1. INTRODUCTION 2. EXPERIMENTAL ARRANGEMENT

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1 THE ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES, 127:527È531, 2000 April ( The American Astronomical Society. All rights reserved. Printed in U.S.A. STUDY OF SUPER- AND SUBSONIC IONIZATION FRONTS IN LOW-DENSITY, SOFT X-RAYÈIRRADIATED FOAM TARGETS O. WILLI, L. BARRINGER, AND C. VICKERS Imperial College of Science, Technology and Medicine, the Blackett Laboratory, Prince Consort Road, London, SW7 2BZ, England, UK AND D. HOARTY Radiation Physics Department, AWE Aldermaston, Reading, Berkshire, RG7 4PR, England, UK Received 1999 June 14; accepted 1999 November 22 ABSTRACT The transition from super- to subsonic propagation of an ionization front has been studied in X-ray irradiated, low-density foam targets using soft X-ray imaging and point projection absorption spectroscopy. The foams were doped with chlorine and irradiated with an intense pulse of soft X-ray radiation with a temperature up to 120 ev produced by laser heating a burnthrough converter foil. The cylindrical foam targets were radiographed side-on allowing the change in the chlorine ionization and hence the front to be observed. From the absolute target transmission the density proðle was obtained. Comparison of experimental absorption spectra with simulated ones allowed the temperature of the heated material to be inferred for the Ðrst time without reliance on detailed hydrodynamic simulations to interpret the data. The experimental observations were compared to radiation hydrodynamic simulations. Subject headings: hydrodynamics È methods: laboratory È shock waves È X-rays: general 1. INTRODUCTION The interaction of intense, soft X-ray radiation with matter is of fundamental interest and is responsible for a host of natural, astrophysical phenomena, perhaps even triggering of the gravitational collapse of gas clouds leading to stellar formation. Other examples can be found in the dynamics of gaseous nebulae and in the formation of ablation fronts as the intense radiation Ðeld from a hot (for example, O-type) star interacts with a remote interstellar cloud. Recently, considerable interest in the generation of intense, soft X-ray radiation in the laboratory has resulted from the possibility of using this radiation as a driver for inertial conðnement fusion (ICF). The laser energy is converted to soft X-rays by irradiating either the inside walls of a gold hohlraum or a thin gold converter foil. When an intense radiation Ðeld, such as that produced from the gold converter foil, is incident onto cold, unionized matter, the X-rays will initially penetrate a mean free path into the medium, which is consequently heated and ionized. As the material is heated and ionized its opacity to the incident radiation is reduced, allowing the source radiation to penetrate deeper into the unheated target. The region where the unheated, unionized material is transformed into an ionized plasma deðnes an ionization front. This front can be driven solely by the radiative Ñux transported through the already heated material from the source (referred to as volumetric, or bulk heating). That is, it is the increasing mean free path of the drive X-rays that constitutes the propagation of the X-ray heating wave. Alternatively, if the optical depth of the heated material is sufficiently high, the X-ray Ñux driving the front can have a signiðcant contribution from the radiative emission of the heated target material. If the ionized matter becomes totally optically thick to the source radiation, the radiative energy transfer in the plasma is fully di usive, with the source providing the boundary conditions. X-ray heating of matter is also ideal to investigate the propagation of di erent waves including supersonic (Afshar-rad et al. 1994) and subsonic ionization fronts (Hoarty et al. 1997). In the supersonic case the density 527 behind the front is similar to the one ahead of the front whereas in the subsonic regime a density compression occurs. Depending on the opacity of the heated material the radiation transport can be di usive as Ðrst considered by Marshak (1958) or nondi usive. The transition from supersonic to subsonic is transient and is difficult to model. For example, analytical models are not able to predict the conditions of an ionization front in this transient regime and there are even uncertainties in the output of sophisticated two-dimensional radiation hydrodynamic codes. These uncertainties are caused, for example, by radiation transport algorithms, the radiative opacity of the plasma, the equation of state data and the zoning of the computational mesh. Consequently experimental data in this transient regime are important. In this paper experimental observations are described which show the transition from super- to subsonic propagation of an ionization front in low density chlorinated foam targets using soft X-ray imaging and point projection absorption spectroscopy. The X-ray heated foam targets were radiographed side-on allowing the change in the chlorine ionization and hence the front to be observed. From the absolute target transmission the density proðle was obtained. The experimental observations were compared with radiation hydrodynamic simulations. 