Experimental astrophysics with high power lasers and Z pinches

With the advent of high-energy-density HED experimental facilities, such as high-energy lasers and fast Z-pinch, pulsed-power facilities, millimeter-scale quantities of matter can be placed in extreme states of density, temperature, and/or velocity. This has enabled the emergence of a new class of experimental science, HED laboratory astrophysics, wherein the properties of matter and the processes that occur under extreme astrophysical conditions can be examined in the laboratory. Areas particularly suitable to this class of experimental astrophysics include the study of opacities relevant to stellar interiors, equations of state relevant to planetary interiors, strong shock-driven nonlinear hydrodynamics and radiative dynamics relevant to supernova explosions and subsequent evolution, protostellar jets and high Mach number flows, radiatively driven molecular clouds and nonlinear photoevaporation front dynamics, and photoionized plasmas relevant to accretion disks around compact objects such as black holes and neutron stars.


I. INTRODUCTION
Over the past two decades, we have seen the emergence of a new experimental capability in the form of high-energy density ͑HED͒ facilities. These include high power lasers and fast magnetic pinch machines ͑"Z pinches"͒, which were developed largely as a result of the national inertial confinement fusion ͑ICF͒ program ͑Lindl et al., 2004;Matzen et al., 2005͒. Hand in hand with the emergence of these HED experimental facilities came the realization that a new class of laboratory astrophysics could be pursued ͑Ripin et Rose, 1991;Drake, 1999;Remington et al., 1999Remington et al., , 2000Takabe, Measurements of these conditions and their evolution, when properly diagnosed, allow theoretical models and computer simulation codes to be tested under the extreme conditions relevant to HED regimes of astrophysics. Examples include measurements of ͑i͒ opacities relevant to stellar interiors ͑Rogers and Iglesias, , 1998Arnett, 2001;Bailey et al., 2002;Chenais-Popovics, 2002;Wang et al., 2004͒, ͑ii͒ the phase, conductivity, and equations of state of matter under conditions relevant to planetary interiors ͑Celliers et Knudson et al., 2004;Saumon and Guillot, 2004͒, ͑iii͒ scaled, strong-shock-driven turbulent dynamics relevant to supernova explosions ͑Robey, Zhou, et al., 2003;Drake, Leibrandt, et al., 2004;Miles, Braun, et al., 2004͒; and ͑iv͒ ionization states of radiatively pumped photoionized plasmas relevant to accretion disks surrounding black holes or neutron stars ͑Foord et al., 2004͒. Such measurements allow astrophysical models and largescale simulation techniques to be tested and verified under relevant conditions. In each of these four areas, astrophysical models and simulations have been tested against HED laboratory data, leading to improvements in the models or modeling techniques, or a realization of the limitations of the simulation methods.
To achieve the relevant high-temperature, highpressure, or strong shock conditions requires focusing macroscopic amounts of energy ͑E տ 1 kJ͒ into small spatial scales ͑L Շ 1 mm͒ over very short time intervals ͑␦t 1 s͒. This allows the heating rates to greatly exceed the losses, resulting in high temperatures, pressures, and densities. High-energy, pulsed lasers achieve this by their ability to focus their energy into microscopic volumes over nanosecond time scales. Magnetic pinch facilities ͑Z pinches͒ achieve this by discharging large currents ͑տ1 MA͒ through a cylindrical can or wire array that then implodes due to the J ϫ B forces. Upon stagnation on the axis, the kinetic energy of imploding wires and the magnetic energy of the axial current is converted into an intense burst of heat and radiation. Both approaches for achieving HED conditions in the laboratory have been developed successfully over the past two decades. Sophisticated time, spatially, and spectrally resolved diagnostics have also been developed ͑Budil et al., 1997;Boehly et al., 1999;Koch et al., 1999;Heeter et al., 2001;Landen et al., 2001͒. It was only after the deployment of such diagnostics on these facilities that the field of HED laboratory astrophysics has emerged and grown.
Connections to astrophysics achievable on these HED facilities have been pursued vigorously over the past decade, and the rate of progress has been steadily increasing. This is the topic of our review article, which is written with two separate audiences in mind: plasma physicists ͑such as laser experimenters, for example͒ and astrophysicists. We try to discuss each topic at a level that an interested researcher, not necessarily expert in the specifics, can still follow the essence of the discussion. Ample references are given, so that more in depth reading can easily be pursued. In Sec. II, a discussion of HED facilities is given, along with descriptions of typical classes of experiments. Section III is dedicated to a discussion of opacities and their impact on pulsating stars, such as the Cepheid variables. We discuss supernovae and supernova remnants, along with relevant laboratory experiments, in Secs. IV and V. Protostellar jets, high Mach number flows, and relevant experiments are discussed in Sec. VI. The dynamics of photoevaporation fronts in radiatively driven molecular clouds, such as the Eagle Nebula, are described in Sec. VII. Planetary interiors and the properties of matter under extreme states of pressure and density are the subject of Sec. VIII, and the radiatively dominated conditions around an accreting compact object are discussed in Sec. IX. We conclude with an outlook for the future in Sec. X.

A. Introduction
The emerging field of high-energy-density laboratory astrophysics could not have developed 20 years ago. The necessary energy sources and diagnostic technologies did not exist. In the present section, we provide an overview of the remarkable facilities that can concentrate energy to levels of MJ/ cm 3 , and then diagnose the results as a function of time, space, and spectral content. We begin with a description of pulsed, high-energy lasers and fast Z pinches and then discuss two examples of typical astrophysics-related experiments.

B. High-energy lasers
A number of high-energy lasers have been constructed during the past 30 years, motivated by the challenge of achieving "inertial confinement fusion." The long-term goal is to create miniature fusion explosions with an energy gain of about 100. Such a laser system begins with a very high-quality laser beam, initially of low energy, which propagates through and extracts energy from Nd-doped laser glass. The first challenge is to prevent defects and diffraction from damaging the laser components as the energy per unit area of the laser beam reaches high levels. The second is to extract a large fraction of the stored energy. The first challenge was met in the 1970s, leading to several high-energy lasers capable of delivering Ͼ1 kJ of laser energy to a target. The largest of these lasers include the Omega laser at the Laboratory for Laser Energetics of the University of Rochester ͑Boehly et al., 1999͒, the Gekko XII laser at Osaka University in Japan ͑Yamanaka et al., 1987͒, and formerly the Nova laser at the Lawrence Livermore National Laboratory ͑Campbell et al., 1986͒. A number of similar but smaller lasers have also contributed to the results discussed below, such as LULI at Ecole Polytechnique in Paris, France; Vulcan at Rutherford-Appleton Laboratory near Oxford, England; Trident at Los Alamos National Laboratory; Helen at Atomic Weapons Establishment laboratory in Aldermaston, England; Janus at Lawrence Livermore National Laboratory; and the Nike laser at the Naval Research Laboratory, which amplifies KrF light in gas. Figure 1͑a͒ shows one example of such a laser system, the Omega facility, which can deliver 30 kJ to a target. The laser occupies approximately the area of one ͑American͒ football field. The initial laser beam, formed and amplified in the center of the laser bay, is split, amplified further, and eventually feeds the 60 amplifier chains that proceed down the sides of the laser bay toward the output end. Frequency conversion crystals then triple the frequency of these laser beams, decreasing their wavelength from 1.05 to 0.35 m, and mirrors direct the laser beams toward the center of the target chamber. Typical laser pulse durations can range over 0.2-10 ns, and can be flat-topped, Gaussian, or customdesigned shapes. Beams can be individually pointed and focused, and within limits individually timed. Spot intensity spatial profiles can be tailored with phase plates, with spot diameters in the range of 0.2-1 mm. Larger spots, up to ϳ3 mm diameter, can be achieved by removing the phase plates and defocusing the beams.
The second challenge cited above, of using the stored energy more efficiently, is being met by the National Ignition Facility ͑NIF͒, now under construction at Livermore ͑Hogan et al., Miller, 2004;Moses, 2004͒ and by the Laser MegaJoule ͑LMJ͒ under construction in France ͑Bettinger and Decroisette, 1999͒. For the laser beam to extract more of the stored energy it must pass through the Nd-doped glass several times, without destroying the quality or the focusability of the laser beam. The NIF and LMJ laser systems, with 192 and 240 beams, respectively, are anticipated to deliver ϳ2 MJ of laser energy to a target. This will enable the study of larger, hotter systems involving stronger shock waves and higher energy density configurations. Important new regimes will become accessible with these higher energy lasers; as discussed briefly in Sec. X.

C. Fast Z pinches and other pulsed power facilities
Pulsed power devices are also proving to be useful for experiments related to astrophysics. A pulsed power machine delivers a large current ͑and voltage͒ to a load, in a short, intense pulse ͑varying from a few ns to a few hundred ns͒. The most common device driven by pulsed power is a Z pinch ͑Ryutov, Derzon, and Matzen, 2000͒. In a Z pinch, stored electrical energy drives a large current through a cylindrical conductor, resulting in a large magnetic pinch force. This force accelerates the conducting matter inward, causing it to collide at the center of the pinch, converting kinetic energy and magnetic energy to thermal energy, much of which is radiated as x rays.
The largest of the existing Z-pinch facilities is the "Z" generator at Sandia, shown in Fig. 1͑b͒, which can generate a current of 20 MA; it is now being refurbished to increase the current to ϳ30 MA and to provide a substantial degree of control over the pulse shape ͑Matzen et al., 2005͒. There exist also two 5-10-MA facilities, the Saturn facility at Sandia and Angara-5 at Troitsk ͑Rus-sia͒, as well as several 1-MA facilities, of which the MAGPIE generator at the Imperial College ͑London͒ is used most actively for experiments in laboratory astrophysics.
Z-pinch experiments permit several possible applications. First, by using an array of hundreds of high-Z wires one can obtain efficient conversion of electrical energy into thermal x rays ͑Sanford et al., 2000͒. The Z machine at Sandia National Laboratories, as shown in Fig. 1͑b͒, for example, can produce nearly 2 MJ of thermal x rays at a temperature above 1 ϫ 10 6 deg. This x-ray energy can be used to launch a shock wave, but with much more energy and over a much larger area than is possible in laser experiments, which can be an advantage ͑Drake, 2002a͒. Second, by using many wires of moderate-Z material, one can produce large fluxes of K␣ x rays at energies of a few keV. This is useful for radiation transport experiments. Third, by manipulating the wires themselves one can produce other effects of interest. For example, by using a conical wire array one can produce a jet of material that radiatively collapses and is relevant to astrophysical jets ͑Lebedev et al., 2002, 2005b͒. FIG. 1. Examples of high-energy-density experimental facilities. ͑a͒ 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 ͑Boehly et al., 1999͒. Image provided courtesy of the University of Rochester Laboratory for Laser Energetics. ͑b͒ Schematic of the Z facility at Sandia National Laboratories ͑Albu-querque͒. 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 MA ͑Matzen et al., 2005͒. Image provided courtesy of the Sandia National Laboratory at Albuquerque.
In addition to Z pinches, it has been demonstrated that pulsed power devices can use J ϫ B forces to accelerate flyer plates. Specifically, the Z machine has accelerated 9-mm-square, 0.35-mm-thick plates of Al to velocities above 20 km/ s ͑Knudson et al., 2001, 2003͒. Used as flyer plates, this permits equation of state experiments at pressures above a Mbar ͑10 12 dynes/ cm 2 ͒, which, together with work done on lasers, is directly relevant to the interiors of gas giant planets.

D. Astrophysics experiments
The experiments discussed in this article typically use one of two basic methods. In "hohlraum" experiments, known in inertial fusion as "indirect drive," a number of laser beams are used to irradiate the inner surface of a cavity made with a high-Z material; beams penetrate the cavity through several ͑small͒ holes. This is a hohlraum. Energies of tens of kJ can heat few-mm-scale hohlraums to temperatures of kT = 100-200 eV. The experimental package may be located inside the hohlraum, to locate a sample within a uniform x-ray environment, outside the hohlraum, to control the orientation of the x-ray flux to it, or on the side of the hohlraum, to produce planar acceleration of the package. Many such experiments begin with the use of ablation by soft x rays the hohlraum contains, in order to create a pressure that drives a shock wave into some material. Other experiments are designed so that x rays in the hohlraum penetrate and heat the material to be studied.
The hohlraum geometry can also be created in the Z-pinch diode. In this case, the fast pinch is formed on the axis of the hohlraum. The experimental package can be situated either inside the hohlraum or on its surface; secondary hohlraums can also be used ͑see Sec. VIII.B in Ryutov, Derzon, and Matzen, 2000͒. An experiment using a Z-pinch driven primary plus secondary hohlraum is shown in Fig. 2͑a͒. This experiment, which is discussed further in Sec. III, measured the opacity of iron under conditions relevant to stellar envelopes, and was directly relevant to reducing uncertainties in the models of pulsating stars, the so-called Cepheid variables ͑Rogers and Springer et al., 1997͒. The Z pinch at the Saturn pulsed power facility at SNLA drove concentric primary and secondary cylindrical hohlraums. An iron sample placed in the secondary hohlraum was heated to equilibrium temperatures of ϳ20 eV at a density of ϳ10 −4 g/cm 3 . Using a high-resolution, transmission grat- FIG. 2. Examples of laboratory astrophysics experiments done on high power lasers and Z-pinch facilities. ͑a͒ 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 Springer et al., 1997. ͑b͒ Measurement of the Fe sample transmission spectrum from the experiment sketched in ͑a͒. Adapted from Springer et al., 1997. ͑c͒ Typical hydrodynamics experiment using direct laser irradiation. In this case, the experiment ͑Robey et al., 2002͒ is to study the interaction of a strong shock with a density clump, which is a typical astrophysical problem ͑Klein et al., 2003͒. Several of the Omega beams are used to generate a source of x rays ͑a backlighter, see text͒ situated at the opposite side of the experimental assembly. ͑d͒ 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 Robey et al., 2002. ing spectrometer, the transmission of broad-band x rays, from the Planckian hohlraum radiation field, through the sample was spectrally recorded, which allowed the opacity of Fe to be determined with high spectral resolution as shown in Fig. 2͑b͒. This data set was used to test models of the opacity of Fe under stellar envelope conditions.
The other typical setting is a so-called "direct drive" setting, used on high intensity lasers ͑not on Z pinches͒, where laser beams are focused directly onto the experimental target. Figures 2͑c͒ and 2͑d͒ illustrate such an experiment at the Omega laser. The Omega system was built to study direct drive laser fusion, in which laser beams directly strike a capsule, causing it to implode and produce fusion. This explains the large number of beams ͑60͒ and their even distribution ͑Fig. 1͒. On Omega, a planar shock can be launched using at most 12 ͑of the 60͒ beams. In this case the ablation by the laser irradiation creates the pressure that launches the shock to initiate the experiment. The experiment shown in Fig.  2͑c͒ shows a ϳ120-m-diameter solid Cu sphere embedded in a solid plastic ͑CH͒ cylinder ͑Klein et al., 2000Robey et al., 2002͒. The laser drive launches a strong shock down the CH ͑ ϳ 1 g/cm 3 ͒, which has decayed to P shk ϳ 12 Mbar by the time it reaches the location of the Cu sphere. Upon passage through the Cu sphere, the shock compresses it, and induces vortical flow, morphologically similar to a smoke ring. The evolution of this shock-sphere dynamics is captured in a sequence of side-on x-ray shadowgraph images ͑radio-graphs͒ shown in Fig. 2͑d͒. The gold spatial resolution grid shown in the upper left-hand corner of the images has a grid spacing of 63.5 m, and is used to simultaneously measure magnification and spatial resolution of the x-ray imaging camera used. This experiment is discussed in more detail in Sec. V.
In many experiments, whether hohlraums or direct laser irradiation are used, additional laser beams produce x rays for diagnostic purposes. In fact, one often uses more laser beams for this purpose than to drive the experiment. Some of the beams may be used to irradiate a small spot on a material plate, situated behind the experimental package and known as a backlighter. Under laser irradiation, this plate produces energetic x rays, typically in an emission line or band. The x-ray energy is chosen so that components or structures in the target selectively absorb these x rays. When they are imaged onto a detector, the result is a radiograph of the target ͓Fig. 2͑d͔͒ not unlike the chest x ray a doctor may request. In addition, these diagnostic x rays can also be used for absorption spectroscopy or for time-resolved measurements. We describe below the results from a wide variety of experiments utilizing similar techniques as those illustrated in Fig. 2. The specific configuration and diagnostic details of each individual experiment presented will not be discussed in any depth, to allow a wider selection of results to be shown. Details for each specific experiment can be found in the references.

