INTRODUCTION
Interactions of high-temperature plasmas with surfaces of solid materials (generally known as plasma-wall interactions, PWI) are extensively studied for their relevance to magnetic and inertial confinement fusion, primarily in the context of a development of future fusion reactors like ITER (Ikeda, Reference Ikeda2007) or the fast ignitor scheme based HiPER (Dunne, Reference Dunne2006). Basic research directed at investigation of transient phenomena occurring near the surface of plasma-exposed materials is of paramount importance, as it contributes to an explanation of the PWI effects, provides data required for verification of advanced theoretical models, and new technological concepts needed to move from the scientific proof of the principle to a commercial reactor stage.
Laser-produced plasmas represent a very efficient tool for investigating plasma-solid interactions. A large span of interaction regimes available at nanosecond, picosecond, and femtosecond lasers (Gibbon & Förster, Reference Gibbon and Förster1996) facilitates the realization of diverse PWI scenarios. By varying the parameters of laser-matter interaction (laser pulse energy, duration, focusing, target composition, and geometry), plasma beams with tailored particle distribution, energy and degree of collimation can be produced (Badziak et al., Reference Badziak, Kasperczuk, Parys, Pisarczyk, Rosiński, Ryc, WoŁowski, Jablonski, Suchanska, Krousky, Láska, Mašek, Pfeifer, Ullschmied and Dareshwar2007; Kasperczuk et al., Reference Kasperczuk, Pisarczyk, Borodziuk, Ullschmied, Krousky, Masek, Pfeifer, Rohlena, Skala and Pisarczyk2007; Laska et al., Reference Laska, Jungwirth, Krasa, Krousky, Pfeifer, Rohlena, Velyhan, Ullschmied, Gammino, Torrisi, Badziak, Parys, Rosinski, Ryc and Wolowski2008). The detailed information on environmental conditions in regions where the high-temperature plasma interacts with solids is typically obtained by optical (primarily infrared and visible) diagnosis (Gauthier et al., Reference Gauthier, Dumas, Matheus, Missirlian, Corre, Nicolas, Yala, Coad, Andrew and Cox2005), by laser interferometry (Pisarczyk et al., Reference Pisarczyk, Kasperczuk, Krousky, Masek, Miklaszewski, Nicolai, Pfeifer, Pisarczyk, Rohlena, Stenc, Skala, Tikhonchuk and Ullschmied2007), and by particle and X-ray diagnostic methods (Hauer et al., Reference Hauer, Delamater and Koenig1991). Among the latter ones, applications of the high-resolution X-ray spectroscopy (Griem, Reference Griem1997; Renner et al., Reference Renner, Uschmann and Förster2004) are particularly useful, as the complex analysis of the intense spectral line emission accompanying the plasma impact is generally the most efficient tool for visualizing the phenomena of PWI in the densest plasma regions opaque for optical probing.
The first experiments directed at laser-produced plasma-wall interaction (LPWI) defined the framework of the processes investigated (Mazing et al., Reference Mazing, Pirogovskiy, Shevelko and Presnyakov1985; Beigman et al., Reference Beigman, Pirogovskiy, Presnyakov, Shevelko and Uskov1989; Shevelko et al., Reference Shevelko, Knight, Peatross and Wang2001). When the plasma jets or intense radiation fluxes strike a solid surface (obstacle), the material is rapidly heated and partially ablated; an interplay of attractive versus repulsive forces results in a formation of strong shock waves (Zel'dovich & Raizer, Reference Zel'dovich and Raizer2002). The elastic pressure (due to repulsive forces) becomes small in comparison with the thermal pressure, the compression, and consecutive unloading (rarefaction) waves induce a partial vaporization of the solid. The highly charged energetic ions approaching the obstacle interpenetrate the near-surface layer, collide with the counter-propagating matter, and capture a large number of electrons to high-lying atomic levels. The characteristics of the impinging plasma (density, temperature, charge, and excited states distribution) are strongly modified, material mixing phenomena result in radiative or three-body recombination, charge exchange (Rosmej et al., Reference Rosmej, Lisitsa, Schott, Dalimier, Riley, Delserieys, Renner and Krousky2006), and formation of hollow atoms (Rosmej & Lee, Reference Rosmej and Lee2007).
