Figure 1

Examples of high-energy-density experimental facilities. (a) The Omega laser facility. Note the “switchyard” at the left: it is used to distribute 60 laser beams as evenly as possible around the vacuum chamber where the target is situated. Such an arrangement is dictated by the principal objective of the Omega facility, which is the study of “direct drive” fusion (30). Image provided courtesy of the University of Rochester Laboratory for Laser Energetics. (b) Schematic of the $Z$ facility at Sandia National Laboratories (Albuquerque). The outermost part is formed by Marx generators. They are connected to 36 water-insulated transmission lines which, in turn, feed magnetically insulated vacuum transmission lines converging at the central “diode,” where energy is delivered to an experiment. This facility is now being refurbished, to increase the current from 20 to $30\mathrm{MA}$ (200). Image provided courtesy of the Sandia National Laboratory at Albuquerque.Reuse & Permissions

Figure 2

Examples of laboratory astrophysics experiments done on high power lasers and Z-pinch facilities. (a) Opacity experiment using a $Z$-pinch driven hohlraum on the Saturn facility. The $Z$ pinch implodes on the axis of a primary hohlraum which is used as a source of a thermal x-ray radiation for probing an iron plasma and measuring its opacity under conditions relevant to the physics of Cepheid variable stars. Adapted from 285. (b) Measurement of the Fe sample transmission spectrum from the experiment sketched in (a). Adapted from 285. (c) Typical hydrodynamics experiment using direct laser irradiation. In this case, the experiment (249) is to study the interaction of a strong shock with a density clump, which is a typical astrophysical problem (164). Several of the Omega beams are used to generate a source of x rays (a backlighter, see text) situated at the opposite side of the experimental assembly. (d) Using a gated x-ray pinhole camera (“x-ray framing camera”), radiographic images are obtained as a function of time showing the evolution of the shocked sphere. Adapted from 249.Reuse & Permissions

Figure 3

Cepheid variable stars offer a useful “galactic yardstick,” based on their pulsation dynamics. (a) Hertzsprung-Russell diagram of magnitude versus spectral type for stars along the main sequence, and variable stars, including those along the Cepheid instability strip. Also shown along the horizontal axis are temperatures (K) in parentheses, and their corresponding spectral types. Adapted from 31. (b) Plots of the stellar pulsation period–magnitude (or luminosity) linear relation, showing that the longer the period of oscillation, the brighter the star (lower magnitude). The three curves result from different analyses of this correlation. These curves form the basis for the use of Cepheid variables as galactic yardsticks, to infer distances. Adapted from 31. (c) The phase relations for the variable star $\delta$ Cephei, showing the correlations between periodic pulsations of visual magnitude $\left(\mathrm{\Delta }m\right)$, i.e., brightness, effective temperature $\left(T\right)$, spectral type (Sp), radial velocity $\left(v_r\right)$, and radius $\left(\mathrm{\Delta }R\right)$. Adapted from 31.Reuse & Permissions

Figure 4

Modern opacity simulations, tested against experiments, have improved our understanding of cepheid variable star pulsation. (a) Opacity versus temperature for a 15-element mixture of solar composition, along a path of constant $\rho ∕T^3$. OPAL calculations are shown for a zero metallicity star (no elements heavier than He, and denoted “$Z=0$”), and for a $Z=0.02$ solar metallicity star (2% mass fraction in elements heavier than He). Results from a previously used set of Los Alamos opacities for $Z=0.02$ are also shown. Adapted from 253. (b) Diagram of the ratio of the first two harmonics periods of a beat Cepheid variable star. Circles represent observations. The upper set of three (dashed) curves correspond to the simulated result using older opacities, which ignore the full fine structure of the metals. The lower (solid) curves correspond to simulations with OPAL-DTA, including the full fine structure, in particular, for Fe. Adapted from 253. (c) Plot showing measured versus calculated transmission through a thin Fe sample heated to conditions of $T\approx 20\mathrm{eV}$ and $\rho \approx 5\mathrm{mg}∕{\mathrm{cm}}^3$. Two OPAL opacity simulations are shown, one using DCA with hydrogenic oscillator strengths, which ignores term splitting (top curve), and the other using full DTA with intermediate coupling, which causes term splitting. The latter, more complete opacity calculation more closely reproduces experimental results. Experiments were carried out on the Nova laser. Adapted from 253. (d) Comparison of theoretical Fe transmission spectra at the measured conditions of $T\approx 20\mathrm{eV}$, and $\rho \approx {10}^{-4}\mathrm{g}∕{\mathrm{cm}}^3$. The calculations correspond to the STA opacity model (upper curve), OPAL-DTA model (intermediate curve, showing the line fine structure), and OPAL-UTA (lower curve). The intermediate curve closely reproduces experimental results [shown in Fig 2b]. Including the transition fine structure changes the predicted average opacities significantly. Adapted from 285.Reuse & Permissions