III. OPACITIES AND CEPHEID VARIABLES
Understanding the evolution of stars from birth to death forms one of the fundamental challenges facing astronomers and astrophysicists. A star begins from an initial "rapid" ͑severalϫ 10 6 yrs͒ gravitational collapse of a dense clump in a molecular cloud, in a region where the Jeans' ͑gravitational͒ instability dominates other dynamics ͓e.g., Jeans = ͑4G͒ 1/2 Ͻother dynamic time scales in the cloud; here G is the gravitational constant and is the mass density͔. If the mass of the star exceeds about 0.1M Sun , the central temperature and density reach the point where thermonuclear fusion of hydrogen into helium becomes the dominant energy source. At this point, the star settles into its main sequence phase in the Hertzsprung-Russell ͑HR͒ diagram, that is, a plot of luminosity versus temperature or, equivalently, magnitude versus spectral type ͑Bohm-Vitense, 1989a; Hansen and Kawaler, 1995͒. When approximately 10% of a star's original hydrogen is converted to helium, hydrogen depletion in the core starts to become significant. At this point, the delicate balance between core-generated thermal pressure due to nuclear burning and the inwardly directed gravitational force is perturbed, upsetting the condition of hydrostatic equilibrium, and the core starts to contract. This contraction increases the temperature and density to the point where helium burning begins, leading to a corresponding rise in the energy generation rate and luminosity. The star enters its "blue-loop" phase ͑Bohm-Vitense, 1989b͒.
If the star is sufficiently massive, M Ն 5M Sun , its blue loop excursion is sufficiently large that its path on the HR diagram crosses and, more importantly, lingers in the Cepheid instability strip shown in Fig. 3͑a͒ ͑Bohm-Vitense, 1989a͒. In this phase, an interesting global dynamics can occur, namely, stellar pulsation. All stars in this strip are observed to pulsate, with luminosities varying by factors of up to 2 or 3 over periods of days to weeks. The classical Cepheids refer to the ␦ Cephei supergiant stars, which are the brightest in this class of variable stars. Several other classes of stars also fall into the Cepheid instability strip and are variable, such as the RR Lyrae, ␦ Scuti, and W Virginis variables. Understanding the mechanisms underlying such stellar pulsations has been an ongoing challenge in astrophysics.
A remarkable feature of Cepheid variable stars is that their pulsation periods P are proportional to their average luminosities as shown in Fig. 3͑b͒ ͑Bohm-Vitense, 1989a͒. Stellar pulsations result from a driven resonant standing compression wave of the star. Bigger stars are more luminous and, by virtue of their larger size, will have longer periods of pulsation. This relationship can be expressed as where Q is a constant, is the average density of the pulsating star, and Sun is the average density of the sun Sun Ϸ 1.4 g / cm 3 . For a given mass, ͑spatially͒ larger stars are more luminous, have lower average densities, and longer periods of oscillation, hence the luminosityperiod correlation. The criteria to set up a global standing wave in a star is based on hitting a resonance between a driving force and one or several normal modes of oscillation ͑pulsa-tion͒ in the star. Consider first a fictitious adiabatic star ͑Bohm-Vitense, 1989b͒, and assume a small pulsation randomly began, say, near to the convection layer. At peak compression, the temperature would be maximum due to the P . dV work done on the star by gravity. At peak expansion, the temperature would be minimum due to the P . dV work done by the star on itself during expansion. The radially outward velocity would be maximum at the equilibrium radius as the star was expanding outwards. If the star were truly adiabatic, this pulsation would continue forever, never growing ͑or decreasing͒ in amplitude. This would definitely not lead to the large global pulsations of ϳ20% in radius characteristic of Cepheid variable stars. To generate a global pulsation requires a resonant driving force, a condition that can result from a nonadiabatic heat flow. Similar to pushing a swing at its resonance frequency, as the star leaves peak compression and moves into its expansion phase, e.g., near the point of peak outward velocity, there needs to be a slightly increased outward push. This can be due, in this case, to a higher interior temperature and, hence, higher pressure. This added outward push, in phase with the oscillation, causes the pulsation amplitude to increase, leading to a variable star. The resulting phase relations are shown in Fig. 3͑c͒ for a ␦ Cephei star, showing periodic oscillations of magnitude, temperature, spectral type, radial velocity, and radius. Notice that the radial velocity peaks in phase with temperature, which is proportional to pressure, and which occurs just after the star leaves peak compression ͑⌬R =0͒ and starts to expand.
Opacity plays a key role in causing this resonant temperature enhancement. For a solar mixture of H, He, and "metals" ͑Z Ն 3͒, the Rosseland mean opacity R is shown as a function of temperature T for a constant value of / T 3 ͑where corresponds to density͒ in Fig.  4͑a͒ ͑Rogers and Iglesias, 1994͒. There are bumps or broad peaks in the average opacity as temperature is increased, corresponding to thermal energies sufficient to excite or ionize H, He, and higher-Z metals through their various electron shells. On the rising side of one of these bumps ͑sometimes called " mountains"͒, resonant conditions can occur in the heat flow that can lead to stellar pulsations. As the star contracts, the temperature rises increasing the opacity, which allows less radiative heat from the core to leak out, raising the temperature and pressure even further. This leads to a slightly enhanced outward push as the star starts its outward movement, in resonance with the oscillatory motion of the star. Near peak expansion, the temperature drops due to the work done by the star on itself. This lowers the opacity, allowing more radiative heat to leak out, dropping the interior pressure, allowing the star to contract more strongly. The result is that in this resonant FIG. 3. Cepheid variable stars offer a useful "galactic yardstick," based on their pulsation dynamics. ͑a͒ 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 ͑K͒ in parentheses, and their corresponding spectral types. Adapted from Bohm-Vitense, 1989a. ͑b͒ Plots of the stellar pulsation period-magnitude ͑or luminosity͒ linear relation, showing that the longer the period of oscillation, the brighter the star ͑lower magnitude͒. 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 Bohm-Vitense, 1989a. ͑c͒ The phase relations for the variable star ␦ Cephei, showing the correlations between periodic pulsations of visual magnitude ͑⌬m͒, i.e., brightness, effective temperature ͑T͒, spectral type ͑Sp͒, radial velocity ͑v r ͒, and radius ͑⌬R͒. Adapted from Bohm-Vitense, 1989a. condition the amplitude of global oscillation increases leading to a pulsating star. These pulsations do not increase in amplitude indefinitely, however. Once the pulsation amplitudes become large enough that the heating during compression takes the opacity over the top of the mountain, the opacity drops on compression, allowing radiation to leak out, and serving as a damping mechanism.
There is an intimate connection between stellar pulsation period and opacity. Global oscillations are standing sound ͑compression͒ waves in the star, so the period must be proportional to the ratio of star diameter to average sound speed. But sound speed varies with temperature as T 1/2 . Since a higher stellar opacity holds in heat by inhibiting radiative heat losses, temperature is a monotonically increasing function of opacity. The result is that an increased stellar opacity leads to a shorter period of pulsation. This is summarized by writing the following approximate relation for stellar oscillation period: where D star and c s correspond to the stellar diameter and average sound speed. For simplicity, we have assumed, over a small enough interval of temperature on the rising side of the bump, that ϳ T m and n =1/m. This period-opacity relation is portrayed rather dramatically in a plot of the period of oscillation of the second harmonic ͑P 1 ͒ versus the period of the fundamental mode ͑P 0 ͒ for beat Cepheids shown in Fig. 4͑b͒. Using older opacities, which did not include all relevant transitions for metals, in particular Fe, the calculated opacities were too low and the calculated pulsation periods were too large ͑Cox and Tabor, 1976͒. When a more complete accounting of the Fe opacities was taken in the opacity code OPAL ͑Iglesias and Rogers, 1991;Rogers and Iglesias, 1992͒ the calculated periods for the beat Cepheids were brought into much better agreement with observations as shown in Fig. 4͑b͒. Opacity calculations are enormously complex, especially for higher-Z materials ͑Z Ͼ several͒. The OPAL calculations have been improved by comparison with experiments under a variety of conditions, as shown in Figs. 4͑c͒ and 4͑d͒. In one of the first Fe opacity measurements, done on the Nova laser, one laser beam with a wavelength of 0.53 m was used to heat a 250-nmthick Au foil by direct irradiation with a square 1-ns pulse of 3.3 kJ ͑Da Silva et al., 1992;Springer et al., FIG. 4. Modern opacity simulations, tested against experiments, have improved our understanding of cepheid variable star pulsation. ͑a͒ Opacity versus temperature for a 15-element mixture of solar composition, along a path of constant / 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 He͒. Results from a previously used set of Los Alamos opacities for Z = 0.02 are also shown. Adapted from Rogers and Iglesias, 1994. ͑b͒ Diagram of the ratio of the first two harmonics periods of a beat Cepheid variable star. Circles represent observations. The upper set of three ͑dashed͒ curves correspond to the simulated result using older opacities, which ignore the full fine structure of the metals. The lower ͑solid͒ curves correspond to simulations with OPAL-DTA, including the full fine structure, in particular, for Fe. Adapted from Rogers and Iglesias, 1994. ͑c͒ Plot showing measured versus calculated transmission through a thin Fe sample heated to conditions of T Ϸ 20 eV and Ϸ 5 mg/cm 3 . Two OPAL opacity simulations are shown, one using DCA with hydrogenic oscillator strengths, which ignores term splitting ͑top curve͒, 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 Rogers and Iglesias, 1994. ͑d͒ Comparison of theoretical Fe transmission spectra at the measured conditions of T Ϸ 20 eV, and Ϸ 10 −4 g/cm 3 . The Including the transition fine structure changes the predicted average opacities significantly. Adapted from Springer et al., 1997. 1992͒. The x-ray flux thus generated volumetrically heated and expanded a 20-nm sample of Fe to a temperature of ϳ20 eV at densities of ϳ5 mg/cm 3 . A second laser beam with a 2-ns square pulse of 0.53-m light irradiated a second Au foil, generating backlighter x rays whose transmission through the sample was measured with a time-resolved ͑"streaked"͒ extreme ultraviolet spectrometer. The measured Fe transmission spectrum, shown in Fig. 4͑c͒, showed a dominant absorption feature centered at 70 eV corresponding to an important ⌬n =0 ͑n =3 to n =3͒ transition, overlooked in previous opacity calculations, such as that shown by the upper curve corresponding to a detailed configuration accounting ͑DCA͒ calculation ͑Cox and Tabor, 1976; Rogers and Iglesias, 1994͒. The newer DTA ͑detailed term account-ing͒ calculations using the OPAL opacity code, including term splitting ͑Iglesias and Rogers, 1991;Rogers and Iglesias, 1992͒ reproduce this feature quite well. Transitions such as this, missing in previous opacity calculations, lead to the enhanced opacities in the models of beat Cepheid variables that allow the models to more closely reproduce the observed pulsation frequencies as shown in Fig. 4͑b͒.
Opacity models differ more significantly at lower densities Ͻ 1 mg/cm 3 , where density-induced line broadening and smearing is lower. Under these conditions, "forests" of fine-structure transitions can be resolved experimentally. The time scales to achieve steady-state, local thermodynamic equilibrium ͑LTE͒ conditions at lower densities, however, is longer. In this regime, large Z-pinch facilities offer a more attractive setting for such opacity measurements. Their characteristic time and spatial scales are longer. An example of a key opacity experiment done on Fe on the Saturn Z-pinch facility is shown in Figs. 2͑b͒ and 4͑d͒ ͑Springer et al., 1997͒ and briefly described in Sec. II. The obtained transmission spectrum of this Fe sample ͑ =10 −4 g/cm 3 ͒ was then compared with predictions of various LTE opacity models, as shown in Fig. 4͑d͒. The supertransition array ͑STA͒ model ͑Bar-Shalom et al., 1989͒, which averages over large groups of configurations, overpredicts the transmission data in this regime, whereas the unresolved transition array ͑UTA͒ model ͑Iglesias and Wilson, 1994͒ underpredicts the data. The OPAL calculation ͑Iglesias and Rogers, 1991;Rogers and Iglesias, 1992͒, which captures the complex arrays of fine-structure absorption lines, falls in between in the figure and is in much better agreement with the data ͓shown in Fig.  2͑b͔͒. Experimental measurements such as those shown in Figs. 4͑c͒ and 2͑b͒ are indispensable in refining and "calibrating" sophisticated opacity models such as OPAL.

