Acta Polytechnica Acta Polytechnica 53(2):233–236, 2013 © Czech Technical University in Prague, 2013 available online at http://ctn.cvut.cz/ap/ X-RAY SPECTROSCOPIC CHARACTERIZATION OF SHOCK-IGNITION-RELEVANT PLASMAS Michal Šmída,b,∗, Luca Antonellic,d, Oldřich Rennera a Institute of Physics of the ASCR, v.v.i., Prague, Czech Republic b Czech Technical University in Prague, FNSPE, Prague, Czech Republic c Dipartimento di Ingegneria Industriale, Universita Roma ‘Tor Vergata’, Roma, Italy d CELIA, Université de Bordeaux 1, Talence, Bordeaux, France ∗ corresponding author: smidm@fzu.cz Abstract. Experiments with multilayer plastic/Cu targets performed at a PALS laser system aimed at the study of matter at conditions relevant to a shock ignition ICF scheme, and, in particular, at the investigation of hot electrons generation. Plasma temperature and density were obtained using high-resolution X-ray spectroscopy. 2D-spatially resolved quasi–monochromatic imaging was observing the hot electrons via fluorescence Kα emission in the copper tracer layer. Found values of plasma temperature 690 ± 10 eV, electron density 3 × 1022 cm−3 and the effective energy of hot electrons 45 ± 20 keV demonstrate the potential of X-ray methods in the characterization of the shock ignition environmental conditions. Keywords: hot electrons, shock ignition, laser-produced plasma, X-ray spectroscopy, Kα radiation. 1. Introduction Shock ignition (SI) scheme is one of the alternative approaches to the inertial confinement fusion. It antic- ipates a compression of the spherical target by a laser beam with intensity ≈ 1 × 1014 W cm−2, followed by an intense pulse (≈ 1 × 1016 W cm−2) which drives the strong converging igniting shock with pressures at the ablation front up to several 100 Mbar [2]. Under these conditions, the igniting (main) beam is not absorbed in the solid target, but interacts with the underdense plasma corona, where paramet- ric instabilities take place. Primarily, the stimulated Raman scattering occurring below the nc/4 limit is a significant mechanism of collisionless absorption. In this process, a plasma wave is excited along the laser direction and a light beam is reflected with a modified frequency spectrum. The plasma wave accelerates free electrons to suprathermal energies. These ‘hot’ electrons may affect the SI target signif- icantly, but their role is not fully understood yet: they can either preheat the compressed material, which would lead to premature target expansion and the target gain decrease, or they may be stopped in the dense shell of the target, thus increas- ing the ablation pressure, improving the symmetry of the converging shock pressure front and increasing the gain [10]. The aim of the experiments performed in the PALS research center [6] was to create plasma with con- ditions relevant for the SI and implement advanced spectroscopic diagnosis to validate the this relevance. The collected data should contribute to the investi- gation of hot electrons generation and propagation in dense target. Figure 1. Experimental setup. 2. Experimental setup The scheme of the experiment shown in Fig. 1 in- cludes the multi-layer target, the irradiating laser beam, the X-ray spectrometer, and the Kα imaging system. The target consisted of a 25 or 40 µm thick layer of chlorine-doped plastic (parylene-C; C8H7Cl) and a 5 µm thick copper tracer layer. The relevance of using doped plastic targets as an SI ablator layer has been discussed, e.g., in paper [3], similar measure- ments have also been performed [4]. The target was irradiated from the plastic side. The prepulse (1315 nm, 70 J, focal spot diameter 700 µm, ≈ 6 × 1013 W cm−2) generates a long-scale 233 http://ctn.cvut.cz/ap/ Michal Šmíd, Luca Antonelli, Oldřich Renner Acta Polytechnica preplasma corresponding to the compression phase of the SI. The frequency-tripled PALS main beam (438 nm, 170 J, focal spot diameter 80 µm, pulse length 300 ps, ≈ 1 × 1016 W cm−2) strikes the target at a vari- able delay, generating a shock wave and the hot elec- trons. These electrons propagate into the copper layer and create vacancies in the K-shell of the Cu atoms which consequently emit the fluorescence Kα radiation. The X-ray spectra were measured using a spher- ically-bent mica crystal spectrometer which was aligned to provide a spatial resolution along the laser axis. In the 4th order, it covered the wavelengths 4.17 ÷ 4.52 Å to image the Cl Heα and Lyα lines. The Heγ ÷ Heη and Lyβ lines were observed in the 5th order. The Cu Kα emission was measured using a spherically-bent quartz (211) crystal, which was set up as a monochromator in imaging mode (Bragg angle θ = 88.7◦) to provide a quasi-monochromatic distribution of Kα intensity, 2D-spatially resolved along the target surface. Both diagnostics used the Kodak AA400 film to de- tect the signal. 