Figure 5

Variation of the density distribution after the explosion of SN 1987A. (277). Time $t=0$ corresponds to the instant just before the explosion. $M_{\mathrm{r}}$ is a Lagrangian mass within a certain radius. Steep density gradients in the progenitor star situated at $M_{\mathrm{r}}∕M_{☉}\approx 2.5$ and $M_{\mathrm{r}}∕M_{☉}\approx 4$ correspond to the oxygen (labeled “core”) -helium and helium-hydrogen transition zones, respectively. After the transit of the shock wave through these zones, the pressure gradient changes sign and the Rayleigh-Taylor instability develops leading to a 3D mixing process which is thought to be important in the explanation of the light curve. The vertical dashed line at $M_{\mathrm{r}}∕M_{☉}\approx 13.5$ indicates the location out to which core ${}^{56}\mathrm{Co}$ has to be pre-mixed for 1D simulations of SN1987A to reproduce light curve observations. This large degree of mixing, which has been difficult to reproduce with large-scale simulations, is referred to here as the “SN mix problem.” Adapted from 277.Reuse & Permissions

Figure 6

Light curve for SN1987A. The “$+$” symbols are the observed light curve, and the thin solid line is an analytic model described by 5. Different dates indicated show when x rays were first detected on day 139 by the Ginga/Mir experiment, when $\gamma$ rays from ${}^{56}\mathrm{Co}$ were detected by the Solar Maximum Mission (SMM) at day 178, and when subsequent detections of $\gamma$ rays occurred by several balloon experiments (CIT, LM, FG). Inset: A calculation of the evolution of temperature versus time as the shock breaks out from the surface of the star. Adapted from 5Reuse & Permissions

Figure 7

(Color) Density distribution $\left(\log \rho \right[\mathrm{g}∕{\mathrm{cm}}^3\left]\right)$ $1500\mathrm{s}$ after core bounce. The supernova shock (outermost discontinuity) is located at $r\approx 9\times {10}^{11}\mathrm{cm}$. A dense shell (visible as a whitish ring) has formed between the SN shock and reverse shock at $r\sim 5\times {10}^{11}\mathrm{cm}$, with its outer boundary coinciding with the $\mathrm{He}∕\mathrm{H}$ interface. The fastest moving RT spikes have just reached the reverse shock. Adapted from 160.Reuse & Permissions

Figure 8

(Color) Jet-induced explosion. Frames show the density in the $x$-$z$ plane passing through the center of computational domain, at $1.08\mathrm{s}$ after the jet initiation. The jet axis (and presumably the rotation axis) is vertical here. The size of the panel is $9\times {10}^9\mathrm{cm}$ vertically and $6\times {10}^9\mathrm{cm}$ horizontally. Adapted from 158.Reuse & Permissions

Figure 9

Hydrodynamic simulations for the supernova and laboratory experiment. (a) Spatial profiles of the pressure and the density for the SN at $2000\mathrm{s}$, and (b) the laboratory experiment at $20\mathrm{ns}$. Adapted from 268. (c) The velocity of the $\mathrm{He}\text{−}\mathrm{H}$ interface in the supernova and in the scaled laser experiment. The curves are essentially identical, up to the scale transformation. This is a prerequisite for making a scaled laboratory experiment on the evolution of 2D or 3D perturbations. Adapted from 151. (d) A radiograph obtained at $t=33\mathrm{ns}$ of the nonlinear RT induced mixing in the first scaled SN experiment. Adapted from 241. (e) A sum over multiple images from the same experiment as shown in (d), corresponding to an average time of $t_{\mathrm{ave}}=35\mathrm{ns}$. Adapted from 240.Reuse & Permissions