A. Introduction
A core-collapse supernova ͑SN͒ marks the explosive death of a massive star. Supernovae ͑SNe͒ involve a very broad range of physical processes. Their description re-quires the coupling of disparate areas of science, such as nuclear physics, general relativity, hydrodynamic stability, and turbulence. To make things even more complex, there are several types of SNe with different mechanisms of energy release.
The kinetic energy release in a typical SN event is ϳ10 51 ergs, but only a few percent of this amount is emitted as visible light. Still, supernovae are sometimes brighter than their entire host galaxy. The light as detected by optical telescopes comes not from the core of the exploding star, where the energy release has occurred, but rather from a photosphere, to which the energy is transported by a complex combination of hydrodynamic flows and radiative transport. In linking the energy release in the SN core with the visible light curve, a correct description of the transport of material and radiation is very important. Opacity models in particular are critical to modeling radiation transport. In this area, laboratory experiments are making significant contributions by providing direct measurements under the conditions relevant to a real problem.
A nice description of SN phenomenology, as well as existing theories of their formation, can be found, e.g., in the book by Arnett ͑1996͒. Other papers of general interest include Bethe ͑1990͒, Woosley ͑1990͒, and Woosley and Eastman ͑1997͒. Some more recent surveys can be found in "Cosmic Explosions" ͑Proceedings of the 10th Astrophysical Conference, College Park, Maryland, 1999, AIP Conference Proceedings No. 522͒. Supernovae are believed to explode by two fundamental mechanisms: collapse of the core ͑in large stars͒ and thermonuclear explosion ͑in small stars below eight solar masses at birth͒. Classification by types is based on spectra and is too involved to discuss here. We will focus on only core-collapse SNe ͑type II͒ and thermonuclear SNe ͑type Ia͒. Type-II SNe are thought to occur as the result of a gravitational collapse and neutronization of the iron core of the star; their formation is accompanied by generation of a short but very intense burst of neutrinos ͑carrying away some 99% of the released energy͒. Neutrinos form a blast wave near the center of the progenitor star, which ultimately, and by a mechanism still not fully understood, blows it apart and gives rise to a tremendous increase of luminosity. The collapsed core forms a neutron star that might later be detected as a pulsar. Experiments discussed in Secs. IV.C-IV.E are relevant to type-II SNe.
Type-Ia SNe are believed to be caused by a thermonuclear burn of carbon-oxygen white dwarfs. One of the key problems in the physics of this system is the propagation of the nuclear "flame" from the ignition point, specifically, the stability of the flame, and the transition from a subsonic burn ͑deflagration͒ to a supersonic detonation. There is a significant amount of information on these issues obtained in experiments on the propagation of chemical flames, summarized in particular by Williams ͑1985͒, with more recent work involving Khokhlov and others reviewed by Drake ͑1999͒. In the present experiments using current high-power lasers it is hard to expect that conditions for a thermonuclear burn of a DT mixture and propagation of ignition from the hot spot can be reached. Perhaps such conditions will be reached with the NIF and Megajoule facilities that are now under construction ͑see Secs. II and X͒. Type-Ia SNe, used to measure the distances to high-redshift galaxies, provide the essential data supporting the present conclusion that the expansion of the Universe is accelerating ͑Kirshner, 1999; Perlmutter et al., 1999͒. From the broad array of problems related to our understanding of SN explosions, we shall concentrate on the laboratory simulation of hydrodynamic phenomena in the type-II SN explosions. We choose this subset because, on the one hand, multidimensional hydrodynamic effects are thought to be very important ͑see Sec. IV.B for more detail͒ and, on the other hand, there already exist successful experiments of this type related to the shock breakout through the He-H interface. In addition, the analysis of the scalability and other constraints can be nicely illustrated; this example can serve as a template for similar analyses of other problems.

B. Multidimensional hydrodynamics in core-collapse supernovae
It is believed that the progenitor star, just before the SN explosion, had a layered ͑"onion-skin"͒ structure, with the dense core surrounded by layers of helium and hydrogen ͑Fig. 5 from Shigeyama and Nomoto, 1990͒. When the core collapses, an outward propagating shock is launched by the "core bounce" process. When this shock reaches the surface of the star, after an interval of ϳ1 h, the star lights up in a burst of luminosity, and the optical SN has begun. The observed light curve for the most famous recent supernova in a Large Magellanic Cloud, SN 1987a, is shown in Fig. 6, and the inset shows temperature versus time at the surface of the star at and following shock break out ͑Arnett, 1996͒.
Theoretical analyses have shown that it is impossible to explain the explosion of SN type II without taking into account two-dimensional ͑2D͒ and 3D hydrodynamic effects. The energy deposition by neutrinos in the zone surrounding the collapsing core is insufficient, in a spherically symmetric case, to drive the explosion of the star's outer layers. Certainly, some complex nonspherically symmetric motions must be involved, and only their inclusion ͑in a phenomenological manner͒ by Bethe and Wilson ͑1985͒ allowed creating a plausible model for supernova explosions.
Another problem where 3D dynamics are important is the postshock mixing of the star's inner parts, mainly heavy core elements, outwards into the overlying envelope of hydrogen and helium. The observed early appearance of heavy elements, such as 56 Ni and 56 Co, in the photosphere of SN 1987A ͓see Sutherland ͑1990͒, and references therein͔ is incompatible with the spherically symmetric expansion; significant effort has been spent on developing a mixing theory based on the Rayleigh-Taylor ͑RT͒ instability ͑Arnett, 1988; Arnett et al., 1989͒. To illustrate the magnitude of mixing required to explain the observations, we show a vertical dashed curve at M r / M ᭪ = 13.4 in Fig. 5 ͑Shigeyama and Nomoto, 1990͒. This corresponds to the location to which 56 Co had to be premixed ͑which is nearly the entire progenitor star͒ so that a 1D explosion simulation reproduced the observed light curve for SN1987A. Figure 7 ͑Kifonides et al., 2000, 2003͒ illustrates the spikes produced FIG. 5. Variation of the density distribution after the explosion of SN 1987A. ͑Shigeyama and Nomoto, 1990͒. Time t = 0 corresponds to the instant just before the explosion. M r is a Lagrangian mass within a certain radius. Steep density gradients in the progenitor star situated at M r / M ᭪ Ϸ 2.5 and M r / M ᭪ Ϸ 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 r / M ᭪ Ϸ 13.5 indicates the location out to which core 56 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 Shigeyama and Nomoto, 1990. FIG. 6. Light curve for SN1987A. The "+" symbols are the observed light curve, and the thin solid line is an analytic model described by Arnett ͑1996͒. Different dates indicated show when x rays were first detected on day 139 by the Ginga/ Mir experiment, when ␥ rays from 56 Co were detected by the Solar Maximum Mission ͑SMM͒ at day 178, and when subsequent detections of ␥ rays occurred by several balloon experiments ͑CIT, LM, FG͒. Inset: A calculation of the evolution of temperature versus time as the shock breaks out from the surface of the star. Adapted from Arnett, 1996 in the strongly nonlinear stage of the RT instability. The RT spikes have just encountered the reverse shock and slowed down abruptly. A principal motivation of the experiments discussed below is that multidimensional simulations of the RT instability had failed to explain the observations. We call this here the "SN mix problem." Two possibilities follow: the simulations might be in error or other physics might be responsible for the observations. Well-scaled experiments have shown, however, that the simulations are probably correct with regard to the large-scale RT behavior.
Experiments have also led to the realization that hydrodynamic turbulence might affect the behavior of SNe in ways the simulations cannot reproduce. This is one example of other physics with the potential to affect the observed quantities. Experiments now underway are addressing this possibility. Another example of other physics is provided by spectropolarimetric studies, which allow an evaluation of the asphericity of an object. These have shown that between two weeks and two months after the explosion most SNe manifest gross deviations from spherical symmetry ͑Jeffery 1991; Trammell et al., 1993;Tran et al., 1997;Leonard et al., 2000;Wang et al., 2002͒. These observations are consistent with the suggestion that the collapse of a rotating, magnetized stellar core might produce bipolar jets that would perforate the outer layers and quickly reach the photosphere, thereby providing one more explanation for the early arrival of heavy elements to the photosphere ͑Fryer, 1999͒. A strong enough magnetic field breaks the spherical symmetry and may generate magnetohydrodynamics instabilities that are typically three-dimensional and might produce such jets ͑LeBlanc and Wilson, 1970;Spruit, 1999;Fryer and Heger, 2000;Wheeler et al., 2000͒. This motivated a recent set of hydrodynamic calculations of jet-driven SNe explosions by Khokhlov et al. ͑1999͒;Fig. 8 shows one of their results. Scaled hydrodynamic experiments relevant to this model are also now underway.
The importance of nonspherically symmetric hydrodynamics is also shown by the fact that neutron stars usually received a strong "kick" during the explosion that creates them ͑Cordes et al., 1993;Lyne and Lorimer, 1994͒. This seems to imply that there are significant gross asymmetries at an early stage of the implosion which are enhanced in the course of the implosion ͑Burrows and Hayes, 1996;Fryer et al., 1998;Scheck et al., 2004͒. In addition, relatively little is known about effects of rotation in the core-collapse process. The angular velocity of a progenitor varies both in radius and in the azimuthal angle. The velocity shear will grow during the implosion causing the development of shear-flow turbulence, whose effect on the mix during the implosion may be an important factor ͑Heger et al., 2000͒. An interesting new 2D computational study ͑Kifonidis et al., 2006͒ offers a different approach to breaking the spherical symmetry of the explosion. Lowering the neutrino luminosity but extending its duration and reducing its decay rate during the first second of the explosion allows hydrodynamic instabilities ͑advective-acoustic in-stability͒ in the neutrino heated postshock layers to grow to sufficient strength in low-order modes to deform the shock. This perturbed inner ejecta and shock allow the highest velocity metal clumps to exit the He layer prior to the formation of the reverse shock at the He-H "interface," and their velocities remain high. The interaction of the perturbed shock with the He-H inter- FIG. 7. ͑Color͒ Density distribution ͑log ͓g/cm 3 ͔͒ 1500 s after core bounce. The supernova shock ͑outermost discontinuity͒ is located at r Ϸ 9 ϫ 10 11 cm. A dense shell ͑visible as a whitish ring͒ has formed between the SN shock and reverse shock at r ϳ 5 ϫ 10 11 cm, with its outer boundary coinciding with the He/ H interface. The fastest moving RT spikes have just reached the reverse shock. Adapted from Kifonidis et al., 2003. FIG. 8. ͑Color͒ Jet-induced explosion. Frames show the density in the x-z plane passing through the center of computational domain, at 1.08 s after the jet initiation. The jet axis ͑and presumably the rotation axis͒ is vertical here. The size of the panel is 9 ϫ 10 9 cm vertically and 6 ϫ 10 9 cm horizontally. Adapted from Khokhlov et al., 1999. face induces the Richtmyer-Meshkov instability, which in turn leads to a deeper mixing of hydrogen into the core at late times. These 2D simulation results are much more consistent with the observations of SN1987A that previous results from this group ͑Kifonidis et al., 2000 Their results draw attention to the importance of capturing early-time, low-order modes and the mutual interaction of multiple stages of hydrodynamic instabilities from the core to the envelope. In the lexicon of HED laboratory experiments this would be called an "integrated simulation." Recent ͑Drake,  and continuing experiments have been addressing the role of low-order modes in mixing. Attacking the more complex problem with divergence and multiple interfaces should become viable on the National Ignition Facility.
In summary, there are several complex and still unresolved hydrodynamic problems which have a deep impact on our understanding of the supernovae starting from the central question of why they explode at all. A concerted attack on these problems, including scaled laboratory experiments, is both necessary and possible.

C. A sample problem: Shock wave breakout through the He-H interface
We use the problem of shock wave breakout through the He-H interface for designing scaled laboratory experiments. This example allows one to clearly identify the most important steps in developing scaled laboratory experiment. These steps ͑which will be described in more detail in the following subsections͒ are ͑i͒ ensure that a hydrodynamic description is adequate, ͑ii͒ evaluate the role of transport processes ͑such as heat conduc-tion͒, ͑iii͒ determine the equation of state, ͑iv͒ characterize initial conditions, and ͑v͒ consider whether some simplification in geometry is possible ͑e.g., can some time interval of evolution of a planar system adequately describe the evolution of a spherically divergent system͒.
As a representative set of plasma parameters in the He-H transition region ͑Table I͒, we have chosen a set of parameters based on the work of Müller et al. ͑1991͒. In Table I, L is the density gradient scale length, v is the characteristic velocity, T is the plasma temperature ͑the electron and ion temperatures are equal͒, and is the plasma density. The blast wave that blows the star apart first accelerates and then decelerates the transition region. During the deceleration the pressure gradient is still outward. Because this opposes the inward density gradient, the transitional zone is RT unstable. The characteristic acceleration experienced by a given fluid element upon arrival of the blast wave can be estimated as v / , with ϳ L / v, to be v 2 / L ϳ 2.5ϫ 10 5 cm/ s 2 ͑Ryutov et al., 1999͒. The gravitational acceleration is orders of magnitude smaller and is also negligible in the laboratory experiment to be discussed. The representative parameters of the first laboratory experiment simulating the He-H interface instability ͑Remington et al., 1997͒ are listed in the right-hand column of Table I.
We will now quickly go through the five questions formulated at the beginning to this section. As was shown by Ryutov et al. ͑1999͒, the hydrodynamic description applies to both systems, although in the case of a supernova the pressure is dominated by radiation, whereas in the laboratory experiment it is dominated by the gaseous pressure. The viscosity and thermal conductivity are small ͑i.e., the Reynolds and Peclet numbers are large͒. Under such circumstances, both systems can be adequately described by the Euler equations ͑e.g., Landau and Lifshitz, 1987͒.
The dominance of the radiation pressure in the case of the supernova means that the equation of state is that for the ideal gas with the adiabatic index ␥ =4/3. It is desirable that the medium used in the laboratory experiment have equations of state deviating not too strongly from that for the polytropic gas with ␥ =4/3. Even if some deviations are present, however, one should not expect the appearance of any dramatic differences, because the Euler equations are structurally stable with respect to variations of ␥.
Setting up appropriate initial conditions for 2D and 3D simulations of the dynamics at or near an "interface" usually starts with a set of 1D simulations, which determine the overall profiles for density, temperature, velocity, and other relevant quantities. There exist numerous simulations describing the propagation of the shock through the He-H interface ͓see, e.g., Müller et al. ͑1991͒ andKane et al. ͑2000͔͒. In their 1D versions, all are quite reliable and all present a similar picture of the main hydrodynamic parameters that are needed as a starting point for studying the 2D and 3D hydrodynamics. An example of the density and pressure profiles is shown in Fig. 9͑a͒.
In the laboratory experiment, the experimental package is driven by the ablation pressure produced by the absorption of the intense radiation on one of the package sides. Changing the shape and power of the laser pulse allows a certain degree of control over the time dependence of the ablation pressure. The temporal evo-TABLE I. Comparing characteristic parameters of a SN 1987a plasma in the He-H transition layer ͑t ϳ 2000 s͒ and of a laboratory experiment at t = 20 ns since the onset of the radiation drive.