Despite a huge progress in LPWI modeling, contemporary theoretical approaches, i.e., fluid hydrodynamic simulations, kinetic particle-in-cell approximations, or their hybrids (Evans, Reference Evans2006), provide only qualitative predictions of the shock formation and the plasma evolution due to the complexity of the problems studied. Novel simulations based on an arbitrary Lagrangian Eulerian hydrocode (Liska et al., Reference Liska, Limpouch, Kucharik and Renner2008) generate promising results; however, their validity must still be experimentally confirmed.
Consequently, the acquisition of complex information on LPWI and, in particular, on processes involved in near-wall plasma collisions, depends mostly on the realization of well characterized experiments. The importance of such studies is emphasized by numerous weighty applications. In addition to the above-mentioned contribution to a construction of the future fusion reactors, knowledge of LPWI environmental conditions influences the design of sophisticated targets in indirect drive fusion schemes (Dittrich et al., Reference Dittrich, Haan, Marinak, Pollaine, Hinkel, Munro, Verdon, Strobel, McEachern, Cook, Roberts, Wilson, Bradley, Foreman and Varnum1999), where different collisional scenarios between individual shells of fusion pellets and between blow-off plasma from inner walls of the hohlraum and the capsule occur. Stagnating and interpenetrating plasmas are frequently met in astrophysics and in laboratory experiments designed to model various astrophysical situations (Remington et al., Reference Remington, Drake and Ryutov2006 and references therein). Further applied problems include investigation of the energy dissipation and instability evolution in the plasmas (Berger, Reference Berger, Albritton, Randall, Williams, Kruer, Langdon and Hanna1991), thermalization of the counter-streaming plasma plumes (Rancu et al., Reference Rancu, Renaudin, Chenais-Popovics, Kawagashi, Gauthier, Dirksmöller, Missalla, Uschmann, Förster, Larroche, Peyrusse, Renner, Krouský, Pépin and Shepard1995), etc.
Most of the previous experiments directed at the X-ray investigation of LPWI were performed with low-resolution instrumentation and with limited knowledge of interaction conditions. Here we report test-bed experiments with the colliding plasma clouds produced at single- or double-side laser-irradiated Al/Mg targets. This experimental configuration represents a well-defined model environment for studying PWI. The plasma interaction close to the Mg surface submitted to an energetic plasma jet is visualized via high-resolution X-ray spectroscopy. The satellite-rich structure observed in emission spectra of the Al Lyα group is interpreted using the atomic collisional-radiative code and discussed in terms of interaction of counter-propagating plasmas, in particular trapping, deceleration and thermalization of Al ions close to the Mg foil. One-dimensional (1D) and two-dimensional (2D) hydrodynamic modeling of the expanding plasma support the analysis of the observed spectra.
PALS EXPERIMENT
The experiment was performed using the iodine laser system at the PALS Research Centre in Prague (Jungwirth et al., Reference Jungwirth, Cejnarova, Juha, Kralikova, Krasa, Krousky, Krupickova, Laska, Masek, Mocek, Pfeifer, Präg, Renner, Rohlena, Rus, Skala, Straka and Ullschmied2001; Jungwirth, Reference Jungwirth2005). In accordance with Figure 1a, the double-foil targets consisting of two parallel foils of Al (thickness 0.8 µm) and Mg (thickness 2 µm) with a variable spacing were irradiated at normal incidence with one or two counter-propagating laser beams. The laser beams delivered 5–200 J of frequency-tripled radiation (0.44 µm) in a pulse length of 0.25–0.3 ns. Being focused to a diameter of 80 µm (main beam) or 50 µm (auxiliary beam), they yielded a maximum intensity of 1×1016 W/cm2 on the target. Here we concentrate on the evaluation of two typical experimental configurations. In the first one, the data was obtained at foils separated by a distance of 360 µm and irradiated from the Al side only with the laser energy of 78 J. In the second one, the foils were separated by a distance of 600 µm and double side irradiated at 115 J (Al foil) and 6 J (Mg foil).
