,, 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 Wavelength Longitudinal profile of the He emission

IV Congresso italiano di fisica del plasma, Arcetri (FI) 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) 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 simulations with a simplified model of ionization equilibrium n e (x,t), T e (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) 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 n e (t) and T e (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) 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 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) 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 dN Z /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 n e =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) 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 Spectral resolution: / 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) 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) 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) 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 Cross-calibration Streak-camera response at different sweep speeds

IV Congresso italiano di fisica del plasma, Arcetri (FI) 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 -> 1sHe : 1s 2 1 S -> 1s3p 1 P 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) 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) 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) 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) Gennaio D maps of the line emission µm 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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