Parameter SN 1987a
Laboratory experiment L ͑cm͒ 9 ϫ 10 10 5.3ϫ 10 −3 v ͑cm/ s͒ a 2 ϫ 10 7 1.3ϫ 10 5 ͑g/cm 3 ͒ 7.5ϫ 10 −3 4.2 p ͑dyn/ cm 2 ͒ 3.5ϫ 10 13 6 ϫ 10 11 Eu b 0.29 0.34 Re 2.6ϫ 10 10 1.9ϫ 10 6 Pe 2.6ϫ 10 5 1.8ϫ 10 3 a The velocity in this table is defined as the rate of broadening of the density peak ͓Figs. 9͑a͒ and 9͑b͔͒, not the interface velocity ͓Fig. 9͑c͔͒. b Eu is the Euler number, Eu= v͑ / p͒ 1/2 . lution of the shock wave strength and the density and pressure distribution near the interface where the RT instability is evolving can, for example, be modified. One can also vary the materials constituting the package and thickness of the layers. Figure 9͑b͒ shows the density and pressure profiles across the interface between copper and plastic obtained in this way. Indeed, these distributions are quite similar to those expected in the SN ͓Fig. 9͑a͔͒. The temporal dependence of the parameters in the simulation experiment can be adjusted to match that of the supernova. This is illustrated in Fig. 9͑c͒ ͑Kane,  with a plot showing the velocity versus time of the interface for the SN and laboratory experiment.
In the experiment by Remington et al. ͑1997͒ a planar geometry was used. This means that this particular experiment can imitate the real SN system only for a limited interval of time within which the radius of the He-H interface has not changed by more than 20% or so. This, in turn, means that only relatively shortwavelength perturbations can be simulated. Figure 9͑d͒ shows a sample radiograph from this experiment showing the RT evolution of a = 200 m wavelength perturbation well into the nonlinear regime.

D. Issues of the hydrodynamic similarity
An attractive feature of laboratory experiments for assessing the 2D and 3D SN hydrodynamics and for code validation is the ability to control and vary the initial conditions, repeat an experiment as many times as needed, and equip it with various diagnostics as required. However, in order to produce relevant results one has to constraint the variation of the parameters in such a way as to maintain the laboratory system to be hydrodynamically similar to its astrophysical counterpart ͑despite the 10-20 orders of magnitude differences in the spatial and temporal scales͒.
By now, a detailed analysis of the similarity constraints met in the hydrodynamics and magnetohydrodynamics is available ͑Ryutov et Ryutov, Drake, and Remington, 2000;Ryutov and Remington, 2002͒. This analysis has shown that the similarity constraints can be easily satisfied within the framework of a so-called Euler similarity, which holds if the Reynolds and Peclet numbers, as well as the magnetic Reynolds number, are very large in both systems.
The Euler similarity stems from the equations of ideal magnetohydrodynamics, FIG. 9. Hydrodynamic simulations for the supernova and laboratory experiment. ͑a͒ Spatial profiles of the pressure and the density for the SN at 2000 s, and ͑b͒ the laboratory experiment at 20 ns. Adapted from Ryutov et al., 2001. ͑c͒ The velocity of the He-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 Kane, Arnett, et al. ͑1999͒. ͑d͒ A radiograph obtained at t = 33 ns of the nonlinear RT induced mixing in the first scaled SN experiment. Adapted from Remington et al., 1997. ͑e͒ A sum over multiple images from the same experiment as shown in ͑d͒, corresponding to an average time of t ave = 35 ns. Adapted from Remington et al., 1999. corresponding to conservation of mass, momentum, and Faraday's law of induction ͑sometimes called the "line tying equation"͒.
Here v, , p, and B are the velocity, density, pressure, and magnetic field, respectively. Assuming that the fluid is polytropic, that is, that energy density is proportional to pressure, one can write the following energy equation ͑e.g., Landau and Lifshitz, 1987͒: ‫ץ‬p ‫ץ‬t where ␥ is the adiabatic index ͑the ratio of specific heats͒. For a fully ionized nonrelativistic gas ␥ is equal to 5/3; for a gas where the radiation pressure is dominant ␥ is equal to 4/3; for a diatomic molecular gas ␥ is equal to 7/5. Equation ͑4.2͒ implies that there are no dissipative processes in the fluid, so that the entropy of any fluid element remains constant. Consider the initial value problem for the set of equations ͑4.1͒ and ͑4.2͒. Let us present the initial spatial distributions of the density, pressure, velocity, and magnetic field in the following way: where L * is the characteristic spatial scale of the problem and the other quantities marked by an asterisk denote the value of the corresponding parameter at some characteristic point; the dimensionless functions ͑vectorial functions͒ f, g, h, and k are of order unity. They determine the spatial shape of the initial distribution. We note that there are five dimensional parameters determining the initial conditions: Let us then introduce dimensionless variables ͑which we denote by tilde͒ in the following way:

͑4.5͒
When one expresses the set of equations ͑4.1͒ and ͑4.2͒ in terms of the dimensionless variables, one finds that this set maintains its form, just all the quantities get replaced by their analogs bearing the tilde sign. Initial conditions presented in the dimensionless variables acquire the following form:

͑4.6͒
One sees that the dimensionless initial conditions for the two systems are identical if the dimensionless functions f, g, h, and k maintain their form, and the two dimensionless parameters v * ͱ * / p * and B * / ͱ p * remain un- ͑the abbreviation "inv" stands for invariant͒. The parameter v * ͱ * / p * is usually called "the Euler number" Eu. In other words, provided these two parameters are invariant and initial states are geometrically similar ͑i.e., the functions f, g, h, and k are the same͒, one would have the same dimensionless equations and the same dimensionless initial conditions for any two hydrodynamical systems meaning that the systems will evolve identically in a scaled sense.
Returning to the dimensional form, it is straightforward to show by substitution that Eq. ͑4.1͒ is invariant under the following scale transformation relating the supernova ͑SN͒ setting to the laboratory ͑lab͒ setting: where h, , p, and correspond to characteristic spatial, density, pressure, and time scales, respectively ͑Ryutov et al., 1999͒. When the transformation ͑4.8͒ is inserted into Eq. ͑4.1͒, the constants a, b, and c cancel, and the dynamics described by Euler's equation are indistinguishable in the SN hydrodynamics and the laboratory experiment. Both settings are probing the same nonlinear hydrodynamics. Any insights gained through the laboratory experiment apply directly to the SN through the mapping described by Eq. ͑4.8͒. For example, the deep nonlinear SN hydrodynamics illustrated in the simulation shown in Fig. 7 could be scaled to the laboratory via Eq. ͑4.8͒ and tested with experiments. It is quite possible that such a properly scaled experiment at this level of nonlinearity would have evolved into the fully turbulent regime ͓see, for example, Figs. 12͑c͒ and 13͔, as opposed to quasilaminar RT spike penetration, which could affect the overall outward core penetration and core-envelope mixing. Normally, similarity arguments are used to ensure that some parameter ͑of interest in a particular problem͒ can be scaled between two systems. This can be, e.g., the hydrodynamic resistance to the body moving in a fluid, or the energy confinement time in a plasma device ͓as in Connor and Taylor ͑1977͔͒. We are demanding much more, that the whole dynamic evolution of two systems with properly scaled initial conditions be similar.
There are only two constraints ͑4.7͒ on five parameters ͑4.4͒ determining the evolution of the system. For the second system, one can choose arbitrarily three parameters, say, L * , * , and p * , and, by choosing the mag-nitude of the characteristic velocity and magnetic field so as to maintain conditions ͑4.7͒, obtain a system which behaves similarly to the first one, up to the change of scales. It is very important to recognize that the Euler similarity applies not only to smooth solutions of the Euler equations, but also to solutions containing shock waves. The proof can be found in the work of Ryutov, Drake, and Remington ͑2000͒.
The Euler similarity holds for scales exceeding the dissipative scales ⌬ diss , which are small compared to the global scale L. In the RT instability driven by the onset of an acceleration, dissipation-scale vortices do not appear instantaneously. It takes several eddy turnover times at the global scale ͑several L / v͒ for them to appear. In other words, the Euler similarity ͑with dissipative terms neglected͒ will correctly describe an early stage of the instability, until small-scale vortices are formed. ͓We are assuming smooth transition layers, with density scale length L; if one deals with a sharp ͑zero-scale͒ transition, small-scale perturbations may appear early in the pulse.͔ During this early stage there is no need to make any assumptions about the turbulent viscosity, introduce Reynolds stresses, and other approximate ways of description: the Euler equations correctly describe this stage, including the formation of smallerscale vortices. In a number of cases, including the SN explosion and its laboratory simulation, this means that much of the evolution relevant to SN core penetration can be adequately described by the Euler equations, with viscosity neglected. Within the time interval of several L / v the system can already reach a strongly mixed state.
It is interesting, however, to assess what would happen later in time, were there is a need to study this later evolution. The question we pose is to what extent will the behavior of the two systems be similar at larger scales if Reynolds numbers, albeit very large, are different in the two systems ͑meaning that the relative values of the dissipative scales are different͒. One suspects that the differences on the global scale will not be very large; they will probably appear in the terms of order of ln͑Re͒, or in terms that depend on Re even more weakly. This assertion is based on the results from a number of relevant problems exhaustively studied experimentally. Examples include turbulent pipe flow ͓see, e.g., Landau and Lifshitz ͑1987͔͒, and a turbulent flow past a body at high Reynolds number ͓see Gjevik ͑1980͒, Cantwell ͑1981͒, and Van Dyke ͑1982͒ for excellent pictures of such flows over a broad range of Reynolds num-bers͔. The issue of the development of dissipative scales in laboratory experiments has been discussed recently by Robey and co-workers ͑Robey et al., 2002;Robey, 2004; see also Dimotakis, 2000͒. The first steps have been made in experiments on the early generation of small-scale turbulence by introducing short-wavelength perturbations at the interface ͑Kuranz et al., 2005͒.
The question of when does scaling break down needs further study. In other words, at what point in the evolution would a scaled SN experiment no longer correctly reproduce the nonlinear or turbulent SN dynamics. It may be informative to conduct a set of experiments related to each other by a broader ͑than the Euler͒ similarity, the so-called "perfect similarity," which holds for an arbitrary equation of state ͑not necessarily poly-tropic͒ ͑Ryutov and Remington, 2003aRemington, , 2003bRyutov et al., 2004͒. The goal would be to determine at what stage of the evolution differences would arise solely due to differences in Re. As this requires a large change of spatial scale and hence of the drive energy, the advent of the NIF laser ͑see Sec. II.B͒ may open up this possibility.