Fig. 1. (Color online) Scheme of the plasma formation at the laser-irradiated double-foil Al/Mg structure (a) and the experimental setup with the vertical dispersion Johann spectrometer (b).
The diagnostic complex included optical spectroscopy, a pinhole camera coupled to a low-magnification X-ray streak camera, and a spherically bent mica crystal X-ray spectrometer (Rosmej et al., Reference Rosmej, Lisitsa, Schott, Dalimier, Riley, Delserieys, Renner and Krousky2006). The primary diagnostics was a vertical dispersion Johann spectrometer (VJS) fitted with a crystal of quartz (100) cylindrically bent to a radius of 76.6 mm. As schematically shown in Figure 1b, the VJS disperses the radiation along a direction λ parallel to the axis of the cylindrically bent crystal, i.e., as a function of the vertical divergence angle φ. The instrument provides simultaneously two sets of 1D spatially resolved spectra symmetrically disposed about the central wavelength λ0 (related via the Bragg equation to the angle θ0); the existence of this axis of symmetry facilitates the computational reconstruction of the detected spectra. Due to the extremely high linear dispersion (~170 mm/Å), the VJS is characterized by the high spectral resolving power (close to 8000) and by the spatial resolution of 8 µm in a direction of the axis y. The raw spectroscopic data corresponding to the double-side laser-irradiated Al/Mg target with the inter-foil distance of 600 µm is shown in the insertion of Figure 1b. The wavelength coverage Δλ/λ < 0.03 is rather restricted but sufficient for a detailed observation of the Al Lyα group including the resonance line and its associated satellites. The time-integrated spectra were recorded on X-ray film and recalculated to the linear wavelength and intensity scale using an algorithm described by Renner et al. (Reference Renner, Missalla, Sondhauss, Krousky, Förster, Chenais–Popovics and Rancu1997). The reference transition Al XII 2p2 1D2-1s2p1P1 (J-satellite with the wavelength of 7.2759 Å) used to calibrate the spectra was defined at the distance of 40 µm from the non-irradiated surface of the Al foil.
An example of the reconstructed spectrum is presented in Figure 2. This spectral emission from the single-side irradiated double-foil target was observed at an angle of ψ =0±0.8°, i.e., in the direction parallel to the Al foil surface. By using the tangential angle of observation, the spectra integration over strong plasma gradients perpendicular to the foil surface was avoided. An outer pair of the strongest spectral lines belongs to the Al Lyα doublet, the inner pairs of lines are identified as dielectronic satellites 2l2l' → 1s2l' with the J-satellite closest to the axis of symmetry. The satellite-rich structure observed at the non-irradiated (rear) surface of the Al foil gradually reduces to the emission of the Al Lyα only, although at 128 µm below the Al foil a weak J-satellite line can still be identified. In contrast to spectra recorded at single-foil Al target, where the observable Lyα and J-satellite emission extends up to 230 µm and 110 µm below the non-irradiated foil surface, respectively, the intensity of the resonance line emitted from the Al/Mg target below the Al foil approximately doubles, the Al Lyα emission is observable throughout the gap between both foils and the satellites reappear near the Mg foil. The intensity of the dominant J-satellite is comparable with that of the resonance transition. The discussion of this spectra behavior is provided in the next section.
Fig. 2. (Color online) Spatially resolved spectra of the Al Lyα group recorded at single-side laser-irradiated Al/Mg target.
