2. EXPERIMENTAL SETUP

The experiment was carried out during the Fall of 2007 at the PALS (Jungwirth 2005; Batani et al., Reference Batani, Dezulian, Redaelli, Benocci, Stabile, Canova, Desai, Lucchini, Krousky, Masek, Pfeifer, Skala, Dudzak, Rus, Ullschmied, Malka, Faure, Koenig, Limpouch, Nazarov, Pepler, Nagai, Norimatsu and Nishimura2007; Kasperczuk et al., Reference Kasperczuk, Pisarczyk, Nicolai, Stenz, Tikhonchuk, Kalal, Ullschmied, Krousky, Masek, Pfeifer, Rohlena, Skala, Klir, Kravarik, Kubes and Pisarczyk2009) with an iodine laser (λ₁ = 1.315 µm). The experimental design (Fig. 1 (color online)) includes two main diagnostics: time-resolved interferometry using a green laser (527 nm) to probe the electron density in the radiative precursor, and time-integrated back side XUV spectroscopy. The main blue laser pulse of the PALS installation, working at λ₃ = 438 nm, is focused on the target that consists of a miniaturized shock tube located in the center of the vacuum chamber. The nominal pulse condition of the main PALS laser had energy of 150 J per pulse lasting 0.35 ns.

Fig. 1. (Color online) Experimental setup (see Section 2 for details).

The PALS beam with a diameter of 290 mm is smoothed by a ColsiCoat Phase Zone Plate (PZP), located behind the main PALS aspherical lens (f = 564 mm at λ₃ = 3/λ₁, diameter d = 290 mm). The PZP is designed to obtain a theoretical focal spot of diameter ~0.55 mm on the target, matching the inner section of the smallest shock tubes, where intensities of 1–2 × 10¹⁴ W/cm² are obtained for an energy pulse of ~150 J. The beam homogeneity on the target is controlled by a time-integrated X-ray pinhole camera imaging system, with a magnification of unity, through a 50 µm aluminum filter.

For the time-resolved interferometry diagnostic, we use an auxiliary (Coherent Evolution 15) laser working at λ_P = 527 nm, with a pulse duration of ~300 ns. The target is located in one arm of a Mach–Zehnder interferometer. After recombination, the two laser beams of the interferometer are imaged on the slit of a C7700 HAMAMATSU streak camera. An interferometric filter at λ₃ and colored glasses, located in front of the slit, remove spurious contributions from the plasma self-emission, or from the scattered light of the PALS laser. Two configurations are used: (1) in the longitudinal interferometry, we image the symmetry axis (z) of the shock tube along the slit of the camera in order to monitor the shock propagation in the tube; (2) in the transverse interferometry, we image a section of the tube, perpendicular (x) to the canal center, to monitor the time variations of the transverse shape of the shock wave (see Fig. 1 for axis orientation), at some fixed distance z ₀ from the piston initial position.

The XUV time-integrated spectroscopic diagnostic consists of a grating spectrometer working between 5 and 30 nm, using a cylindrical gold coated grating (curvature radius of 5649 mm, 1200 groves per mm, efficient grating area of 45 × 27 mm, blaze angle 3.7°) placed at about 250 mm from the back side of the target. The spectral resolution is about 0.25 nm and the collection angle ~1.4 × 10⁻⁴ rad. The signal is filtered with a 1.6 µm aluminum foil and recorded on a cooled ANDOR DX 440 CCD, located at a distance of 237 mm from the grating. The wavelength calibration has been performed with carbon lines from polypropylene targets and the aluminum L edge (at λ = 17.1 nm) of aluminum foils.

The targets were manufactured at the Pôle Instrumental of Observatoire de Paris. We use miniaturized shock tubes filled with xenon at low pressure with two generic geometries: (1) Aluminum parallelepiped tubes with a square internal section, two metallic sides and two lateral glass windows (Fig. 2a (color online)) allowing for interferometric studies and (2) blind cylindrical metallic tubes without any lateral window (Fig. 2b (color online)) for backside XUV spectroscopy in the direction of shock propagation.