E. Experiments on SN type-II hydrodynamics
For the past several years a team of researchers has conducted a series of experiments aimed at the problem of RT instabilities at the H-He interface. The point of these experiments is to observe the nonlinear dynamics of this process in a well-scaled environment. In the context of the results, one can then ask whether the simulation codes in fact calculate the deeply nonlinear behavior of the RT instability correctly, and whether any other physics, not present in the simulations, appears in the experiments. All these experiments begin by producing a blast wave, as discussed above, applying the initial ablation pressure either through direct laser irradiation or through x-ray irradiation ͑see Sec. II͒. The subsequent structure in the target then determines which aspects of RT dynamics are being explored.
The first such experiments ͑Kane, Kane et al., 1997;Remington et al., 1997 used the Nova laser to examine RT growth from a single-mode initial perturbation at a planar interface. The target structure involved a 85-m-thick Cu layer followed by 500 m of plastic ͑CH 2 at = 0.95 g / cm 3 ͒. The profiles of density and pressure 20 ns after the laser pulse began are shown in Fig. 9͑b͒ ͑Ryutov et al., 1999͒. The Cu-plastic interface was rippled by a sinusoidal perturbation with a 200-m wavelength and a 20-m amplitude. Figure 9͑d͒ shows a radiograph of the resulting structure at 33 ns ͑Remington et al., 1997͒ and Fig. 9͑e͒ shows the result averaged over multiple images corresponding to an average time of 35 ns ͑Remington et al., 1999͒. The distance from the valleys to the peaks in the observed modulations ͑known as the "bubble-to-spike" distance͒ has become approximately equal to the initial wavelength of 200 m, meaning that the evolution has entered the nonlinear regime. Simulations using the astrophysical code PROMETHEUS ͑Fryxell, Müller, and Arnett, 1991;Arnett, 1996͒ and the laboratory code CALE ͑Tipton, 1990͒, reproduced this result, but the detailed shape of the structures did not closely resemble what was observed in this first experimental attempt.
Subsequent experiments ͑Robey et al., 2001͒ have both improved the quality of the data and explored other aspects of RT dynamics, using the Omega laser. One aspect explored has been RT growth in diverging systems, both cylindrical and spherical ͑Drake et al., 2002͒. In the spherically expanding case ͑not shown͒ a hemispherical plastic capsule ͑of density 1.37 g / cm 3 , in-side radius 220 m, and thickness 110 m͒ was irradiated from the inside. It included a patch of Gedoped plastic as a tracer for radiography, and was in some cases modulated with an initial mode ͑70-m wavelength, 10-m peak-to-valley amplitude͒. The capsule was mated to a large volume of low-density ͑50-100 mg/ cm 3 ͒ foam. The unmodulated capsule retained its shape while expanding nearly a factor of 3 in radius. The modulated capsules developed highly nonlinear structures. This experiment was simulated using CALE and the front-tracking hydrodynamics code FRONTIER ͑Glimm et al., 2001͒. Here again, and in the presence of better data, the simulations reproduced the qualitative features but not the exact quantitative details.
Another aspect of RT dynamics explored by experiments has been the coupling between interfaces. In an exploding star, the initial modulations of interior layers can induce structure into the blast wave that can affect layers outside it. The experiment to examine this ͑Kane et al., 2001͒ used the target structure shown in Fig. 10͑a͒, with details described in the caption, and the results are shown in Fig. 10͑b͒. One can see the Cu spikes, extending upward from below, and the modulations in the second interface, made visible by the tracer strip in the plastic below the interface. Detailed simulations of this experiment were carried out as part of a validation study by Calder et al. ͑2002, 2004͒ for the astrophysical code FLASH, which includes adaptive grids and other advanced features. Comparison of the simulation results with experimental images supports the same conclusion as in the previous cases. The qualitative features of the data are reproduced very well by simulations. Quantita-tively, several details are not accurately reproduced, including the exact spike length, the height of the structures in the interface, and the behavior at the edges of the system. In the specific case of the FLASH simulations, the length of the Cu spikes was found to change with the number of levels of mesh refinement in the simulation, but did not appear to be converging toward the experimental value.
Experiments on the development of multimode perturbations and the transition to a turbulent mix at the interface have been carried out and analyzed in the context of their correspondence to the code results ͑Robey, Zhou, et al., 2003Miles, Braun, et al., 2004Miles, Edwards, et al., 2004͒. Robey, Zhou, et al. ͑2003͒ observed the evolution of an eight-mode pattern ͓Fig. 11͑c͔͒, and the simulations, shown in Fig. 11͑a͒ as a numerical radiograph and in Fig. 11͑b͒ with experimental noise artificially added in, are in a reasonable agreement down to the scales determined by the experimental resolution of ϳ10 m Miles, Braun, et al. ͑2004͒. In the simulations and experiment described by , the instability was driven by a strong blast wave giving rise to a Mach number for the growing perturbations as high as 0.2-0.4. Surprisingly, their simulations suggest that the instability "remembers" small-scale details of the initial conditions well into nonlinear stage of the evolution. An example of the experimental results over the range of 13-37 ns is given in Figs. 12͑a͒-12͑c͒. The initial perturbation corresponded to an initial wavelength ͑͒ and amplitude ͑ 0 ͒ of 50 and 2.5 m, with a =5 m, 0 = 0.25 m "noise" mode superposed ͑Miles, through the polyimide-͑ = 1.41 g / cm 3 ͒ CRF foam ͑ = 0.05 g / cm 3 ͒ interface. Approximately laminar RT spike evolution is observed at 13 ns. By 25 ns, the spikes are starting to interact through the KH-induced broadening of the spike tips. By 37 ns, it appears that the evolution has entered a fully mixed, fully turbulent regime. This late-time experimental image looks quite different from the laminar, albeit chaotic, RT spikes from the SN simulation shown in Fig. 7. It would appear that the SN simulation is not capturing the transition to a fully mixed, fully turbulent state, due to the finite numerical Re.
A computational development that holds great promise for these types of simulations is the adaptive mesh refinement technique, which now allows such integral simulations to be done in three dimensions. In Fig. 13, we show initial results from such a simulation ͑Miles et al., 2005͒ for a proposed NIF experiment. The simulation corresponds to a 2D single mode perturbation with =50 m wavelength, 0 = 2.5 m initial amplitude, superposed with a random 3D noise function, and was driven with a similar strong blast wave ͑M ϳ 20͒ across a polyimide-foam interface. The simulations were done in both two dimensions ͑top row͒ and three dimensions ͑bottom row͒. The differences are striking. The 2D and 3D simulations are similar up to the / ϳ 2.5 ͑where / corresponds to the peak-to-valley perturbation amplitude over the dominant perturbation wavelength͒.
Beyond this stage of evolution, however, the 3D simulation undergoes a dramatic mixing transition, and enters the fully mixed, fully turbulent regime, whereas the 2D simulation is chaotic, but still largely laminar. Although these simulations assumed a NIF-scale drive, it is interesting that the transition to a fully mixed state occurs at a similar / in the Omega experiment, shown in Figs. 12͑b͒ and 12͑c͒. The conclusion, for the SN blast-wave drive, is that once / տ5, the RT evolution should transition into a fully mixed, fully turbulent state. If anything, this transition slightly slows down the overall spike and bubble front penetration ͑Miles et al., 2005͒.
As a result, based on the experiments shown in Fig. 12 and the 3D adaptive mesh refinement simulations shown in Fig. 13, it seems very unlikely that 3D turbulent mixing in the SN problem could resolve the "SN mix problem." It seems one needs, rather, to examine the initial conditions for the explosion for a resolution to this problem of core penetration. The impact of initial conditions on mixing has been addressed in recent experiments ͑Drake, Leibrandt, et al., 2004͒, and is continuing. At this point one can ask what are the implications of the experiments to date for the questions asked above. Based on comparisons with experiments, the simulations appear to correctly calculate deeply nonlinear RT dynamics, although the details are not precisely reproduced and obtaining good agreement with experiment often requires iteration. From the point of view of global evolution, it would appear unlikely that the simulations are sufficiently in error to explain the observations from SN 1987A.
As to whether other physics appears in the dynamics that the codes do not address, the answer is twofold. At the level of these simple yet deeply nonlinear systems, other physics does not appear to be a significant effect. ͑To be sure, the systems were set up to emphasize pure hydrodynamics.͒ An issue of the effect of the Reynolds number, which, although very large in both laboratory and astrophysics, differs substantially between the two systems, is more subtle. It seems likely that this will be addressed in future experiments ͑Robey et al., 2003͒. In conclusion, this work has shown that laser experiments can be carried out for parameters that are scalable to the dynamics of actual SNe. The results have demonstrated rather conclusively that the hydrodynamics codes work well, even into the deep nonlinear regime, in scaled SN settings. Discrepancies between SN models and SN observations seem more likely to be due to the initial conditions assumed, rather than due to the complexity of the nonlinear hydrodynamics simulations.

A. Introduction
The explosion of a star lasts only a few months. In contrast, the remnants from these explosions, that is, supernova remnants ͑SNRs͒, can be observed for centuries if not millennia. SNRs are the observable structures that form through the interaction of the ejecta from a stellar explosion with the surrounding ͑circumstellar͒ environment. In addition, SNRs are widely believed to produce most of the cosmic rays that irradiate the Earth. Laboratory experiments can help improve our understanding of some of the mechanisms present in SNRs, and can help test the computational models we build to interpret their behavior. In Sec. V.B, we provide some background regarding SNRs, whereas in the rest of this section we summarize existing experiments.

B. General features of supernova remnants
Supernova remnants are created from the kinetic energy of the exploding star, typically about 10 51 ergs. The stellar ejecta from the explosion undergo a homologous expansion, with velocity , radial distance r, and time t related by = r / t. Expansion cooling reduces the temperature of this material to a low value early on, so that nearly all the energy of the ejecta is in kinetic energy. The first phase of SNR evolution is the free expansion ͑or "young remnant"͒ phase, during which the leading edge of the expanding ejecta drives a "forward shock" into circumstellar matter at velocities of order 10 000 km/ s. A "reverse shock" propagates from the contact discontinuity ͑i.e., the "interface" where the SN ejecta meets the ambient medium͒ back into the ejecta; in the laboratory frame this reverse shock at this phase still moves in the outward direction ͑Chevalier, 1982͒. Eventually, the mass of the accumulated circumstellar matter exceeds the mass of the stellar ejecta. This is generally taken to mark the ͑gradual͒ transition to the Sedov-Taylor phase. As this phase begins, the reverse shock runs in to the center of the SNR and disappears, after which the SNR is believed to develop the characteristic structure of a Sedov-Taylor blast wave ͑Whitham, 1974, p. 192͒. During this phase, the SNR has a single shock behind which the density and pressure decrease, and a radial size that increases with time as R͑t͒ϳt 0.4 . Eventually the SNR becomes an old remnant, corresponding to essentially a big bubble in the sky, with denser material around it.
Throughout the development of the SNR, the shocked matter radiates energy, which escapes because the SNR is optically thin. The role of radiation varies depending on the specific parameters of the particular FIG. 13. ͑Color͒ 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 ϳ 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 highfrequency noise spectrum, the deep nonlinear RT evolution is observed computationally to pass through the mixing transition, and enter a fully turbulent regime. Adapted from  event and on the phase that the remnant is in. In particular, conditions can be met ͑usually late in the explo-sion͒ where radiation causes a collapse of the shocked material into a thin shell ͑Cioffi et al., 1988;Blondin et al., 1998;Cohen et al., 1998͒, which can manifest a number of specific instabilities ͑Vishniac, 1983; Bertschinger, 1986;Innes et al., 1987;Ryu and Vishniac, 1987͒. The Cygnus Loop, a 15 000-year-old remnant that is close enough to be six times the size of the Moon on the night sky, is in this phase. A small part of this remnant is shown in Fig. 14͑a͒ ͑Levenson and Graham, 2001͒. The structures evident in the Cygnus Loop are not an excep-tion: the remnants almost universally reveal complex 3D structures. The origin of these structures can be related to initial 3D nonuniformities of circumstellar medium, to instabilities at the contact discontinuity or the blast wave, to 3D features "imprinted" on the ejecta during the SN explosion itself, or to various combinations of these.
In particular, the massive stars that are thought to be the progenitors for core-collapse supernovae are usually formed in regions where dense molecular clouds are present. Therefore there is a significant chance that the ejecta from the star will interact with other matter such FIG. 14. ͑Color͒ Supernova remnants offer a visual example of strong shock dynamics in the universe. ͑a͒ Hubble Space Telescope Wide-Field Planetary Camera 2 observations in H␣ of the Cygnus Loop supernova remnant ͑SNR͒, which is located at a distance of ϳ0.75 kpc, and is the result of a supernova that occurred ϳ15 000 yr ago. The image shows the SNR blast wave interaction with an interstellar cloud on physical scales of 10 15 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 Ϸ 10 −15 cm −3 are observed to have velocity v s = 170 km s −1 . The image is scaled linearly from 0 ͑white͒ to 4 ϫ 10 −14 ergs cm −2 s −1 pixel −1 ͑black͒. Adapted from Levenson and Graham, 2001. ͑b͒ Interaction of a supernova remnant ͑the hemispherical object to the lower left͒ and a molecular cloud ͑the elongated object above͒. The figure shows a grayscale image of the x-ray emission, overlaid with a contour image of the radio emission. Adapted from Guo and Burrows, 1997. ͑c͒ 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 spectrum͒. Adapted from Gaetz et al., 2000. ͑d͒ Cassiopea-A remnant. Colors correspond to three different energy bands: 0.6-1.65 keV ͑red͒, 1.65-2.25 keV ͑green͒, and 2.25-7.50 keV ͑blue͒. Adapted from  ͑e͒ Rosat x-ray image of Puppis A supernova remnant. Reproduced from Hwang et al., 2005. ͑f͒ Chandra x-ray image of the Bright Eastern Knot region of Puppis A SNR. Reproduced from Hwang et al., 2005. ͑g͒ Same as ͑f͒, only in black and white with contrast enhancement, and with the shock-cloud "cap" and "bar" features indicated. Adapted from Hwang et al., 2005. as a molecular cloud. Figure 14͑b͒ shows such an interaction ͑Guo and Burrows, 1997͒. An example that is thought to be related to the Rayleigh-Taylor instability at the contact discontinuity ͑Gull, 1973; Shirkey, 1978;Dickel et al., 1989;Gaetz et al., 2000͒ is shown in Fig. 14͑c͒ which shows one of the Chandra images of SNR E0102. 2-7219 ͑Blair et al., 2000;Gaetz et al., 2000;Hughes, Rakowski, and Decourchelle, 2000;Rasmussen et al., 2001͒. One can see modulations, spectroscopically identified to be at the contact surface, that seem likely to have been produced by Rayleigh-Taylor instabilities. It is notable that the mode number of these modulations appears larger than the mode number typically seen in simulations.
A memory of the initially unstable and structured explosion of the core-collapse supernova may be responsible for an amazing array of knots, filaments, and flocculi in the relatively young ͑300-year old͒ Cassiopeia A remnant shown in Fig. 14͑d͒ ͑Anderson and Rudnick, 1995;Reed et al., 1995;Keohane, et al., 1996; Again, there are "bubbles" and "spikes" at various places around the outer boundary that appear Rayleigh-Taylor-like.
An example of x-ray images of a prominent shockcloud interaction in the Puppis A SNR is shown in Figs. 14͑e͒-14͑g͒ ͑Hwang et al., 2005͒. Figure 14͑e͒ shows the entire SNR, in an x-ray image taken with the Rosat x-ray satellite. This remnant sits at a distance of ϳ2.2 kpc, and is the result of a core-collapse SN IIL/b explosion of a ϳ25M progenitor some ϳ3700 years ago. A higher resolution x-ray image of the region called the Bright Eastern Knot was taken with the Chandra x-ray observatory, and is shown in Fig. 14͑f͒. Here the colors correspond to the soft band ͑O͒ in red, medium band ͑Ne͒ in green, and hard band in blue. A contrastenhanced, black and white version of this image is shown in Fig. 14͑g͒, with a region identified as a shockcloud interaction identified. In particular, features called the "cap" and "bar" are indicated. These will be discussed in more detail in Sec. V.D, in the discussion of a scaled, strong shock, laboratory experiment ͑Klein et al.,

2003͒.
Many of these aspects of SN explosions can be simulated in laboratory experiments with high-intensity lasers or Z pinches. In the rest of this section we discuss experiments of various degrees of complexity related to ͑i͒ the overall 1D dynamics, ͑ii͒ the interaction between high-speed flows and density clumps, and ͑iii͒ studies of various aspects of radiative shocks.

C. Simulating one-dimensional dynamics
In order to create an experimental setting that can be scaled to actual SNR conditions, one must produce a system in which flowing, cool ejecta encounter a reverse shock, with the shocked material driving a forward shock through low-density matter. The first experiments to accomplish this were those of Drake and co-workers ͑Drake, Carroll, et al., 1998 using the Nova laser facility ͑Campbell et al., 1986͒. These experiments were in a planar geometry, intended to simulate a small segment of the overall SNR expansion. The experiment began when an intense x-ray flux, produced by laser heating of a gold cavity, irradiated a 200-m-thick layer of plastic. The x rays ablated the plastic, launching a strong shock wave through it, at a pressure of 5 ϫ 10 13 dynes/ cm 2 ͑50 Mbars͒. This was the analog of the initial blast wave produced by the SN explosion. This shock wave compressed, accelerated, and heated the plastic. When the shock broke out of the plastic, the ejecta from its rear expanded, accelerated, cooled, and decompressed across a 150-m-wide gap. In an actual SNR, spherical expansion provides the decompression ͑McKee, 1974͒. Here the gap served an analogous function. The ejecta then launched a forward shock into the ambient matter, in this case a foam whose density was less than 1% of the density of the compressed plastic layer. The ejecta stagnated against the ͑moving͒ contact surface with the foam, which launched a reverse shock into the ejecta, just as occurs in an SNR. In a young SNR and in this experiment, respectively, Re= 6 ϫ 10 8 and 7 ϫ 10 6 , Pe=10 7 and 10 4 . Radiative losses are unimportant in both systems. Based on Euler scaling, the relation of the time scales is that 1 ns in the experiment corresponds to 1 year in the SNR. This system can be used for basic setup and benchmarking of hydrodynamic simulations.