2. EXPERIMENTAL ARRANGEMENT The experiments were carried out at the Rutherford Appleton Laboratory using the VULCAN laser system. The targets consisted of low density triacrylate foam with a density of 50 mg cc~1. The samples used were either pure triacrylate or were chemically doped with a chlorine monomer (C H O Cl ) 25% by weight. Cell sizes in the foam were less 9 3 than km in diameter, with a very high degree of homogeneity throughout the foam. The foams were cylindrical and between 180 and 250 km in length with a diameter of 200 km and were irradiated with a soft X-ray pulse of either 1.0 or 1.5 ns (FWHM) duration emitted from the rear of a laser-irradiated burnthrough ÏÏ converter foil.

2 528 WILLI ET AL. Vol. 127 FIG. 1.ÈSchematic of the soft X-ray imaging system using a spherical multilayered mirror. The operating wavelength is 50 A. The burnthrough foil consisted of 100 nm of gold (Au) supported on 1 km of CH and was positioned parallel to the sample target and separated from it between 30 and 60 km. The laser energy was delivered into a 200 km focal spot on the burnthrough target through f/10 lenses by up to six separate beams arranged in the VULCAN cluster conðguration (13 cone angle). Laser irradiances of up to 1014 W cm~2 were used. The soft X-ray Ñux and pulse shape emitted from the rear of the burnthrough foil was measured using an absolute calibrated time-resolving photodiode. Allowing for experimental uncertainties and spatial and angular variations in the emitted radiation, it is estimated that the peak soft X-ray Ñux at the surface of the foam was FIG. 2.ÈExperimental arrangement for side-on absorption spectroscopy measurements of X-ray heated foam targets. The soft X-ray pulse to heat the foam is produced by using a gold converter foil arrangement. between 2 ] 1012 Wcm~2 and 8 ] 1012 Wcm~2. The ionization wave propagating through the foam was diagnosed with two independent diagnostics. First, the foam target was imaged perpendicularly to the soft X-ray drive with a spherical multilayered mirror, reñecting at a central wavelength of about 50 A ( D 250 ev). The bandwidth of the mirrors was measured to be better than 3 A. The foam sample was backlit by a thermal X-ray source, generated by irradiating a 500 km diameter Au wire with around 10 J of green laser light. The 50 times magniðed image of the cylindrical target was recorded by a two frame gated microchannel plate (MCP) intensiðer with the target image placed across the two frames. This allowed information on the two-dimensional response of the target to be monitored at two di erent times. The spatial resolution of the imaging system was found to be 2 km by the use of a ray tracing program, in good agreement with past experimental measurements. The temporal resolution of X-ray imager has been measured to be approximately 120 ps. The backlighter was positioned in a plane parallel to the target surfaces and at a distance from the target of approximately 3 mm. The X-ray Ñux at the foam target due to the backlighter emission was negligible. Figure 1 shows a schematic of the soft X-ray imaging system (Desselberger et al. 1991; Willi et al. 1992). The second diagnostics was point projection K-shell absorption spectroscopy (Lewis & McGlinchey 1985). Again the X-ray heated foam was probed side-on by a quasi-continuum, 70 ps soft X-ray pulse provided from a bismuth coated gold backlighter pin irradiated with 0.53 km laser light that was focussed with an f/2.5 lens. The pin was positioned typically 2.5 mm away from the foam target resulting in an image magniðcation of approximately 50]. The data were recorded using a Ñat crystal spectrometer with a RbAP (2d \ A ), with a spectral resolution of 3 ev, and Kodak Industrex C-type Ðlm. The spectral range of the spectrometer was set to record the absorption spectrum of chlorine due to transitions from the K shell to the 2p and 3p orbitals (2.5È3.1 kev). Figure 2 shows the arrangement of the point projection absorption spectroscopy diagnostic.