3. X-ray spectra evaluation The measured spectral records were digitized us- ing a calibrated table-top scanner and recalculated to optical densities. The raw record with lines identi- fication is in Fig. 2. This record was split into regions corresponding to the 4th and 5th spectroscopic orders, each recalculated into emitted intensity using theoret- ical energy-dependent reflectivity, filter transmission, and film response. The dominant Lyβ and Heδ lines were selected for the evaluation. The ratio of these two lines, reflect- ing the ratio of hydrogen- and helium-like ions, is very sensitive to plasma temperature, while their width is given mainly by the Stark broadening thus provid- ing a very sensitive tool for plasma density estima- tion. Though their recorded intensities are compa- rable to the α lines, their emissivities are relatively low. This is because the crystal reflectivity and filter transmission are increasing with the decreasing wave- length. The low optical thickness of these lines is very beneficial for the diagnostic purposes, as it minimizes undesirable effects like opacity broadening or reab- sorption in inhomogeneous plasma. The temperature and density were determined from the best fit of the observed spectra with simula- tions. A set of needed spectra with variable parame- ters was generated by using the PrismSpect code [8] under the assumption of homogeneous planar plasma and a steady-state approximation. The fitting was done using the least square method. The logarithm of the least squares of differences be- tween the experimental and synthetic spectra for a typ- ical experimental data, shown as a function of the tem- perature and density of the theoretical spectra, is plot- Figure 2. Raw spectral record with lines identification. Figure 3. The dependence of the merit function on T and ρ; the diagonally-elongated minimum indicates the uncertainty of the plasma parameters estimation. ted in Fig. 3. This figure characterizes the uncer- tainty of the parameter estimation: the diagonally- elongated minimum represents a set of synthetic spec- tra with a good agreement to the experimental one. To increase the precision of the plasma parameters estimation, the density has been separately derived using the FWHM width of the Lyβ line. Having the density fixed, the uncertainty of the temperature estimation was about 20 eV. Figure 4 shows the comparison of the reconstructed experimental spectrum with the best fitting theoretical one; the 5th order lines are magnified in the inset. 4. Kα evaluation The 2D-spatially resolved Kα record directly provides the information on radius and intensity of the Kα sig- nal. This data was used to evaluate the hot electrons effective energy and absolute population. 4.1. Effective energy The effective energy of the hot electron beam was estimated by analyzing the attenuation of the signal in dependence on the plastic layer thickness. As the ex- periments were conducted with various thicknesses, 234 vol. 53 no. 2/2013 X-ray Spectroscopic Characterization of Shock-Ignition-Relevant plasmas Figure 4. Comparison of the reconstructed experi- mental spectrum and the best fitting theoretical one. Figure 5. The dependence of the normalized inte- grated Kα intensity on the plastic layer thickness, its experimental values and fitted attenuation curve. namely 0, 25 and 40 µm, the signal intensity could be plotted as a function of this thickness and fitted with an assumed exponential attenuation (Fig. 5). Comparing the attenuation with the stopping power from the Estar database [1], the mean electron energy was found to be about 45 ± 20 keV. This high uncertainty is caused mainly by the hot electron production process. In the relevant intensity regime, hot electrons are generated by strongly non- linear processes (stimulated Raman scattering and two plasmon decay) which are correlated to the stabil- ity of the laser system and laser-plasma interaction. As a consequence, the energy of hot electrons can vary a lot between comparable shots. For our purposes, the essential information is the order of magnitude of this energy which equals to tens of keV. 4.2. Absolute calibration To perform the absolute calibration of the measured data, it is necessary to relate the detected signal to the Kα emission, and to relate this Kα emis- sion to the number of hot electrons propagating through the copper layer. The first problem was solved using a detailed quan- titative analysis based on a ray-tracing procedure. The calculations follow the standard algorithms de- scribed, e.g., in paper [11]. The simulation