Figure 10

(Color) Code simulations vs experiment on coupled interface effects. (a) The laser beams strike a $10\text{−}\mathrm{\mu }\mathrm{m}$-thick ablator layer on the front surface of the Cu $({\rho }_0=8.9\mathrm{g}∕{\mathrm{cm}}^3)$, which is of $85\mathrm{\mu }\mathrm{m}$ average thickness. The Cu interface is modulated at a wavelength of $200\mathrm{\mu }\mathrm{m}$ and an amplitude of $15\mathrm{\mu }\mathrm{m}$, backed by a polyimide plastic layer, 150 $\mathrm{\mu }\mathrm{m}$ thick, with a $75\text{−}\mathrm{\mu }\mathrm{m}$-thick CH tracer with a 4.3 at. % doping of Br. Both have a density of $1.4\mathrm{g}∕{\mathrm{cm}}^3$. The final layer is $1700\mathrm{\mu }\mathrm{m}$ of CRF foam at ${\rho }_0=0.1\mathrm{g}∕{\mathrm{cm}}^3$. In the experiments, the resulting structures are radiographed from the side by x-ray backlighting as discussed in Sec. 2. Adapted from 150. (b) The experimental radiograph at $39\mathrm{ns}$ (bottom) and $65\mathrm{ns}$ (top) for the experiment corresponding to the design simulation shown in (a). Adapted from 150. (c) The results from FLASH simulations of this same experiment. Adapted from 42.Reuse & Permissions

Figure 11

Comparison of numerical simulations and experiment on a multimode RT instability. (a) A numerical radiograph from simulations. (b) Same as (a), except with experimental noise added into the simulated output. (c) The experimental radiograph at $t=13\mathrm{ns}$, on strong shock-driven experiments done at the Omega laser. Adapted from 205.Reuse & Permissions

Figure 12

Experimental observation of a possible transition to turbulence in the deeply nonlinear stage of the RT instability. Side-on radiographs at (a) $t=13\mathrm{ns}$, (b) $t=25\mathrm{ns}$, and (c) $t=37\mathrm{ns}$ (246; 204). Adapted from 204.Reuse & Permissions

Figure 13

(Color) Results from adaptive mesh refinement simulations of a proposed scaled SN hydrodynamics experiment for NIF. The hypothetical experiment simulated was assumed to be similar to that described in Fig. 12, except that it was driven harder, with a $M\sim 20$ shock. Also, a 3D high mode number noise spectrum was added onto the 2D single-mode perturbation as a seed. The top row was for simulations run in 2D, versus the bottom row was done in 3D with an adaptive mesh refinement code. With simulations run in 3D, with a 3D high-frequency noise spectrum, the deep nonlinear RT evolution is observed computationally to pass through the mixing transition, and enter a fully turbulent regime. Adapted from 204.Reuse & Permissions

Figure 14

(Color) Supernova remnants offer a visual example of strong shock dynamics in the universe. (a) Hubble Space Telescope Wide-Field Planetary Camera 2 observations in $\mathrm{H}\alpha$ of the Cygnus Loop supernova remnant (SNR), which is located at a distance of $\sim 0.75\mathrm{kpc}$, and is the result of a supernova that occurred $\sim 15000\mathrm{yr}$ ago. The image shows the SNR blast wave interaction with an interstellar cloud on physical scales of ${10}^{15}\mathrm{cm}$. Shocks viewed face-on produce diffuse emission, while sharp filaments are characteristic of correspond to shocks viewed edge-on shocks. Individual shocks in the cloud of density $n\approx {10}^{-15}{\mathrm{cm}}^{-3}$ are observed to have velocity $v_s=170\mathrm{km}{\mathrm{s}}^{-1}$. The image is scaled linearly from 0 (white) to $4\times {10}^{-14}\mathrm{ergs}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{pixel}}^{-1}$ (black). Adapted from 185. (b) Interaction of a supernova remnant (the hemispherical object to the lower left) and a molecular cloud (the elongated object above). The figure shows a grayscale image of the x-ray emission, overlaid with a contour image of the radio emission. Adapted from 117. (c) An image of SNR E0102.2-7219 from Chandra. Colors encode the x-ray photon energy (red is softer, blue is harder, white is the mean spectrum). Adapted from 107. (d) Cassiopea-A remnant. Colors correspond to three different energy bands: $0.6–1.65\mathrm{keV}$ (red), $1.65–2.25\mathrm{keV}$ (green), and $2.25–7.50\mathrm{keV}$ (blue). Adapted from 130. (e) Rosat x-ray image of Puppis A supernova remnant. Reproduced from 131. (f) Chandra x-ray image of the Bright Eastern Knot region of Puppis A SNR. Reproduced from 131. (g) Same as (f), only in black and white with contrast enhancement, and with the shock-cloud “cap” and “bar” features indicated. Adapted from 131.Reuse & Permissions