Fig. 2. (Color online) Parallelepiped target with lateral glass windows (a) and blind cylindrical target (b) (courtesy of Observatoire de Paris).

For the interferometric diagnostic, we use two different targets. The first target, F7, consists of a gilt aluminum, 6 mm long and U-shaped tube closed laterally by two BK7 glass windows with internal gold coating (15 nm thick). These windows allow for interferometric diagnostics with the auxiliary green laser. The internal section of this square tube is 0.7 × 0.7 mm². The drilled tube socket (2 mm thick), also in gilt aluminum, is used for gas filling through capillaries and is closed at the back by an “XUV window” for backside XUV spectroscopic study. The second square target, F61, is similar to F7, but without the gold coating. The internal section of the tube is larger (1.2 × 1.2 mm²), and the internal faces of the BK7 windows have an aluminum coating (5 nm thick). The shock thus propagates in an aluminum channel for the F61 target, whereas it is a gilt channel in the first case (F7). The nature of the channel coating affects the albedo of the tube walls, thus the radiative properties of the shock, and must therefore be taken into account in the numerical simulations (González et al., Reference González, Stehlé, Audit, Busquet, Rus, Thais, Acef, Barroso, Bar-Shalom, Bauduin, Kozlova, Lery, Madouri, Mocek and Polan2006, Reference González, Audit and Stehlé2009; Busquet et al., Reference Busquet, Audit, González, Stehlé, Thais, Acef, Bauduin, Barroso, Rus, Kozlova, Polan and Mocek2007).

The cylindrical targets are used only for spectroscopic purposes. Two targets, G32 and G35, are in aluminum, with a length of 2.8 mm. The last target, G50, is in gold, and is also 2.8 mm long. They are closed on the backside by an “XUV window” for backside spectroscopic measurements, in the direction of the shock propagation.

All targets are closed on the backside by various “XUV windows”: aluminum (200 nm), SiC (100 nm), and Si₃N₄ (500 nm). They are closed on the top by a composite film, made from polystyrene (10 μm) with gold coating (0.5 μm thick). The PALS laser, focalized on the foil (hereafter called the piston), ablates the polystyrene. The piston is accelerated by rocket effect and launches a strong, radiating shock in the xenon gas. The gold foil aims at preventing the X-ray radiation emitted in the ablated CH plasma corona to heat the gas inside the tube. The characteristics of the different targets are summarized in Table 1.

Table 1. Summary of the characteristics of the different targets

3. LONGITUDINAL INTERFEROMETRY

Longitudinal interferometry traces the instantaneous variation of the optical index n(x = 0, z, t, λ), at the wavelength λ of the probe laser, versus the position z on the cell axis (i.e., x = 0), along the direction z of the shock propagation, and integrated over the path of the probe laser (y direction). The variations of the plasma optical index, n(λ)-1, are usually attributed to free electrons, and related to the electron density N _e/N _c,λ, where N _c,λ is the critical density at the wavelength λ of the probe laser,

(1)

The interferometric measurements thus provide the instantaneous electron density at the center (x = 0) of the tube, as a function of the position z, and averaged over the transverse section d of the plasma

(2)

3.1. General Features

We present in this section the results obtained with the longitudinal interferometric diagnostic for target F7, filled with xenon at 0.1 bar. The post-mortem target analysis indicates that the PALS laser impact was satisfactorily centered on the target. The X-ray pinhole record shows a smooth distribution of the laser intensity. The raw image is presented without (1) and with (2) annotations in Figure 3. The vertical axis is the time t (100 ns, 0.2 ns/pixel). Time zero at the bottom of the figure corresponds to the laser arrival on the target. The horizontal axis is the position z along the tube center, which is imaged on the slit (6 mm, 12 µm/pixel in z). The time resolution is shorter than 1 ns. Due to the delayed synchronization, we did not record the fringes before the time of arrival of the PALS laser pulse on the gilt plastic foil, which is located on the left in Figure 3. The time of laser arrival may be recognized in the small fringe deviations, which are visible at the bottom of the figure (t < 4 ns). These deviations may be attributed to electromagnetic perturbations in the streak camera or to spurious heating of the target associated to unshielded stray light from the PALS laser. However, these deviations are associated in the worst case with low electron densities, and may be discarded in the interpretation of the interferogram.