RESULTS AND DISCUSSION
A qualitative explanation of the observed spectral characteristics follows from 2D simulation of the plasma evolution performed using the Prague Arbitrary Lagrangian Eulerian hydrocode (PALE) (Kucharik et al., Reference Kucharik, Limpouch and Liska2006; Liska et al., Reference Liska, Limpouch, Kucharik and Renner2008). In this approach, after several steps of Lagrangian simulations, the deformed moving mesh is reconstructed and the conservative quantities are remapped (Eulerian part) on to a smoother grid. The hydrodynamics was based on a quotidian equation of state (QEOS), classical Spitzer-Harm model for the heat conductivity, and a simple approximation of the laser energy deposition at the critical density surface.
An example of the simulated distribution of the electron density n e and temperature T corresponding to the double-foil Al/Mg target irradiated by the main laser beam only (78 J, 0.3 ns, 5×1015 W/cm2) is shown in Figure 3. Here r is a polar axis of the used cylindrical coordinate system; its longitudinal axis y again coincides with the laser beam axis. The simulations indicate that the upper Al foil burns through before the laser pulse maximum, thus the Al ions are not trapped by the cold Mg foil but collide with the well developed Mg plasma. A validity of this scenario is supported by the streak camera records demonstrating that a relatively strong emission from the plasma region close to the Mg foil appears before the intensively emitting Al ions reach the Mg surface (Renner et al., Reference Renner, Adámek, Dalimier, Delserieys, Krousky, Limpouch, Liska, Riley, Rosmej and Schott2007). A similar scenario, i.e., the plasma jets interaction with preplasma build-up at the secondary target due to the combined effects of the strong shock and rarefaction waves formation, scattered laser light, and intense plasma radiation (Morice et al., Reference Morice, Casanova, Loiseau, Teychenné and Rousseaux2008), should always be considered even if the residual laser energy does not directly strike the second foil. This means that the phenomena occurring in the near-wall region are to be interpreted in terms of the plasma collision, interpenetration, and ion trapping.
Fig. 3. Two-dimensional ALE code simulation of the colliding plasmas. The laser beam irradiates the upper Al foil from above, the Mg foil is positioned at the distance of y = 360 µm. The shown electron density and temperature distribution corresponds to the laser pulse maximum.
The environmental conditions in the plasma interaction zone were derived from the high-resolution spectra of the Al Lyα group recorded by the VJS. An analysis of the spectra shown in Figure 2 was performed by using the multilevel collisional-radiative code MARIA (Rosmej, Reference Rosmej1997, Reference Rosmej2001); the resonance doublet profile and its satellite structure were interpreted in terms of the macroscopic plasma characteristics. The main input parameters (electron density n e, temperature T e, the photon path length L, and differential plasma motion) were varied until the best fit between the experiment and simulation was achieved. The prospective overlap of the H- and He-like Mg ion emission with the Al Lyα spectra was checked by recording the emission from laser-irradiated single Al and Mg foils. The comparison of the spectra presented in Figure 4 suggests a possible interference of the Al Lyα and 1S-satellite (satellites are grouped according to their final single excited states) with the Mg Heε and Heζ lines. Despite the contribution of the He-like Mg higher series members to the resulting spectra is rather weak, the neglect of the spectral lines overlap may result in the erroneous spectra interpretation. The model-independent decomposition of such composite spectra containing broadened line profiles with very close transition energies is frequently ambiguous (Adámek et al., Reference Adámek, Renner, Drska, Rosmej and Wyart2006), thus the diagnostic role of the non-disturbed J-satellite emission is of primary importance.
Fig. 4. Prospective overlap of the spectra emitted from the lase-explded Al and Mg foils.