3 No. 2, 2000 SUPER- AND SUBSONIC IONIZATION FRONTS EXPERIMENTAL RESULTS AND COMPUTATIONAL INTERPRETATION Two-dimensional gated images were taken at two di erent times in the evolution of the ionization front by placing the target across two frames of the MCP intensiðer camera. Figure 3a shows images taken at 300 ps and 900 ps after the start of an X-ray pulse which irradiated an undoped foam of density 30 mg cc~1 at an intensity of 8 ] 1012 Wcm~2. In the early time frame, the foam target remains relatively undisturbed since the drive was just starting to rise. At later time, however, the ionization wave can be seen to have penetrated deep into the target (about 50 km in 600 ps). An important point to note is that the diameter of the foam target at the position of the ionization front remains unchanged from its original value. This is an indication of the supersonic nature of the propagation and the consequent lack of signiðcant material compression behind the front, since with ablative (sonic) Ñow a large degree of twodimensional motion is to be expected in the vicinity of the shock front. This is observed at much lower drive irradiances (2 ] 1012 Wcm~2). A rolling-up ÏÏ of the foam can be seen as shown in Figure 3b. In this case the timing of the MCP intensiðer was set to be 3.0 and 5.3 ns, respectively. Data taken with point projection absorption spectroscopy clearly shows the transition from supersonic to subsonic propagation. Absorption spectroscopy radiographs are shown in Figure 4. Absorption lines are clearly observed in the radiographs. Line scans of the absorption spectra were taken and were compared with a model of the population of chlorine charge state conðgurations which assumed local thermodynamic equilibrium (LTE). The material density was obtained from the measured continuum transmission and input to the model. Saha-Boltzmann statistics was used to calculate the relative populations in conðgurations of the chlorine charge states with a full K shell, including all permutations of L-shell electrons, satellites in M and N shells, and detailed term structure. A detailed spectrum was then constructed, using transition energies and oscillator strengths from ab initio calculations by the multiconðguration Dirac Fock code GRASP (Dyall et al. 1989). K-edge energies and cross sections were calculated from parametric Ðts. The model included the continuum lowering treatment by Stewart & Pyatt (1966). A Gaussian instrument resolution function was used in the simulated spectra. The assumption of LTE was checked by performing collisional radiative calculations using a model based on the GALAXY code (Rose 1995) with improved energy levels and Stewart and PyattÏs continuum lowering treatment. Temporal and spatial gradients were taken into account by a weighted sum of the contribution of calcu- FIG. 3.ÈTwo-dimensional gated soft X-ray images showing (a) super- and (b) subsonic propagation. The dark band in the middle of the targets is caused by the nonconducting region separating the two frames.