The interferogram presents four distinct zones of moving fringes (see Fig. 3b): The first zone, A, corresponds to t < 50 ns and z < 4 mm. In this zone, the fringes are unperturbed (i.e., vertical) until they start to bend toward the right and to become narrower. The location of this bending (corresponding to about one-quarter of the fringe deviation) is qualitatively reported in Figure 3b with the dotted black line. The bending is the signature of a positive gradient of the electron density column, and is the characteristic signature of the ionization produced by the radiative precursor of the shock (Fleury et al., Reference Fleury, Bouquet, Stehlé, Koenig, Batani, Benuzzi-Mounaix, Chièze, Grandjouan, Grenier, Hall, Henry, Lafon, Leygnac, Malka, Marchet, Merdji, Michaut and Thais2002; Bouquet et al., Reference Bouquet, Stehlé, Koenig, Chièze, Benuzzi-Mounaix, Batani, Leygnac, Fleury, Merdji, Michaut, Thais, Grandjouan, Hall, Henry, Malka and Lafon2004), which is visible in second zone, B. The velocity of the ionization front decreases from 120 to 65 km/s as the shock propagates from left to right.

Fig. 3. (Color online) Images of the interferometric longitudinal diagnostic for the target F7 at 0.1 bar. Time along the vertical axis is in ns. The horizontal axis reports the position z in mm of the shock propagation from left to right. The laser pulse comes from the left. Superimposed lines in the right panel give an approximate guide to the different time and space domains discussed in the text.

For z > 3 mm, and time greater than 25 ns, the narrow bent fringes of the radiative precursor disappear. The location of this event is approximately reported by a full thick grey line, and corresponds to a velocity of 65 ± 7 km/s. For z < 1.8 mm, t < 20 ns, the fringes, originally vertical, bend toward the right, and then toward the left. The inflexion points are located over the full thick red line, and are associated to a velocity of 75 ± 13 km/s. Close to this inflexion point, some fringes present a small discontinuity.

The third zone, D, in the upper part of the image is located above the two thick lines. Whereas the interface between the piston and the gas, as inferred from multi one-dimensional (Ramis et al., Reference Ramis, Schmalz and Meyer-Ter-Vehn1988) simulations for typical PALS laser conditions (1.5 × 10¹⁴ W/cm²), is close to these two thick lines (see Fig. 4 (color online), the presence of fringes in the left part of D (i.e., around z ~ 1–1.5 mm, t ~ 5–15 ns) just above the thick lines, is not expected from these simulations and will require separate studies. Note that they are also seen at the canal centre up to 20 ns after the shock front in the transverse interferogram performed with larger cell sections (Section 4). For z larger than 1.5 mm and times longer than 15 ns, the fringes behavior and their interpretation is similar to previous studies (Bouquet et al., Reference Bouquet, Stehlé, Koenig, Chièze, Benuzzi-Mounaix, Batani, Leygnac, Fleury, Merdji, Michaut, Thais, Grandjouan, Hall, Henry, Malka and Lafon2004). Hereafter, we shall mainly focus the discussion on this part of the interferogram.

Fig. 4. (Color online) Section of the interferogram plotted in Figure 3, showing the fringe maxima in dashed blue lines. Time is on vertical axis (60 ns), and position z in horizontal axis (4.2 mm). The symbols on the horizontal axis at t = 0 report the location of the unperturbed fringes maxima from a previous record. The square symbols on the fringes locate isocontours of <N _e> for 2 × 10¹⁷ (dark blue), 7 × 10¹⁷ (blue), 2 × 10¹⁸ (green), 5 × 10¹⁸ (yellow) and 10¹⁹ cm⁻³ (red). The position of the gold-xenon interface computed with multi one-dimensional, not visible on the record, is reported for reference (black dashed line).