The detailed experimental spectra emitted from three characteristic plasma regions and their resulting fits are shown in Figure 5. The left- and right-hand side experimental spectra are well symmetric, this indicates an isotropic character of the plasma emission. The overall agreement between the synthesized and observed profiles is very good. The peak intensity of the J-satellite in the upper spectrum is overestimated due to lack of detailed width calculations of this satellite; however, its integral intensity is not substantially influenced. The plasma conditions corresponding to the Al Lyα group emission at the rear surface of the Al foil are characterized by the effective parameters n e=3×1021 cm−3, T e = 300 eV, and L = 200 µm. The Al line emission decreases monotonically with the distance from the Al foil. Between the foils, the satellite emission is suppressed and the effective plasma parameters at the mid-plane are characterized by electron densities of the level of 3 × 1020 cm−3 and temperatures above 700 eV. In the interaction region close to the Mg foil surface, the effects connected with the collision and interpenetration of counter-propagating plasmas are visualized via an increased emission of the Al Lyα line and its J-satellite. The plasma conditions at the Mg foil are best fitted by n e~(1–3)×1021 cm−3, T e~220 eV, and L = 500 µm.
Fig. 5. MARIA code fitting (solid lines) of experimental Al Lyα spectra (points) observed close to the non-irradited surface of the Al foil (a), 128 µm below it (b), and at the Mg foil (c).
The area close to the Mg foil is of particular interest for studying the effects of the ion-wall interaction and plasma interpenetration phenomena. The presence of the Al emission near and below the Mg foil (Renner et al., Reference Renner, Adámek, Dalimier, Delserieys, Krousky, Limpouch, Liska, Riley, Rosmej and Schott2007) provides clear evidence of the plasma interpenetration. The increased integrated intensities and Doppler-broadened line widths of the Al Lyα emission (with the maximum observed at 40–60 µm above the Mg foil) consistently define the region of the density build-up and ion heating, i.e., the spatial range where collision and stagnation of the Al and Mg plasmas occurs. In addition to the intense plasma thermalization (conversion of the ion kinetic energy to thermal energy in a localized region), the gradual stopping of the Al ions in the counter-propagating Mg plasma is envisaged. Here we demonstrate the potential of high-resolution X-ray spectroscopy to measure precisely this ion deceleration via Doppler shifts of the emitted spectral lines.
These challenging measurements are conditioned by a proper choice of the experimental geometry and the investigated spectral transition. As mentioned before, the application of shallow angles ψ prevents the spectra integration over extended regions of plasma jets with strongly variable macroscopic parameters. On the other hand, this geometry results in sub-mÅ Doppler shifts due to 1D-ion velocity components directed normal to the target surface. Reliable identification of such small line shifts requires the application of high precision instruments like the VJS with its limiting precision of the relative wavelength measurements at the level of (1–2)×10−5 (Renner et al., Reference Renner, Missalla, Sondhauss, Krousky, Förster, Chenais–Popovics and Rancu1997).
The observations of the frequency shifts in the optically thick Al Lyα emission are affected by the radiation transfer effects, by the formation of higher-order satellites (Renner et al., Reference Renner, Rosmej, Krouský, Sondhauss, Kalachnikov, Nickles, Uschmann and Förster2001) and by its overlap with the Mg Heζ line. In contrast, at given plasma parameters, the J-satellite is always optically thin. Calculations performed using the code FLYCHK (Chung et al., Reference Chung, Chen, Morgan, Ralchenko and Lee2005) indicate the J-satellite optical depth in the line center τ0 = 0.5 close to the Al surface and τ0≤0.4 near the Mg foil. At these optical depths, the combination of the radial plasma expansion and radiation transfer effects should only result in symmetric broadening of the line profile. Therefore, the J-satellite represents a suitable candidate for the visualization of the Al ion stopping. Indeed, the analysis of the near-wall spectra shown in Figure 2 revealed almost monotonically decreasing red shifts of the Al J-satellite with the decreasing distance from the Mg foil. This J-satellite behavior agrees with the expected stopping of the Al ions at the Mg foil.
The more complicated dependence of the ion deceleration close to the wall was found in plasmas at the double-side irradiated Al/Mg targets. The environmental conditions in these colliding and interpenetrating plasmas depend on a direct energy deposition of both laser beams in Al and Mg foils (resulting in a creation of counter-streaming plasma plumes), on deposition of the laser energy scattered through both plasma clouds and on their mutual radiative heating. The current version of the PALE code with its simple one fluid multi-material approximation obviously cannot model all relevant processes in interpenetrating plasmas, however the more detailed simulations of the energy deposition are in progress.