Figure 15

Experimental images from the early-time evolution of the strong shock $(M=v_{\mathrm{shk}}∕v_{\mathrm{sound}}\sim 10)$ compression of a $\sim 100\text{−}\mathrm{\mu }\mathrm{m}$-diameter solid copper sphere embedded in plastic (initial density contrast ${\rho }_{\mathrm{Cu}}∕{\rho }_{\mathrm{CH}}\sim 10$). The initial experiment was done on the Nova laser (164). This set of images spans the interval of 20–$26\mathrm{ns}$, where $t=0$ corresponds to when the laser first turns on. The first image on the left shows the shock approaching the uncompressed Cu sphere. The final image on the right shows the fully compressed, umbrella shaped Cu sphere. The images in between show the shock progression through the sphere. Adapted from 164.Reuse & Permissions

Figure 16

Late-time evolution of the Cu sphere (scaled cloud) shock-cloud experiment, done on the Nova laser (164). The experimental images span 30.2–$61.2\mathrm{ns}$, and show the evolution from the early-time aftermath of shock compression (30–$40\mathrm{ns}$) to the formation of vortex rings (42–$49\mathrm{ns}$), through the initial stages in the transition to turbulence (55–$61\mathrm{ns}$). Adapted from 164.Reuse & Permissions

Figure 17

(Color) Simulations of the shock-cloud experiment done on the Nova laser. (a) One result, showing a color density plot at $54\mathrm{ns}$, from a 2D simulation of the experiment shown in Fig. 16. The 2D simulation shows the formation of an unperturbed vortex ring in the “skirt,” and a Kelvin-Helmholtz instability induced roll-up in the “cap.” (b) Simulated 2D radiograph, assuming 4.5-keV $\mathrm{Ti}\mathrm{He}\alpha$ x rays. (c) 3D simulations of the laboratory experiment with realistic EOS. Adapted from 249. (d) The result from a 3D simulation of a strong astrophysical shock interacting with an isolated cloud, using an ideal EOS, and an adaptive mesh refinement hydrodynamics code. Adapted from 164.Reuse & Permissions

Figure 18

Formation of a radiative precursor in a strongly shocked Xe gas experiment. (a) Results from 1D design simulations with the radiative hydrocode ASTROLABE, showing that compressions as high as 50 were predicted, due to strong radiative cooling. The initial shock heating was predicted to initially go into ions $\left(T_i\right)$, with $T_e=T_i$ equilibration occurring downstream from the shock. (b) The shock trajectory and ionization precursor were measured with optical diagnostics, allowing the average shock speed of $67\mathrm{km}∕\mathrm{s}$ to be determined. (c) The electron density profile was also measured with a Mach-Zehnder interferometer, showing the strong ionization precursor, compared with the simulation. Adapted from 36.Reuse & Permissions

Figure 19

Data from the radiative precursor experiment of 156. Temperature profile inferred from the absorption spectroscopy, along with results of a simple 1D radiation hydrodynamics simulation. Adapted from 156.Reuse & Permissions

Figure 20

(Color) Formation of a collapsed layer in dense Xe gas. (a) Density profiles calculated with the HAYDES code for the case with radiation (solid line) and no radiation (dashed line). Adapted from 238. (b) Simulations using FCI2, of the 2D geometry, with the finite radius of the shock tube taken into account. (c) Radiographic image showing remarkable agreement with 2D simulations. Adapted from 238.Reuse & Permissions

Figure 21

Effects of the equation of state and radiation on the shock. (a) Radiative precursor for the shock wave in Xe (initial density $1.5\times {10}^{-4}\mathrm{g}∕{\mathrm{cm}}^3$, initial temperature $2\mathrm{eV}$). Adapted from 202. (b) Shock compression solutions vs initial temperature, including radiation, assuming an ideal polytropic $(\gamma =5∕3)$ gas. (c) Same as (b) only now treating the atomic structure and ionization, assuming ${\rho }_1=5\times {10}^{-4}\mathrm{g}∕{\mathrm{cm}}^3$, and $T_1=0.1\mathrm{eV}$ for the hydrogen gas. Adapted from 203.Reuse & Permissions