Finally, the last feature of the interferogram, C, located toward the end of the tube (z > 4.5 mm), is identified by the full yellow line on the right-hand side of the figure. This feature corresponds to the development of a reverse ionization wave expanding from the heated backside of the tube (z = 6 mm) at a velocity of about 15–20 km/s. The interaction zone between this ionization wave and the radiative precursor in xenon is located between 4 and 5 mm and t < 50 ns. The development of this plasma from the end of the tube explains the absence of record on the XUV spectrometer from the backside from the tube. The plasma expansion from the end of the square channel may be due to gas preheating, which may originate either from particles (fast electrons, which seems however unlikely for the moderate laser irradiance, 10¹⁴ W/cm², see for instance, Drake et al., Reference Drake, Turner, Lasinski, Estabrok, Campbell, Wang, Phillion, Williams and Kruer1984 and Batani et al., Reference Batani, Strati, Telaro, Löwer, Hall, Benuzzi-Mounaix and Koenig2003) or from parasitic laser irradiation. A possible explanation of this expansion may come from the direct irradiation of the backside of the tube by the residual infrared PALS laser beam (few J). This infrared beam is less focused than the main beam at 438 nm and, therefore, it is not perfectly screened off by the piston foil. Consequently, this beam may reach the end of the square tube before being blocked by the socket. In the following, we shall thus restrict the interpretation of the interferometric diagnostic to times shorter than 50 ns and to distances smaller than 4 mm that are not impacted by the effect of the reverse plasma expanding from the backside. We stress however that the pre-heating does not influence the XUV diagnostics realized in the blind targets.

3.2. Shock dynamics and structure

Let us follow the fringes displacement with time. We shall assume that the dephasing is mainly due to free-free absorption, which relates the average transverse electron density <N _e (z,t)> _x=0 to the phase shift over the section d of the tube. The phase shift is given by:

(3)

where λ = 527 nm is the wavelength of the probe laser, <N _e (z,t) > _x=0 is given by Eq. (2), N _c,λ = 4 10²¹ cm⁻³ is the critical density at 527 nm, and d = 0.7 mm is the tube section.

We disregard the first fast dephasing discussed in the previous section. The fringe maxima and the reconstructed isocontours of <N _e (z,t)>_x=0 are reported in Figure 4 for densities between 2 × 10¹⁷ and 10¹⁹ cm⁻³. The distance between two fringes corresponds to about 17 pixels and a density of 6 × 10¹⁸ cm⁻³.

Each isocontour profile is concave, and tends approximately toward the same linear slope between 20 ns and 40 ns, corresponding to a velocity v _s of 63 km/s (±10%), similar to the velocity of the gold-xenon interface calculated with the one-dimensional radiative-hydrodynamical code MULTI (Ramis et al., 1988). This interface is not observed in the image, but reported for reference as the black dashed line. In this time interval, the residual extension of the radiative precursor is small, and the shock approaches the quasi-stationary limit.

Previous studies (González et al., 2006, 2009; Busquet et al., Reference Busquet, Audit, González, Stehlé, Thais, Acef, Bauduin, Barroso, Rus, Kozlova, Polan and Mocek2007) have already shown that the lateral radiative losses play an important role in the shock structure and dynamics. In particular, the precursor is curved and less extended in presence of radiative losses. The curvature is associated with the presence of colder layers close to the tube walls. Moreover, it was shown that the time to reach the stationary limit decreases with radiative losses.