D. Interaction of shocks and clumps
The local structures observed in SNRs may result from instabilities, but much of it probably is due to clumpiness in the circumstellar matter or in the ejecta. The clumpiness may in turn affect the development of instabilities, as has been explored in some simulations ͑Jun et al., 1996; Since clumps introduce substantial vorticity into the fluids that interact with them, experiments with clumps test the accuracy of simulations somewhat differently than shock waves and interface instabilities do. To date, no experiment has addressed the impact of multiple clumps, like those explored by Jun et al. ͑1996͒, on SNR evolution. However, two experimental studies have made relevant measurements with a single clump.
The issue of cloud destruction by a shock has been addressed in some detail in experiments begun at the Nova laser ͑Klein et al., 2000, 2003͒ and continued at the Omega laser ͑Robey et al., 2002͒. Both sets of experiments involve the generation of a nearly planar blast wave, within a shock tube, its propagation over a significant distance, and its subsequent interaction with a dense sphere of material. The geometry of the Omega experiment has been shown in Fig. 2͑c͒. In this experiment, by the time when the shock arrives at the location of the solid Cu sphere, it ͑the shock͒ has long since been overtaken by the rarefaction from the front surface of the irradiated material, giving it a blast-wave structure not unlike that present in a Sedov-Taylor phase SNR.
When the shock wave traverses the sphere, the sphere compresses ͑gets "crushed"͒. The interaction of the sphere with the postshock flowing plasma produces vortex rings, visible in the last panel of Fig. 2͑d͒. The vortex rings are subject to an azimuthal bending instability ͑the "Widnall instability"͒ that then produces threedimensional structure. These experiments provide an excellent test of the ability of astrophysical codes to simulate this type of shock-cloud interaction. Threedimensional ͑3D͒ simulations are required to reproduce these observations. The results from the original experiment on the Nova laser are shown in the full time sequence in Figs. 15 and 16 ͑Klein et al., 2003͒. In Fig. 15, the strong ͑ϳMach 10͒ shock is shown traversing a ϳ100-m-diameter Cu sphere embedded in solid plastic ͑CH͒, with an initial density contrast of Cu / CH ϳ 10. The shock passes through the Cu sphere over the time interval of 20-26 ns ͑where t = 0 corresponds to when the laser turned on͒. During this transit interval, the Cu sphere compresses and distorts into an "umbrella" shape. At later times ͓Figs. 16͑a͒-16͑f͔͒, the vorticity deposited into the Cu by the shock-sphere interactions cause the Cu plasma "cloud" to evolve into a vortex ring ͑something like a smoke ring͒ with a central "cap" or plasma reservoir lagging behind. In the side-on x-ray radiographs shown in Fig. 16͑d͒ these features are labeled bar and cap, respectively. At the latest times ͓Figs. 16͑e͒ and 16͑f͔͒, this vortex ring evolution has triggered an azimuthal ͑Widnall͒ instability, and the plasma "smoke ring" starts to break up and evolve towards turbulence in this 3D instability. Simulations of these shock-cloud dynamics are shown in Fig. 17. The 2D simulations ͓Figs. 17͑a͒ and 17͑b͔͒ capture the early-time, cloud compression phase, but fail to reproduce the late-time ͑i͒ evolution into a cap and bar shape, ͑ii͒ triggering of the Widnall instability, and ͑iii͒ transition to turbulence. ͓Note that we have corrected a typographical error of a factor of 10 in the axes of Figs Correspondence can now be made between 3D simulations ͓Figs. 17͑c͒ and 17͑d͔͒, experiments ͓Figs. 16͑c͒ and 16͑d͔͒, and x-ray observations of SNR shock-cloud interactions ͓Figs. 14͑e͒-14͑g͔͒. The correspondence is striking and compelling, and demonstrates a new capability in HED astrophysics to couple observations, simulations, and scaled laboratory experiments ͑Hwang et al., 2005͒. In other experiments, Kang et al. created the density structures present in a young SNR and observed their interaction with a ͑rather large͒ spherical obstacle ͑Kang et . The setting was similar to that realized by Drake and co-workers described at the beginning of Sec. V.C ͑Drake, Carroll, et al., 2000͒, but now the low-density foam contained a 150-m-diameter ZrO 2 sphere to observe the interaction of the shock and the ejecta with this sphere. The authors have clarified some details of this experiment for us that may prove useful in reading their papers. The structure of the C 10 H 14 O 4 foam consists of a thin fiber network, with m-scale cell sizes. The total laser intensity, and not the intensity of each beam, was 2 ϫ 10 14 W/cm 2 . The simulations in the papers are all for an initial CH layer thickness of 50 m. The experiment produced images that show the forward shock, the layer of denser stagnated ejecta, and some complex structures that developed

E. Radiative effects in shocks
Radiative shocks exhibit a range of behavior that depends on the optical depth of the downstream and upstream regions relative to the shock ͑Drake, 2005͒. Present-day laboratory experiments provide the possibility to address issues of the radiative cooling of shocked material and the formation of ionized precursors by the radiation of the shocked material. As an example, we present Fig. 18 based on experiments discussed by Bouquet et al. ͑2004͒ and carried out at the LULI nanosecond laser facility. We first show the result of an illustrative simulation with the ASTROLABE code ͓Fig. 18͑a͔͒. We see the characteristic structure of a strongly radiating shock, with the ion temperature initially very high, nearly ϳ1 keV ͑roughly corresponding to a standard Rankine-Hugoniot relation͒, then decreasing because of the energy exchange with electrons. Electrons, in turn, are cooled by atomic excitation and ionization processes, with a substantial part of this energy radiated away from the shock region. Eventually, the temperature decreases to a mere 20 eV, whereas the density reaches a value ϳ30 times higher than the initial density.
In this experiment, laser beams were focused onto a thin ͑2 m͒ polyethylene ablator which pushed a 25m layer of a polyethylene foam; the ablator and foam were separated by a 3-m titanium x-ray shield to prevent x rays formed at the ablation front from preheating the foam "piston." On the other side of the foam, a Xe gas at a density of 1.3ϫ 10 −3 g/cm 3 was situated. The whole design was aimed at driving a shock in matter at low density, so that, at a given laser intensity, the shock velocity would be high, and one would reach temperatures sufficient to make radiative effects important. The foam/gas interface acted as a piston that moved at a velocity of ϳ70 km/ s, driving a strong shock into the Xe gas.
A Mach-Zender interferometer was used to measure the electron density; an interferogram is shown in Fig.  18͑b͒. One sees the trajectory of the shock in Xe ͑dashed curve͒, as well as the trajectory of the front end of the ionized precursor ͑solid curve͒ produced by photoionization of the unshocked gas by the radiation from the shock region.
Shown in Fig. 18͑c͒ is a comparison of the experimental and calculated profiles of electron density, 200 m away from the foam surface ͑which serves as a pusher͒. The position of the shock corresponds to the steep part of the curve; the left part of the curve corresponds to an ionization precursor. The difference between measurements and simulations is attributed to 2D effects and early preheat. FIG. 17. ͑Color͒ Simulations of the shock-cloud experiment done on the Nova laser. ͑a͒ One result, showing a color density plot at 54 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." ͑b͒ Simulated 2D radiograph, assuming 4.5-keV Ti He␣ x rays. ͑c͒ 3D simulations of the laboratory experiment with realistic EOS. Adapted from Robey et al., 2002. ͑d͒ 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 Klein et al., 2003. Experiments by Keiter et al. ͑2002͒ on the Omega laser also involve the initial acceleration of a block of material to high velocity. Up to ten laser beams struck the front surface of this target, delivering several kJ of en-ergy to an 800-m-diameter spot in a 1-ns pulse. The laser irradiation shocked and accelerated a 60-mthick plastic layer, which crossed a 160-m vacuum gap to impact a low-density foam, usually of density 0.01 g / cm 3 . This drove a shock wave through the foam at ϳ100 km/ s. The structure of the precursor was diagnosed using absorption spectroscopy. Additional laser beams irradiated a thulium backlighter plate, permitting an imaging crystal spectrometer to obtain absorption spectra. Absorption lines were detected from up to six different ionization states. The lines from higher ionization states appear at higher temperatures. This allows one, with the help of the OPAL atomic code ͑Iglesias and Rogers, 1996;Iglesias, 1994, 1998͒, to determine the temperature profile in the precursor. Figure 19 shows an example of the results, and of an initial comparison to results from a very simple radiation hydrodynamic model. One can anticipate that such experiments could provide quality benchmark data for astrophysical modeling.
The observation of a radiatively collapsed shocked layer has also been demonstrated in the experiment by Reighart et al. ͑2006͒, who used a 3-mm-long, 0.6-mm inner diameter shock tube filled with xenon gas at a density of 6 ϫ 10 −3 g/cm 3 . The pusher ͑"piston"͒ was a 50m-thick beryllium layer. Simulations with the 1D Lagrangian code HYADES ͑Larsen and Lane, 1994͒ have shown the formation of a collapsed layer in the case when radiation losses were taken into account ͓see Fig.  20͑a͔͒ ͑Reighard, 2006͒. Note the logarithmic vertical scale: the density in the radiatively collapsed layer is twice as high as in the case with no radiation. Twodimensional simulations using the code FCI2 ͑Buresi et al., 1986; Busquet, 1993͒ allowed accounting for the effect of a finite radius of the shock tube ͓Fig. 20͑b͔͒. The 2D experimental radiographic image ͓Fig. 20͑c͔͒ shows remarkable agreement with simulations. Note that the velocity of the collapsed layer was quite high, ϳ140 km/ s. FIG. 18. Formation of a radiative precursor in a strongly shocked Xe gas experiment. ͑a͒ 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 ͑T i ͒, with T e = T i equilibration occurring downstream from the shock. ͑b͒ The shock trajectory and ionization precursor were measured with optical diagnostics, allowing the average shock speed of 67 km/ s to be determined. Progress has also been made in the theory of radiative shocks, within the approximation of high opacity and local thermodynamic equilibrium. In particular, Michaut and co-workers ͑Michaut, Stehle, et al., 2003; have considered the role of radiation in the jump relations for strong shocks in monatomic gases. These approximations, unfortunately, were never fully satisfied in any of the aforementioned experiments. Still, some interesting qualitative features are worth mentioning: It turns out that the density compression ratio is not a monotonic function of the shock velocity. At a small velocity, when radiation, excitation, and ionization are unimportant, the compression ratio 2 / 1 is 4 ͑for monatomic gases͒. At higher velocities, when the excitation and ionization "consume" a considerable fraction of the energy of shocked matter, but the radiation pressure is still small, the compression ratio can be quite high, more than 10 ͑in other words, the equation of state can be very "soft"͒. However, at yet higher velocity where the radiation pressure becomes dominant in the shocked material, the compression ratio drops to 7 ͑corresponding to the adiabatic index of radiation ␥ =4/3͒. All this is illustrated for Xe in Fig. 21͑a͒  FIG. 21. Effects of the equation of state and radiation on the shock. ͑a͒ Radiative precursor for the shock wave in Xe ͑initial density 1.5ϫ 10 −4 g/cm 3 , initial temperature 2 eV͒. Adapted from . ͑b͒ Shock compression solutions vs initial temperature, including radiation, assuming an ideal polytropic ͑␥ =5/3͒ gas. ͑c͒ Same as ͑b͒ only now treating the atomic structure and ionization, assuming 1 =5 ϫ 10 −4 g/cm 3 , and T 1 = 0.1 eV for the hydrogen gas. Adapted from  As long as the initial gas temperature is not too hot, there is a range of shock velocity, ϳ10-100 km/ s, that leads to the strong shock ͑nonradiative͒ compression limit of 2 / 1 = ͑␥ +1͒ / ͑␥ −1͒ = 4. At higher shock speeds radiative effects become strong, the gas becomes an optically thick, radiation-dominated, ␥ =4/3 fluid, for which 2 / 1 = 7. The situation changes strongly when atomic structure ͑namely, bound, excited states, and ion-ization͒ is taken into account. In this case, over the regime where bound excited states and ionization occurs, the gas has a lower effective ␥, and is much more compressible. This is shown in Fig. 21͑c͒ Shigemori, Ditmire, et al., 2000;Edwards et al., 2001͒ andspherical ͑Grun et al., 1991;Edens et al., 2004Edens et al., , 2005Hansen et al., 2005 blast waves have been studied. Effects observed include the dependence of the expansion trajectory on the equation of state and on the role of radiation, in the spirit of Keilty et al. ͑2000͒, Liang andKeilty et al. ͑2000͒, and the effects of the Vishniac instability of thin shells. We discuss here in detail two recent experiments of this type.
The first was performed by Edens et al. ͑2004͒ on the Janus laser facility at Livermore ͑Glaze, 1976͒ and at the Z-Beamlet facility at Sandia ͑Rambo et al., 2005͒. A 1-ns laser pulse with energy ranging from 10 J to 1 kJ was focused onto the tip of a metal or nylon pin situated in a target chamber filled with Xe or N 2 at a pressure of between 5 and 10 Torr. The fast energy release at the pin tip created a blast wave, visualized by dark field imaging.
In the case of Xe, the blast wave trajectory initially followed the r ϳ t 0.25 law corresponding to strong radiative losses from the material assembled by the blast wave ͑Keilty et al., 2000; Liang and Keilty et al., 2000͒. Later in the pulse, when the gas cooled down, a transition to the Sedov-Taylor dependence r ϳ t 0.4 occurred. In the case of nitrogen, the t 0.4 dependence was observed throughout the whole experiment ͓Figs. 22͑a͒ and 22͑b͔͒.
The dynamics of a blast-wave-induced thin shell should manifest the overstability predicted by Vishniac. Indeed, in the Xe plasma small-scale structures were clearly visible, whereas in the case of nitrogen the scale of the structures was larger ͓Figs. 22͑c͒ and 22͑d͔͒-in agreement with the simple observation that the Xe shell should be thinner because of stronger cooling. In a recent experiment by Edens et al. ͑2005͒, the evolution and decay of the amplitude of a rippled blast wave in nitrogen gas was measured and compared with predictions from the Vishniac theory. This comparison showed that the ripple amplitude decay rate was consistent with a polytropic index ͑gamma͒ of 1.4, which was higher than predicted by simulations with a 1D radiationhydrodynamics code. One interpretation given was that the nitrogen gas was ionized more than expected due to the radiative precursor preceding the shock front.
An interesting effect was observed by Hansen et al. ͑2005, 2006͒. They used the technique just mentioned to FIG. 22. Blast waves in nitrogen and xenon. Measured shock trajectories for ͑a͒ nitrogen and ͑b͒ xenon. Measured structure by dark-field imaging of the blast wave for 500-J energy input for ͑c͒ nitrogen and ͑d͒ xenon. Adapted from Edens et al., 2004. launch a shock wave into Xe gas and then followed the evolution of the system over a long time scale, up to ϳ30 s. At t = 150 ns, both the shock and gas ahead of the shock are visible ͓Fig. 23͑a͔͒. Later in time the initial shock weakens and is no longer visible. However, at t =4 s, a second shock appears, at a position well ahead of the possible position of the first shock ͓Fig. 23͑b͔͒. This suggests that the second shock is driven by the energy deposited in the radiative precursor region, a conclusion supported by numerical simulations shown in Fig. 23͑c͒.