4 530 WILLI ET AL. Vol. 127 FIG. 4.ÈAbsorption radiographs of X-ray heated chlorinated foam targets indicating (a) supersonic propagation and (b) subsonic propagation lational cells at di erent temperatures and densities. The contribution to the continuum opacity and the electron density from the other constituents of the foam was also included. The measured density was input to the atomic physics model and the temperature inferred by iterating the temperature in the model until the best match to the experimental absorption spectrum was obtained. Simulations were performed using a two-dimensional Lagrangian radiation-hydrodynamics code (Roberts 1980). Radiation transport is modeled using either a multigroup di usion approximation using KershawÏs di usion algorithm or multigroup implicit Monte-Carlo (IMC) transport (Fleck & Cummings 1971). The temporal behavior and absolute levels of the X-ray drive were taken from the absolutely calibrated diode measurements, with the spectrum of the radiation assumed to be blackbody. The blackbody assumption has been previously validated in similar measurements and the addition of long mean free path X-rays originating from the gold M band was found to have little e ect on the results. Opacities were generated using the detailed opacity code, IMP (Rose 1992). Figure 5 shows a comparison of the experimental temperature proðle with the predicted one from the two-dimensional hydrodynamic simulations. For supersonic propagation the experimentally measured front position and the density were reproduced well by the simulation though the detail of the front temperature proðle shows some di erences. In Figure 6 a comparison for the subsonic case is shown. The subsonic temperature proðle is reproduced well by the simulation. The data at the boundary of the supersonic and subsonic regime show a density ratio of approximately two. The ionization front is not preceded by the shock but both propagate together. In the subsonic case the front was preceded by a shock as shown in Figure 6. In this case the shock has a density ratio of approximately CONCLUSIONS In summary, the transition from supersonic to subsonic propagation of an ionization front in low density foam targets which were irradiated with an intense pulse of soft X-ray radiation has been observed using soft X-ray imaging and point projection absorption spectroscopy. From the absorption radiographs density and temperature proðles of the heated material were obtained without reliance of detailed hydrodynamic simulations to interpret the data. The experimental data have been compared with predictions of a two-dimensional radiation hydrodynamic code that reproduced the measured conditions reasonably well. The change from supersonic propagation (deðned as the point at which the density disturbance associated with the passage of the front reaches a density ratio of 2) was measured to occur at a density perturbation of 0.1 g cc~1 at a time of 1.8 ^ 0.1 ns for a drive Ñux of 8 ] 1012 Wcm~2. We are grateful to the laser and target preparation sta at the Rutherford Appleton Laboratory for their considerable support and e ort during the experiments. This work was funded jointly by the SERC and MoD.

5 No. 2, 2000 SUPER- AND SUBSONIC IONIZATION FRONTS 531 FIG. 5.ÈTemperature proðle (a) and density proðle (b) inferred from a radiograph taken at a backlighter delay of 1.6 ns with an incident Ñux of 8 ] 1012 Wcm~2. The solid curves are the NYM simulation, the markers with error bars are the experiment. The two curves from simulation are 100 ps apart and have been convolved with the measured spatial resolution. The ionization front is at the limit of supersonic propagation. FIG. 6.ÈTemperature proðle (a) and the density proðle (b) inferred from a radiograph taken at 1.9 ns backlighter delay. The Ñux was reduced relative to the data of the previous Ðgures to 4 ] 1012 Wcm~2. The density ratio has increased to over 3 and there is a separation of the shock and ionization front. The two simulations are 100 ps apart and have been convolved with the measured spatial resolution. Afshar-rad, T., et al. 1994, Phys. Rev. Lett., 73, 74 Desselberger, M., Afshar-rad, T., Khattak, F., Viana, S., & Willi, O. 1991, Appl. Opt., 30B, 2285 Dyall, K. G., et al. 1989, Comp. Phys. Comm., 55, 425 Fleck, J. A., & Cummings, J. D. 1971, J. Comput. Phys., 8, 313 Hoarty, D., Iwase, A., Meyer, C., Edwards, J., & Willi, O. 1997, Phys. Rev. Lett., 78, 3322 Lewis, C. L. S., & McGlinchey, J. 1985, Opt. Commun., 53, 179 REFERENCES Marshak, R. E. 1958, Phys. Fluids, 1, 24 Roberts, P. D. 1980, AWE Rep. (unpublished) Rose, S. J. 1992, J. Phys. B, 25, 1667 ÈÈÈ. 1995, J. Quant. Spectrosc. Radiat. Transfer, 54, 333 Stewart, J., & Pyatt, K. 1966, ApJ, 144, 1203 Willi, O., Afshar-rad, T., Desselberger, M., Dunne, M., Edwards, J., Khattak, F., & Taylor, R. 1992, Rev. Sci. Instrum., 63, 4818