We have studied numerically the properties of a radiative shock in a two-dimensional (2D) geometry for different values of the wall radiative losses and for a constant piston velocity of 63 km/s. The choice of this velocity follows from the measured velocity of the isodensity contours between 20 ns and 40 ns. The simulations were performed with the HERACLES 2D radiation hydrodynamic code (González et al., Reference Busquet, Audit, González, Stehlé, Thais, Acef, Bauduin, Barroso, Rus, Kozlova, Polan and Mocek2007), which includes radiation transport, super transition array opacity (Bar-Shalom et al., Reference Bar-Shalom, Shvarts, Oreg, Goldstein and Zigler1989), and an equation of state from the OPA-CS hydrogenic model (Michaut et al., Reference Michaut, Stehlé, Leygnac, Lanz and Boireau2004). Figure 5 (color online) shows the calculated and the measured average transverse electron density in the precursor at two different times (20 ns and 40 ns), for two values of the radiative losses (20% and 40%) at the gilt walls of the tube. The experimental results indicate that the radiative losses are on the order of 30 to 40 %. These losses measured in a tube with gold-coated walls are smaller than those measured in earlier studies (60%) with tubes of aluminized glass (González et al., 2006; Busquet et al., Reference Busquet, Audit, González, Stehlé, Thais, Acef, Bauduin, Barroso, Rus, Kozlova, Polan and Mocek2007).

Fig. 5. (Color online) Transverse electron density <N _e (z,t) > _x=0 at two times (20 ns in red and 40 ns in blue): experimental value (circles) and calculated electron densities with HERACLES for two values of the radiative losses (40 % in dashed; 20 % in full line). Due to measurement uncertainties, from the interferogram, the point at 2 × 10¹⁷ cm⁻³ at 20 ns has been discarded. The precision of the measurement is ~0.1 mm

4. TRANSVERSE INTERFEROMETRY

Longitudinal interferometry probes the time variation of the averaged transverse electron density <N _e(z,t)>_x=0 along the canal center (x = 0), versus the direction z of the shock propagation. This diagnostic allows the study of the propagation of the ionization front in the tube, but it does not give any direct information about the 2D structure of the radiative shock. To investigate the 2D structure, we performed a few transverse interferometric studies where the slit of the streak camera records the image, at a fixed distance z ₀ from the piston, in the direction x perpendicular to the shock propagation. Transverse interferometry probes the time variation <N _e(x,t)>_z=z0 of the electron density averaged over the transverse direction y, for a fixed value of z ₀ along the tube.

For this study, we have used a different target (F61, see Table 1). Its BK7 windows have an aluminum coating and the other faces of the tube are massive aluminum. The section of the cell, 1.2 × 1.2 mm² is larger than the nominal focal spot (~0.55 mm diameter) and the tube length is 6 mm. The target is filled with xenon at 0.1 bar, and we imaged the section of the tube at z ₀ ~ 3 ± 0.25 mm.

The interferogram is displayed in Figure 6. The horizontal axis corresponds to the transverse direction x (1.2 mm) and the vertical axis is the time (100 ns). The position of the time arrival of the laser pulse is reported in the figure by a dashed line. The figure shows that the shock section varies from less than 0.7 mm at 36 ns (precursor) to a section smaller than 1 mm at 42 ns. Although we did not see any evidence of the laser beam in the post-mortem analysis of the target, the record shows that the shot was not perfectly centered in the channel. Following the fringes vertically from top to bottom in the figure, after the time of shock arrival, we point to a small bending (black arrow) to the right at ~33 ns (precursor), reaching up to one fringe shift at  ~40 ns in the half right part of the image. After 40 ns the shock starts to be more opaque, especially on the left part of the figure. The location of the densest part of the shock is visible on the right part of the interferogram by this darkening and fringe discontinuity (large arrow). The corresponding time of arrival is ~42 ns, yielding a shock velocity of 71 ± 6 km/s. The precursor duration is ~7 ns, which is smaller than the duration that can be derived from Figure 4 at z = 3 mm (which exceeds the 14 ns measured between 7 × 10¹⁷ and 10¹⁹ cm⁻³). The fringes remain visible up to the canal center and bend toward the left after the shock, where their topology becomes irregular (bottom of the figure). The precursor (t ~ 33–40 ns) is smoothly bent as a consequence of both hydrodynamical expansion and radiation effects.