Figure 22

Blast waves in nitrogen and xenon. Measured shock trajectories for (a) nitrogen and (b) xenon. Measured structure by dark-field imaging of the blast wave for 500-J energy input for (c) nitrogen and (d) xenon. Adapted from 86.Reuse & Permissions

Figure 23

The emergence of a second shock driven by the ionized precursor in strongly shocked Xe. (a) Schlieren image at $t=150\mathrm{ns}$ and (b) at $t=4\mathrm{\mu }\mathrm{s}$. (c) The corresponding spherically symmetrical modeling. Adapted from 119.Reuse & Permissions

Figure 24

(Color) Jets from young stellar objects in the galaxy. (a) Optical image of the protostellar jet, Herbig-Haro (HH) 47. The bipolar HH 47 complex embedded in the dense Bok Globule 1500 light years away at the edge of the Gum Nebula: (red) [SII] emission; (green) Hα; (blue) [OIII]. (b) Optical image of the jet, HH 111. Adapted from 239.Reuse & Permissions

Figure 25

Simulations of high Mach number jets relevant to HH jets. (a) Simulations showing the effect of Mach number in the jet morphology. Adapted from 222. (b) Simulations of high Mach number jets relevant to HH jets, showing the sensitivity to the amount of radiative cooling. Adapted from 27. (c) Simulations showing the effect of radiative cooling on a high Mach number, magnetized jet. Adapted from 101.Reuse & Permissions

Figure 26

Simulations and experiments of high Mach number jets on high power laser and Z-pinch facilities. (a) Simulations and (b) experimental images of a high Mach number, purely hydrodynamic (nonradiatively cooled) Al jet experiment done on the Omega laser. Adapted from 98. (c) High Mach number jet image taken on an experiment at the $Z$ magnetic pinch facility. Adapted from 281. (d) Image of a high Mach number jet driven by direct laser illumination of the target package, on the Omega laser, and backlit late in time, at $300\mathrm{ns}$. Adapted from 99. (e) Simulation of the high Mach number turbulent jet, carried out prior to doing experiments, suggesting that the jet might indeed transition into turbulent hydrodynamics. Adapted from 296.Reuse & Permissions

Figure 27

(Color) Jet experiments and simulations from the Magpie magnetic pinch facility. (a) Images of jets of Al, Fe, and W plasma created by conical arrays of wires of the same material at the Magpie magnetic pinch facility. Adapted from 178. (b) Experimental image of a high Mach number, radiatively cooled W jet impacting a CH foil downstream, causing the working surface to reheat, and emit soft x rays. Adapted from 178. (c) Similar to (b), but this jet is being deflected transversely, due to the lateral flow of plasma (laboratory “stellar wind”) impacting the jet, creating a lateral ram pressure. Adapted from 180. (d) Images of a magnetic tower jet created by a radial wire array. Adapted from 177. (e) Simulations of a magnetic tower jet created by a radial wire array. Adapted from 54. These jet experiments were carried out on the Magpie $Z$-pinch facility.Reuse & Permissions

Figure 28

Lines of constant magnetic Reynolds number ${\mathrm{Re}}_M=\mathrm{const}$ for a fully stripped carbon plasma as a function of the characteristic length scale and temperature. Adapted from 268.Reuse & Permissions

Figure 29

(Color) The Hubble Space Telescope image of the Eagle Nebula. Radiation is absorbed in a very thin layer near the surface of the cloud. Adapted from 125.Reuse & Permissions

Figure 30

The projection of the Eagle Nebula and neighboring stars on the plane of the sky. From 230. The size of the symbols indicates the relative strength of the Lyman continuum flux. Adapted from 230.Reuse & Permissions

Figure 31

Results of (a) a simulation and (b) an experiment on the ablation front Rayleigh-Taylor instability. Perturbations are viewed side-on at $4.4\mathrm{ns}$. The ablation front corresponds to the lower side of the material. The initial wavelength was $100\mathrm{\mu }\mathrm{m}$ and the initial peak-to-valley variation was $4.6\mathrm{\mu }\mathrm{m}$. Three nearly simultaneous gated x-ray pinhole images are juxtaposed. Due to the $\sim 100\mathrm{\mu }\mathrm{m}$ of parallax differences between the views, the full extent of the foil is observed. Adapted from 242.Reuse & Permissions