G. Summary
Experiments addressing the dynamics of supernova remnants have demonstrated that blast waves can be produced in laboratory experiments that are scalable to real astrophysical objects. Shock crushing of isolated dense clumps has been reproduced and successfully simulated by hydrodynamic codes, thereby creating a high degree of confidence in the validity of 3D numerical simulations of similar astrophysical objects. Blast wave instabilities have been observed and related to the corresponding astrophysical phenomena. This provides substantial support to the existing astrophysical models of blast waves, their instabilities, and their interactions with clumps. These experiments, for example, dramatically illustrated the need for 3D simulations to reproduce the details of the dynamics of shock-cloud interactions, and demonstrated what is missed with 2D simulations ͑Robey et Klein, et al., 2003͒. What will be established in the future is the global effect of radiative cooling as a strong shock traverses a medium, such as a molecular cloud, where inhomogenieties exist. The effect of radiative cooling on strongshock-induced turbulent mixing is an exceedingly difficult problem to address quantitatively, yet it occurs routinely in astrophysics. A good example is the proposed jet-induced shock triggering of star burst activity. A particularly interesting case, pointed out recently by Fragile and co-workers, is the jet-induced star formation in "Minkowski's object," a small irregular starburst system associated with a radio jet in the nearby cluster of galaxies Abell 194 ͑Fragile et al., 2004͒. The mechanism proposed by Fragile et al. suggests that shocks generated by a galactic jet propagating through an inhomogeneous medium, such as a clumpy molecular cloud, can trigger the collapse of localized overdense regions, which then become active star-forming sites. Simulations of these high Mach number interactions show both the complexity of and need for coupled radiative, nonlinear hydrodynamics for shock-induced star formation. Given the enormous complexity of the coupled radiative, nonlinear hydrodynamics of these simulations, benchmark data are crucial, and now possible. Experiments under development today on HED facilities will be invaluable in the future in establishing benchmarks for this particularly difficult problem.
It is worthwhile mentioning that, in addition to the hydrodynamic phenomena discussed in this section, there exist a broad range of collisionless effects, which, in particular, are thought to be responsible for cosmic ray generation in supernova remnants. In principle, HED facilities might contribute to simulations of such phenomena ͑Drake, 2000͒, although experiments of this type remain rare to date ͑Woolsey et al., Drake, 2002b;Courtois et al., 2004;Gregory et al., 2005͒.

VI. PROTOSTELLAR JETS AND HIGH MACH NUMBER FLOWS
Astrophysical jets present some of the most visually intriguing images that we encounter in the galaxy and FIG. 23. The emergence of a second shock driven by the ionized precursor in strongly shocked Xe. ͑a͒ Schlieren image at t = 150 ns and ͑b͒ at t =4 s. ͑c͒ The corresponding spherically symmetrical modeling. Adapted from Hansen et al., 2005. universe ͑DeYoung, 1991; Reipurth and Bally, 2001͒. These jets cover an enormous range of spatial scale, from 10 17 cm for jets from young stellar objects, as shown in Fig. 24, to 10 24 cm for jets associated with quasars or active galactic nuclei harboring massive black holes ͑Birkinshaw and Davies, 1985;Chiaberge et al., 2003͒. The class of stellar jets known as Herbig-Haro ͑HH͒ objects are thought to be collimated bipolar outflows emerging from accretion disks during the star formation process. Examples of a Herbig-Haro jets, HH 47 ͑Heathcote et al., 1996͒ andHH 111 ͑Hartigan et al., 2001͒, are shown in Fig. 24 ͑Reipurth and Bally, 2001͒. Typical velocities of HH jets are a few hundred km/s at densities of n jet = 10-100 cm −3 . In terms of density contrast, it is thought that = n jet / n ambient Ϸ 10, where n jet and n ambient are the jet and ambient number density, respectively ͑Morse et Reipurth and Bally, 2001͒. High Mach number, high-density jets can be radiatively cooled, which greatly affects the dynamics and morphology ͑Blondin et al Stone and Norman, 1994;Frank et al., 1998͒. Models of jet formation generally fall into two broad categories. One category assumes that jets are formed as a consequence of matter falling into a compact central object from a magnetized rotating accretion disk ͑Pudritz and Norman, 1986;Lovelace et al., 1993;Shu et al., 1995;Livio, 1999͒. In the case of HH jets, the compact central object is the protostar or young stellar object. A second class of models assumes that the accretion process onto a central object results in a toroidal accretion disk, with density maximum along the equator and minimum at the poles, which define the symmetry ͑and rotation͒ axis. Spherically symmetric, outflowing winds from the central object then interact with this toroidal density profile, which leads to a funneling of the wind into bipolar jets following the rotation axis ͑Icke et al., 1992͒. A variation on this is the formation of jets by convergence of supersonic conical flows, in particular, in the presence of strong radiative cooling ͑Tenorio-Tagle et al., 1988͒. Observational data are insufficient at this time to conclusively discriminate between these classes of models, and indeed both may be operating simultaneously.
The jet internal Mach number ͓jet velocity/sound speed inside the jet, i.e., v jet / c s ͑jet͔͒ is one of the parameters used in describing jet dynamics and evolution. In astrophysical jets, the jet Mach number is generally very large, M jet Ͼ 10. One effect of high Mach number on jet dynamics is to reduce the level of tip broadening due to Kelvin-Helmholtz instabilities in the working surface. An additional effect is to reduce the amount of mixing along the sides of the jet. These effects are illustrated by the three simulations show in Fig. 25͑a͒ ͑Norman et al., 1982͒. The effect of radiative cooling is even more dramatic ͑Blondin et al., 1990;Stone and Norman, 1994;Xu et al., 2000͒. Radiative cooling lowers the pressure inside the jet, leading it to compress further, increasing the collimation, such as shown by the simulations in Fig. 25͑b͒ ͑Blondin et al., 1990͒. As radiative cooling increases, as quantified by the cooling parameter = L cool / R jet , the jet density and collimation increase. A fundamental question is how these jets remain so well collimated over propagation distances exceeding ϳ10 jet diameters or more ͑Reipurth and Bally, 2001͒. The effect of radiative cooling on jet morphology is still strong, even when magnetic field effects are included in the jet evolution, as shown in Fig. 25͑c͒ ͑Frank et al., 1998͒.
An emerging new experimental capability may prove useful in testing aspects of these models in addressing the collimation question. With the development of sophisticated high power lasers and magnetic pinch facilities around the world, the ability to conduct wellcontrolled and well-diagnosed laboratory experiments on high Mach number hydrodynamic jets is now becoming possible ͑Stone et al., 2000͒. Laboratory experiments allow the effects of high Mach number, radiative cooling, and possibly magnetic fields on jet dynamics to be probed individually or in combinations ͑Shigemori et Lebedev et al., 2002;Foster et al., 2005͒. The potential benefit of this research to astrophysics is only starting to be recognized and pursued.
One example, done on the Omega laser at the University of Rochester, is a purely hydrodynamic ͑nonradiative, nonmagnetic͒, high Mach number jet, shown at two different times in Figs. 26͑a͒ and 26͑b͒ ͑Foster et al., 2002͒. In the experiment, a set of 12 laser beams at a total energy of ϳ6 kJ enters a cylindrical gold cavity ͑hohlraum͒ on one end through the laser entrance hole, and converts to x rays at or near the inner gold wall surface, generating a burst of radiation of temperature T r Ϸ 200 eV, which lasts of order ϳ1 ns. A solid Al cy- FIG. 24. ͑Color͒ Jets from young stellar objects in the galaxy. ͑a͒ Optical image of the protostellar jet, Herbig-Haro ͑HH͒ 47. The bipolar HH 47 complex embedded in the dense Bok Globule 1500 light years away at the edge of the Gum Nebula: ͑red͒ ͓SII͔ emission; ͑green͒ H␣; ͑blue͒ ͓OIII͔. ͑b͒ Optical image of the jet, HH 111. Adapted from Reipurth and Bally, 2001. lindrical plug of dimensions 200 m diameter by 150 m length is mounted on a hole on the wall of the hohlraum opposite the laser entrance hole, with 100 m of the Al protruding into the hohlraum. This Al cylinder is butted up against a ϳ1-mm-long tube filled with a solid-density plastic ͑CH͒ reservoir. The radiation bath in the hohlraum ablatively launches converging shocks into the Al cylindrical plug. The magnitudes of the observed early-time jet and shock velocities suggest that an initial, very high-pressure region in the center of the Al cylinder, P Ͼ 100 Mbar ͑i.e., 10 14 dyne/ cm 2 ͒, is created. The Al-CH interface at the entrance to the CH reservoir is at ambient pressure, hence the high internal pressure in the Al launches a high Mach number jet of Al moving axially down the CH tube. This jet is imaged radiographically, by generating a timed burst of hard x rays behind the target, and imaging the jet as a shadow ͑to "backlighter" x rays͒. This external source of backlighter x rays is generated by focussing several of the Omega beams onto an auxillary planar disk of material such as Ti, generating a bright source of He-␣ x rays at 4.7 keV. The jet shown in Fig. 26͑a͒ has moved about three jet diameters, and a very prominent Kelvin-Helmholtz ͑KH͒ rollup is observed at the jet tip. The bow shock in the plastic is also very evident in these images. Simulations of the experiment are shown in Fig. 26͑a͒, and the experimental data are in Fig. 26͑b͒. The internal Mach numbers in these jets are M int = v jet / c s ͑jet͒Ϸ3, whereas the external Mach numbers are M ext = v jet / c s ͑ambient͒ Ϸ 5. The density ratio at the time of the images is = jet / ambient ϳ 0.3, due to the decompression of the Al, and the shock compression of the plastic. Once launched, these jets were purely hydrodynamic, with effects due to radiation being insignificant other than generating the initial ablation pressure source. For hydrodynamic jets such as these, a rigorous scale transformation can relate the laboratory experiments to the astrophysical setting. ͑See the scaling discussion in Sec. IV on supernova hydrodynamics.͒ A scaled up version of this experiment has now been done on the Z magnetic pinch facility, and observed considerably later in time at 150 ns, as shown in Fig. 26͑c͒ ͑Bennet Sinars et al., 2004͒. This image used a bent spherical crystal, monochromatic imaging diagnostic to cast the image onto x-ray film and onto an image plate. Here, the high Mach number hydrodynamic jet has propagated 5-10 jet diameters, and still appears to be well collimated, and apparently reasonably laminar. Another approach using direct laser illumination to drive a shock that launches a jet of titanium through a collimator ͑acting like a microgun barrel͒ has been developed on the Omega laser, and backlit imaging out to several hundreds of ns has been demonstrated. An image from such a jet, using point projection imaging, is shown in Fig. 26͑d͒ ͑Foster et al., 2005͒. In this case, the jet tip or working surface displays an interesting appearance suggesting a transition to turbulence. Simulations done prior to these laser shots, one result of which is shown in Fig. 26͑e͒, did indeed suggest that the jet evolution might transition into turbulence ͑Taylor et Rosen et al., 2005͒. Postshot simulations, compared with experiment, suggest that j Ϸ 0.1 g / cm 3 , j / a Ϸ 1, T Ϸ 3 eV, v j Ϸ 10 km/ s, M int Ϸ 3, ReϷ 10 6 , and PeϷ 10 3 for regions near the head of the primary jet at t = 300 ns ͑Foster et al., 2005͒. The primary jet is followed by a secondary jet, caused by the collapsing collimator ͑"gun barrel"͒. This secondary jet overtakes the primary jet causing a multitude of internal shocks and shock re-  Frank et al., 1998. verberations between the jet and bow shock. The behavior of grossly asymmetric ͑3D͒ jets has begun with the use of four beams ͑out of 192͒ at the National Ignition Facility ͑Blue et al., 2005͒.
On the Z-pinch field facility Magpie, high Mach number jets were produced by applying fast-rising current, reaching 1 MA in 240 ns, to a conical array of fine metallic wires ͑Lebedev et al., 2002͒. The resistive heating of the wires by current rapidly converts the outer surfaces of the wires to plasma, and through the J ϫ B force, a fraction of this plasma implodes onto the axis. Due to the initial conical shape of the wires, the im-ploded "precursor" plasma has a net axial velocity component which turns the plasma stagnated on the axis into a jet. If the wires are high Z, such as tungsten, the jet is radiatively cooled, which increases its collimation and Mach number. Three jets thus produced with wire arrays of Al ͑little radiative cooling͒, Fe ͑moderate radiative cooling͒, and W ͑strongly radiatively cooled͒ are shown in Fig. 27͑a͒ ͑Lebedev et al., 2002͒. As the W precursor plasma stagnates on axis, the jet radiatively cools and remains well collimated as it emerges from pinch regions. This high Mach number jet can then be impacted into an ambient medium, such as a CH plasma target.  Foster et al., 2002. ͑c͒ High Mach number jet image taken on an experiment at the Z magnetic pinch facility. Adapted from Sinars et al., 2004. ͑d͒ 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 ns. Adapted from Foster et al., 2005. ͑e͒ 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 Taylor et al., 2004. During this impact the jet tip region ͑working surface͒ reheats and starts to radiate in the soft x ray again. An example of such an impact from jet experiments done on the Magpie pinch facility is shown in Fig. 27͑b͒ ͑Lebedev et al., 2002͒. Shown in Fig. 27͑c͒ is the case where a radiatively cooled W jet is deflected sideways by a scaled "stellar wind," caused by ablating a suitably placed CH foil ͑Lebedev et al., 2005b͒. Such jet deflections have been observed in some HH jets. Detailed images of the working surface of such jets have been obtained on the Magpie facility ͑Ampleford et al., 2005͒. An even newer development is the ability to create "magnetic tower" jets in the laboratory using a radial array of wires, instead of a cylindrical or conical array, as shown in Fig. 27͑d͒ ͑Lebedev et al., 2005a, 2005b͒. Such magnetized, high Mach number jets resemble aspects of magnetically formed protostellar jets, and thus add one more capability to the techniques available to study jet dynamics in the laboratory. The radial flow of current converges to the center then runs axially down the stem or stalk. The net magnetic forces cause the radial wire "sheet" to bulge upwards. Once the wires "break," the magnetic cavity expands and rises. This is illustrated schematically on the left side of Fig. 27͑d͒. An image in x-ray emission for an experiment where the radial wires were W is shown on the right side of Fig. 27͑d͒. Simula- FIG. 27. ͑Color͒ Jet experiments and simulations from the Magpie magnetic pinch facility. ͑a͒ 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 Lebedev et al., 2002. ͑b͒ 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 Lebedev et al., 2002. ͑c͒ Similar to ͑b͒, 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 Lebedev et al., 2005b. ͑d͒ Images of a magnetic tower jet created by a radial wire array. Adapted from Lebedev et al., 2004. ͑e͒ Simulations of a magnetic tower jet created by a radial wire array. Adapted from Ciardi et al., 2005. These jet experiments were carried out on the Magpie Z-pinch facility. tions show in detail the dynamics and conditions of these laboratory high Mach number magnetic tower jets, an example of which is shown in Fig. 27͑e͒ ͑Ciardi et al., 2005͒. Based on comparison of simulations with experiment, it is estimated that the Mach number of the magnetic cavity in the axial direction is M ϳ 10 and in the central jet column T ϳ 120 eV, Z ϳ 20, ␤ = P thermal / P magnetic ϳ 1, and Re M ϳ 10 ͑Lebedev et al., 2005a͒.
In order to experimentally simulate aspects of the magnetohydrodynamics of astrophysical jets, the magnetic Reynolds number Re M in the laboratory experiment must be at least an order of magnitude higher than 1. Recall that Re M ϵ sL * / D M , where D M is the magnetic diffusivity, s is the sound speed, and L * is the characteristic length scale in the laboratory experiment ͑Ryutov, . Under typical astrophysical conditions, Re M is extremely large, due to the large spatial scales involved. For example, for a hydrogen plasma at a temperature of ϳ0.1 eV, and at the scale typical for Herbig-Haro jets ͑L * ϳ 10 17 cm͒, Re M is of the order of 10 15 . Reaching such values of Re M in laboratory experiments with laser-driven or Z-pinch-driven targets is very difficult if not impossible. On the other hand, reaching values of Re M 1 may be possible ͑Fig. 28͒. A key parameter is the plasma temperature. ͓Note that there is a factor of 10 error in Eqs. ͑19͒ and ͑20͒ of Ryutov, Drake, and Remington ͑2000͒, where the analogous figure was first presented: the righthand side of Eq. ͑19͒ is actually ten times smaller, and the right-hand side of Eq. ͑20͒ is ten times larger. Therefore our Fig. 28 here is somewhat different from Fig. 1 of that paper or Fig. 3 of Ryutov et al. ͑2001͒.͔ As an example, consider ϳ͑1 mm͒ 3 of plasma. At a temperature of T ϳ 10 eV, the magnetic Reynolds number would be Re M ϳ 10, whereas the same ͑1 mm͒ 3 of plasma at 100 eV would have Re M ϳ 10 3 . This increase is because Re M ϳ sL / D M , where sound speed s ϳ T 1/2 and D M ϳ 1/T 3/2 ͑Ryutov, Drake, and . Hence Re M ϳ LT 2 . So at a factor of 10 higher temperature, Re M increases by a factor of 100, from Re M of ϳ10 to ϳ10 3 . This suggests that a possible direction for research on next generation, high power HED facilities such as NIF or ZR could be to generate hotter hydrodynamics conditions to increase Re M well beyond ϳ10, where magnetic-field effects could start to play an interesting role in coupling to the evolution of turbulent hydrodynamics.