Fig. 6. Transverse interferogram of the shock (target F61), versus time t (vertical axis) and transverse direction x (horizontal axis) for z ₀ ~ 3 mm along the cell axis. Scales are 100 ns for the time and 1.2 mm for x. The dashed line corresponds to the time of laser pulse arrival. Contrarily to other figures, time increases from top to bottom.

5. REAR SIDE XUV SPECTROSCOPY

Whereas interferometry probes the plasma electron density, the plasma ionization and temperature can be investigated using spectroscopy. Photometric and spectroscopic signatures of the radiative shocks provide some critical tests to radiation hydrodynamic codes. In the present case of a radiative shock, the opacity variation along the shock structure is key to understanding the line spectrum formation. As pointed out already by González et al. (2006), the average opacity of the dense part of the shock is large. The opacity is small in the heated precursor, but large again in the cold unshocked gas. Hence, the XUV photons emerging from the shock front propagate almost freely up to the precursor front where they are reabsorbed. This process contributes to the ionization of the gas in front of the precursor and thus to increase its length. Qualitative synthetic spectrum calculations (Stehlé et al., Reference González, Audit and Stehlé2009a, 2009b), carried out for shocks in similar conditions than the present experiment, show that the emerging flux varies strongly with time because of the intrinsic time variations of the shock conditions. Additionally, flux variations may also be expected as a result of the decreasing thickness of the cold absorbing gas between the shock and the rear face of the tube as the shock propagates in the tube.

We have carried out an initial investigation in order to check the feasibility of characterizing the radiative flux emerging from the back face of the tube. Since the maximum emission from the shock is expected to be in the XUV range, we have realized an experimental setup with a flat field XUV spectrometer, with time integration over 16 µs, to study the spectral signatures of a radiative shock in xenon around λ=15 nm for shock velocities of ~65 km/s. The recorded spectrum shown in Figure 7 (color online) extends from 12 nm to 23 nm. As an aluminum filter of 1.6 µm is used to protect the grating against debris from the target in addition to the backside XUV window, the flux at wavelengths shorter than 17.1 nm (L edge cut-off of aluminum) is severely reduced by the filter extinction. The experimental setup is described in Section 2, with the collection angle Ω on the CCD camera, estimated to 1.4 × 10⁻⁴ rad, chosen to probe the central section of the tube.

Fig. 7. (Color online) XUV spectra, normalized at 19 nm, for three different shots: black line: xenon at 0.1 bar in aluminum tube, and an aluminum XUV window (cell G35); red line: xenon at 0.1 bar in aluminum tube, and an SiC XUV window (cell G32); blue line: mixture of air and xenon (50%–50% in number of moles) at 0.17 bar in an gold tube (cell G50) and aluminum XUV window.

For this spectroscopic study, we used blind targets either in aluminum (G32, G35) or in gold (G50). The inner diameter of the shock tube is 0.7 mm and the length is 2.8 mm. These 2 mm are followed by an expansion chamber (diameter 2 mm and length 0.1 mm) to weaken the shock wave. An XUV filter is placed at the backside of the tube, and is made of sub-micron foils of SiC or aluminum. The gas is either xenon at 0.1 bar or a 50–50 mixture of air and xenon at 0.17 bar (Table 1). The G35 shot (black) was poorly centered, and the recorded conditions therefore differ from the plasma conditions probed in the G32 shot.

We show the recorded spectra for the three different targets in Figure 7. These spectra present four main spectral features at ~17.2, 18.3, 19.2, and 20.0 nm. The two last lines, which are present in all the targets, are attributed to xenon. The two other features are attributed to oxygen (with possible blending from aluminum in the case of G35 and G32) coming from the walls.

While the measured count numbers for the G32 and G35 targets filled with xenon (about 1000 counts/pixel) are in qualitative agreement with numerical predictions, the interpretation of the time-integrated spectra remains difficult and is beyond the scope of this paper. However, this preliminary experiment shows the feasibility of backside spectroscopic investigations. Future studies will benefit of improved time and spectral resolution and will require accurate monochromatic opacities for comprehensive spectrum analyses.