Figure 32

Numerical simulations accounting for the absorption of the ionizing radiation in the ablation outflow. (a) The initial perturbation on the cloud surface. (b) This panel shows that when the absorption is artificially turned off the amplitude of perturbations grows approximately according to the Rayleigh-Taylor model. If the absorption is “turned on,” however, the exponential growth is replaced by a damped oscillation. (c) The 2D simulation result showing that nonlinear perturbations can grow even in the presence of absorption. Adapted from 210.Reuse & Permissions

Figure 33

The interior structure of Jupiter is sensitive to the high pressure, high density properties of hydrogen. (a) Schematic of the interior of Jupiter. Adapted from 115. (b) Phase diagram of high-pressure hydrogen. Reproduced from 272. Curve $a$ corresponds to the interior of Jupiter. Curves $b$, $c$, and $e$ represent the interiors of main sequence stars of mass 0.3, 1.0, and 15$M_{☉}$, respectively. Curve $d$ corresponds to the hydrogen envelope of a white dwarf. The heavy solid line labeled PPT represents the predicted plasma phase transition.Reuse & Permissions

Figure 34

(Color) The interior structure of Neptune is sensitive to the high pressure properties of water. (a) Schematic of the interior of Neptune. Reproduced from 128. (b) Phase diagram of high-pressure water. Adapted from 46.Reuse & Permissions

Figure 35

Models used to predict the interior structure of Jupiter are tested with strong shock experiments. (a) Summary plot of recent high-pressure shock Hugoniot measurements of $D_2$. Adapted from 168. (b) Plot showing the sensitivity of calculations of the interior of Jupiter to the models of the high-pressure EOS of hydrogen. Adapted from 273. Different curves correspond to the following models. LM-A: Modified Ross linear mixing model. LM-H4: Linear mixing, with ${\mathrm{D}}_4$ chains, ${\mathrm{D}}_2$ molecules, and a ${\mathrm{D}}^{+}+e^{-}$ fluid metal. LM-SOCP: Ross linear mixing model, only with the one component plasma (OCP) replaced with a screened OCP for the metallic (atomic) fluid free energy. SCVH-I: The Saumon-Chabrier, Van Horn EOS. SESAME-p: original SESAME, patched to better reproduce data in the molecular regime for $P<0.2\mathrm{Mbar}$.Reuse & Permissions

Figure 36

The high-pressure properties of water are probed with strong shock experiments. (a) Plot of the measured EOS of water along the principle Hugoniot, at pressures up to $\sim 1000\mathrm{GPa}$. (b) Measurements of the reflectivity of shocked water vs shock velocity and shock pressure. (c) Analysis of the decomposition of the dc conductivity of water at high pressure along the isentrope appropriate for the interior of Nepture. Adapted from 47.Reuse & Permissions

Figure 37

Models of accreting compact objects, such as neutron stars or black holes, and an x-ray spectrum from such an object. (a) Accretion disk model for low-mass x-ray binaries. Adapted from 139. (b) Stellar wind model for high-mass x-ray binaries. Adapted from 317. (c) X-ray spectrum from the Chandra medium energy grating spectrometer of the photoionized plasma in the immediate vicinity of Cyg X-3 x-ray binary. The Cygnus X-3 binary system sits at a distance of $\sim 10\mathrm{kpc}$, and has a binary orbital period of $4.79\mathrm{hr}$. Adapted from 226.Reuse & Permissions

Figure 38

The results from experiments on the Z facility test models of photoionized plasmas. (a) $Z$-pinch x-ray flux spectral measurement at peak power with an XRD array (stepped lines), a transmission grating spectrometer (solid circles), and a PCD array (solid squares). Shown for comparison is a peak-normalized $T_r=165\mathrm{eV}$ black-body spectrum. Adapted from 96. (b) X-ray spectrum in a scaled experiment done on the $Z$-pinch facility. The figure shows the absorption spectrum of iron lines from ions with an open $L$ shell and of sodium and fluorine lines from ions with an open $K$ shell. Adapted from 96. (c) Calculations of the ionization distribution from the photoionized plasma models GALAXY, CLOUDY, and FLYCHK compared with observations. Adapted from 96. (d) Calculations of the ionization distribution from the photoionized plasma models NIMP and GALAXY, compared with that observed in the experiment of (a). Adapted from 256. (e) A calculation using the GALAXY model of the average ionization of iron vs electron density for input conditions described in the text, which were similar to those of the experiment of (a). Adapted from 228.Reuse & Permissions