assumes a point source giving an origin to a fan of isotropic quasi monochromatic X-rays, each ray carries an equiv- alent part of the emitted intensity. By default, it is as- sumed that the source is emitting 1 photon into the full solid angle. The reflection curve of the spherically bent crystal is calculated by using the modified Taupin equation [5]. By taking into account all relevant geometric factors (source-to-crystal and crystal-to- detector distances, crystal and detector dimensions), the directions and amplitudes of the rays reflected from the crystal are found and the signal distribu- tion at the detector plane is calculated. The col- lection efficiency is then determined by integrating the signal over the active detector area. The result- ing ratio of the detected to emitted radiation is only 2.4 × 10−6, which is more than one order of magni- tude less than might be expected when neglecting the variation of the incidence angle. The full number of the emitted Kα photons is determined with re- spect to the transmission of the protective filters and the characteristic curve of the X-ray film used. To relate the number of hot electrons (nHE) to the number of Kα photons (nKα) emitted, the as- sumption of monoenergetic 50 keV electron beam was made. The collisional cross section for Cu K-shell ionization is σ = 4 × 10−22 cm−2 [9]. Using the thin target approximation, the number of excited copper ions is nCu∗ = σdnCunHE , (1) where nCu is the number density of copper atoms. The probability that the excited copper ion will decay through radiative recombination is Wk = 0.39 [7] and the final relation is nKα = σdnCuWknHE . (2) Using this formula, the absolute number of hot electrons propagating through the copper layer can be estimated. 5. Results and discussion Several shots with similar conditions and with variable delays between the prepulse and the main beam have been analysed. The measured parameters did not show any dependence on the delay, so the impact of the prepulse in this situation can be considered as negligible. The found plasma temperature was T = 690 ± 10 eV, and the density ρ = 0.10 ± 0.02 g cm−3 (which corre- sponds to ne = 3 × 1022 cm−3). The total number of Cu Kα photons emitted was in the range 3 ÷ 30 × 109, which corresponds to the production of hot electrons nHE = 2 ÷ 20 × 1011. Since this number is lower than theoretical predictions, further experiments are planned to revise this mea- surement in the future. The important value mea- sured is the effective energy of hot electrons, estimated as 45 ± 20 keV. 235 Michal Šmíd, Luca Antonelli, Oldřich Renner Acta Polytechnica 6. Conclusion High-resolution X-ray spectroscopy combined with monochromatic Kα imaging was implemented in laser- plasma interaction experiments with laser intensities ≈ 1 × 1016 W cm−2 and with weaker prepulse using variable delay to the main beam, thus in this matter relevant for the shock-ignition ICF scheme. The usabil- ity of this diagnostics was demonstrated, and sample data needed for the explanation of hot electrons gen- eration, which is decisive for the success of the shock- ignition scheme, were collected. The measured data did not exhibit any distinct dependence on the pre- pulse timing. There are several alternate scenarios explaining this unexpected behavior, their validity should be confirmed by further experiments and sim- ulations. Acknowledgements This research has been supported by the Czech Sci- ence Foundation, grant No. P205/10/0814, LASERLAB- EUROPE (grant no. 228334), and by the CTU grant SGS10/299/OHK4/3T/14. The work has been done within the activities of the Working Package 10 (Fusion experiment) of the HiPER Project. References [1] M. J. Berger, et. al. ESTAR, PSTAR, and ASTAR: computer programs for calculating stopping-power and range tables for electrons, protons, and helium ions. http://physics.nist.gov/Star. Version 1.2.3. [2] R. Betti, et al. Shock ignition of thermonuclear fuel with high areal density. Phys Rev Lett 98(15):155001, 2007. [3] R. Cook, et al. Production and characterization of doped mandrels for inertial-confinement fusion experiments. 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Shock ignition: A new approach to high gain inertial confinement fusion on the national ignition facility. Phys Rev Lett 103(4):045004, 2009. [11] S. G Podorov, et al. Optimized polychromatic X-ray imaging with asymmetrically cut bent crystals. J Phys D: Apl Phys 34:2363, 2001. 236 http://physics.nist.gov/Star Acta Polytechnica 53(2):233–236, 2013 1 Introduction 2 Experimental setup 3 X-ray spectra evaluation 4 K evaluation 4.1 Effective energy 4.2 Absolute calibration 5 Results and discussion 6 Conclusion Acknowledgements References