The PALE 2D output data does not provide effective plasma characteristics relevant for time-integrated X-ray line emission at a given distance from the foil surfaces. In order to complete the scenario of the observed deceleration of the Al ions, the plasma evolution at single-side laser-irradiated Al foil was alternatively simulated by using the 1D hydrodynamics code MEDUSA supplemented by an average–atom model (Djaoui & Rose, Reference Djaoui and Rose1992). The effective plasma characteristics were calculated by using the emission rate of the Al Lyα group as a weighing factor (Renner et al., Reference Renner, Sondhauss, Peyrusse, Krousky, Ramis, Eidmann and Förster1999). The validity of this simple 1D approximation for a detailed quantitative description of the 2D plasma expansion is limited, thus the obtained results are used only for a qualitative interpretation of the experimental data.
The plasma expansion at the two-side irradiated (115 J and 6 J, 0.3 ns, 7×1015 W/cm2 and 1×1015 W/cm2 at Al and Mg foil, respectively), 600-μm-spaced double-foil Al/Mg target was observed at an angle ψ = 0.8° in relation to the Al foil surface. Assuming that the Al ion expansion follows the MEDUSA predictions, then the expected Doppler shifts of the Al J-satellite emission are depicted by the solid line in Figure 6 (valid until the Al/Mg plasma collision area) and subsequently by the dashed line. The measured Doppler shifts are generally small but within their error bars, they agree well with the simulations. The prospective spurious effects introduced by the density- and temperature-dependent plasma polarization shifts are below the 0.1 mÅ level (Renner et al., Reference Renner, Adámek, Angelo, Dalimier, Förster, Krouský, Rosmej and Schott2006). Starting from the inner Al foil surface, the J-satellite is stepwise shifted to red until a distance of about 250 µm from the Mg foil surface (the intense collision zone). After passing this distance, the Al ion deceleration reveals in the decreasing Doppler shifts. Assuming the gradual deceleration and simple trapping of the Al ions at the Mg surface, the J-satellite shift should monotonically decrease to zero. In contrast, the envelope of the observed Doppler shifts indeed tends to zero; however, their detailed spatial distribution exhibits distinct oscillations and even negative values (blue shifts) which reflect the more complicated scenario of the ion deceleration including the ion back-scattering. The detailed interpretation of this phenomenon based on rigorous 2D description of interpenetrating plasmas and post-processing of hydrodynamic data is in progress.
Fig. 6. Measured Doppler shifts of the J-satellite from the Al Lyα spectral group (points with error bars) and their comparison with theoretical predictions (solid and dashed line).
CONCLUSION
We report the high-resolution X-ray measurements demonstrating the feasibility of spectroscopic investigation of laser-produced plasma-wall interactions. Using advanced methods of X-ray spectroscopy, the spectral line emission from the colliding plasmas produced at single- and double-side laser-irradiated Al/Mg targets was investigated. A detailed analysis of the complex dielectronic satellite structure in the Al Lyα group characterized the spatial distribution of the plasma parameters between inner surfaces of the target foils, their validity was supported by 1D and 2D hydrodynamic modeling. The unusual formation of Al spectra close to the Mg foil surface was explained in terms of thermalization and interpenetration of two colliding plasmas. The deceleration and trapping of Al ions at the Mg foil was studied via Doppler shifts of the J-satellite from the Al Lyα group, oscillations in the ion deceleration profile were discovered. The experimental configuration used provides a well-defined model environment for plasma interaction studies.
ACKNOWLEDGMENTS
This research was supported by the Czech Science Foundation Grant No. P205/10/0814, Ingo Grant No. LA08024, and the CNRS PICS project No. 4343. The experiments and their simulations were performed under the patronage of the Czech Ministry of Education, Youth, and Sports projects No. LC528 and 6840770022. The authors gratefully acknowledge the assistance of scientific and technical staffs from PALS in performing the experiments.