A. Introduction
Cold gaseous clouds illuminated by neighboring bright massive stars may experience an intense ablation of material from their surfaces. The UV radiation from stars is absorbed by photoionization and photodissociation processes near the surface of the cloud, causing a continuous ablation of surface layers and generating a flow of ionized gas directed away from the surface of the cloud. This process, first discussed by Oort ͑1953͒, Spitzer ͑1954͒, and Oort and Spitzer ͑1955͒, is commonly called "photoevaporation." One of the best-known objects of this type is the Eagle Nebula ͑White et al., 1999͒. Figure 29 shows the Hubble space telescope ͑HST͒ image of this object and Fig. 30 shows its orientation with respect to the nearest young stars. Long pillars visible in the picture are sometimes called "elephant trunks" ͑Frieman, 1954͒. Other examples of photoevaporation flows have been found; see, e.g., Leung ͑1985͒ andPound et al. ͑2003͒. Detailed studies of the ionization front dynamics have been carried out by Kahn ͑1954, 1958͒, who laid the groundwork for classifying various possible regimes, as well as Dalgarno and McCray ͑1972͒ and Bertoldi ͑1989͒, who produced a comprehensive analysis of the process with a detailed account of ionization and recombination processes. Dense molecular clouds in the vicin-  Hester et al., 1996. ity of bright young stars are of broader interest because these clouds may serve as "cosmic nurseries," where star formation occurs ͑Shu et Elmegreen, 1998;Sugitani et al., 2002͒. In recent years, detailed information about the physical conditions in both the hot ionized flow and cold gaseous cloud in the Eagle Nebula has been obtained. The hot ionized part was characterized by Hester et al. ͑1996͒ on the basis of Hubble Space Telescope observations in H␣, ͓SII͔, and ͓OIII͔ lines. Imaging of the cold interior of the cloud at millimeter-and submillimeter-range wavelengths ͑emitted by molecules of the cold gas͒ was carried out by Pound ͑1998͒ and White et al. ͑1999͒. Levenson et al. ͑2000͒ have characterized the photodissociation zone as well as parameters of the ionized matter. These data make possible a much more detailed analysis of the physics processes responsible for the formation of visible structures. In particular, hydrodynamic velocities inside the cold gas have been found by Pound.
Below we discuss hydrodynamic phenomena occurring during photoevaporation of gas clouds, with the main emphasis made on possible instabilities of the cloud surface. We argue that a significant part of the problem can be correctly described in the framework of ideal hydrodynamics and modeled in scaled experiments.

B. Main physical processes
It has been realized many years ago ͑Spitzer, 1954͒ that complex hydrodynamic motion and, eventually, the shape of photoevaporated clouds is largely determined by the ablation force arising from the intense photoevaporation. Molecular clouds are typically quite cold: the balance of heating the cloud material by cosmic rays and radiation cooling in the microwave range ͑Spitzer, 1978͒ establishes an initial ͑preshock͒ temperature of only ϳ30 K. Ultraviolet radiation of bright young stars is absorbed in a very thin layer near the cloud surface by photoionization and photodissociation of hydrogen. The ionized gas thus formed begins to expand away from the cloud surface. The pressure from the "rocket effect" then compresses the cloud. Typical ablation pressures are orders of magnitude higher than the initial pressure of the cold cloud interior. A strong shock is launched into the cloud, compressing and heating it. Once the shock wave has traversed the cloud, a rarefaction wave from its far surface travels back to the front surface, after which the whole slab is accelerated. For the Eagle Nebula, the time scale for these developments is ϳ10 5 yr and is comparable to the time scale inferred by Pound ͑1998͒ to develop the structures.
The properties of the material in the Eagle Nebula have been determined by Hester et al. ͑1996͒, Pound ͑1998͒, and Levenson et al. ͑2000͒. They are discussed by Ryutov and Remington ͑2002͒ and are summarized in Table II. In addition, Pound determined that the velocity difference between the heads and bases of the pillars is ⌬v ϳ 10 6 cm/ s, implying that the characteristic acceleration g of the cloud material is g ϳ͑⌬v͒ 2 / L ϳ 3 ϫ 10 −7 cm/ s 2 .
One can readily show that the hydrodynamic description applies to these objects. The mean free path of H 2 molecules is determined by molecular collisions with a cross section ϳ2 ϫ 10 −16 cm 2 . For the density as in Table  II, one has ϳ 10 11 cm, many orders of magnitude less than any other characteristic dimension of the cloud. The Reynolds number for motions on the scale L is very large Reϳ 10 7 -10 8 . The viscous effects at the scales of interest are therefore unimportant. The particulate heat transport is also negligible. We therefore conclude that the interior of the gas cloud can be adequately described by the inviscid hydrodynamics.  Characteristic length scale L 3 ϫ 10 18 cm 6 ϫ 10 −3 cm Average density of the cloud 1.5ϫ 10 −19 g/cm 3 2 g/cm 3 Ablation pressure p a 5 ϫ 10 −9 dyn/ cm 2 10 13 Density of the ablation flow a 3 ϫ 10 −21 g/cm 3 0.02 g / cm 3 Temperature in the ablation flow T a 1 eV 10 eV Velocity of theablation flow v a 2 ϫ 10 6 cm/ s 5 ϫ 10 6 cm/ s In the ablative flow, which is almost totally ionized, the collisional mean free path is determined by Coulomb collisions, which at a temperature ϳ1 eV have a cross section ϳ3 ϫ 10 −13 cm 2 . Therefore, despite a smaller density, the collisional mean free path c in the ablation flow is very small: c ϳ 3 ϫ 10 9 cm for density of n a ϳ 10 3 cm −3 . Therefore the particulate heat and momentum transport are both negligible here. One can check that radiation losses from the ionized low-density gas are also small.
Despite being quite cold, molecular clouds are electrically conducting, because of finite ͑albeit small͒ ionization. This ionization is nonthermal, it is produced by cosmic rays for which clouds are transparent. A substantial fraction of electrons are probably attached to dust grains ͑which are present in cold clouds͒. Estimates of the degree of ionization for conditions typical for the Eagle Nebula yield the value ϳ3 ϫ 10 −8 ͑Elmegreen, 1979͒. The magnetic Reynolds number turns out to be very large ͑Ryutov and  Detailed estimates of radiation losses from molecular clouds have been done by Neufeld et al. ͑1995͒. Basically they showed that the cooling time, defined as the ratio of the thermal energy density to the power radiated from a unit volume, is very short, of order of 100-1000 yr. This means that the shocked material cools down very quickly, orders of magnitude quicker than it takes for the shock to traverse the cloud ͑ϳ10 5 yr͒. This brings up a paradox. Because of strong radiation cooling, the shocked material must collapse to a high density to maintain pressure balance, nT = p abl , at a low temperature ͑T ϳ 3 ϫ 10 −3 eV͒. This yields a density n ϳ 3 ϫ 10 6 cm −3 , which directly contradicts observed values.
Several solutions to this paradox have been proposed: the effect of ram pressure from a small-scale turbulence; the presence of a quasihomogeneous magnetic field; the presence of small-scale MHD turbulence; and the presence of force-free, random, static magnetic field. The latest discussion of these models was by Ryutov et al. ͑2004, 2005͒, where references to earlier models can be found. The present authors assume that one or a combination of these effects restores a hydrodynamic picture of the shock-compressed gas, with some effective adiabatic index.
There are multiple time scales involved in this problem. As pointed out by Pound ͑1998͒, there is a characteristic time scale for hydrodynamic motion dyn ϳ͑⌬vЈ͒ −1 , where ⌬vЈ is the velocity shear inside the cloud. According to Pound, dyn ϳ 3 ϫ 10 12 s ϳ 10 5 yr. The significance of this is that it establishes the maximum time that has passed since this shear motion began: At times much greater than dyn , the cloud would have become much larger than we actually see it. In this sense, the time dyn sets the upper limit for the time when the photoevaporation began ͑when the nearby O-type stars have "turned on"͒. It was noted by Pound that the time dyn is much shorter than the evolutionary time of the typical O-type star ͑ϳ10 7 yr͒. Therefore we are witnessing a very early stage of the photoevaporation process. This is a very important circumstance, because it points at a possibility that stars are still in a transient stage of their formation, and their luminosity may have varied significantly during the past 10 5 yr. Such variations, including nonmonotonic variations, with the luminosity passing through a maximum are a common phenomenon in the evolution of very young stars ͑e.g., Iben and Talbot, 1966;Cohen and Kuhi, 1979͒. The time scale for photoevaporation to remove a considerable amount of the initial molecular hydrogen is much longer: ϳ10 7 yr. In other words, the loss of cold gas from the molecular cloud due to photoevaporation up to the present time is very small.

C. Hydrodynamic models of the formation of the elephant trunks
There exist several models that attempt to explain the origin of the pillars in the Eagle Nebula. The earliest one was suggested by Spitzer ͑1954͒ and is based on the observation that after the shock breaks out at the back side of the cloud and the resulting rarefaction wave reaches the front side, the cloud as a unit begins to accelerate. This drives the Rayleigh-Taylor instability at the ablation front ͑remember that n abl n͒. The pillars are then identified with the familiar "spikes" of a heavy fluid penetrating through the light fluid ͑Frieman, 1954͒.
We note that if the intensity of UV radiation grows with time, the interface will be accelerated into the cloud even before the return of the rarefaction wave to the front surface. This would allow the early onset of the RT instability. Generally, the possible effects of the temporal dependence of the ionizing radiation have not been studied in any detail.
Another popular model relates the formation of the pillars to the assumed presence of the preexisting dense "clumps," whose density is substantially higher than the density of the surrounding cloud. The ablation pressure is unable to move these heavy clumps, which stay, roughly speaking, at their initial places, and shadow the cloud material downstream. Then, whereas the rest of the cloud is moved over a significant distance by the ablation pressure, the shadowed parts remain static, giving rise to the pillar structure. This process has been studied numerically by Williams et al. ͑2001͒.
A third possible model is that pillars are formed from the gas evaporated from stand-alone dense clumps situated in front of the gaseous cloud. A part of the clump material is pushed by the ablation pressure away from the radiation source, forming a cometary-like structure ͑Bertoldi, 1989; Bertoldi and McKee, 1990;Lefloch and Lazareff, 1994͒, whence a name "cometary model." The long tail eventually reaches the cloud and mixes with it, making the whole structure very similar to the one observed.

D. Laboratory experiments
Provided that our conclusion regarding the applicability of ordinary compressible hydrodynamics for the de-scription of the cloud interior is correct, one can simulate, in a scaled fashion, any of these models. Experiments using x-ray irradiation from hohlraums seem to be more relevant than experiments based on a direct laser irradiation of the target, since experiments of the first type involve the direct photoevaporation of the material by x rays. It also matters that the density of the material in the ablation flow is at least an order of magnitude less than the density of the underlying material. Experiments of the second type ͑"direct drive" experiments, Sec. II͒ are less relevant to astrophysical photoevaporation fronts, because they introduce complications not present in astrophysical systems. Specifically, the absorption zone for the laser radiation is spatially decoupled from the ablation zone, with heat being transported between these two regions by electron heat conduction. Additional complications involving laserplasma interactions are also possible ͑Kruer, 2000͒.
Because of the importance of Rayleigh-Taylor instabilities at ablating surfaces to inertial confinement fusion, there have been many experiments related to this subject. The first paper on this subject was that by Remington et al. ͑1993͒. Weber et al. ͑1994͒ carried out an exhaustive study of radiation transport and ablation front structure for conditions close to those of these experiments. The density of the ablated material was small compared to the density of the initial foil. Absorption in these experiments occurs in a relatively narrow layer, as is the case in the Eagle Nebula. Ablative stabilization ͑see below͒ plays a role only for short wavelengths, Ͻ 10 m, whereas the range of wavelengths studied was up to 150 m. It is interesting to note that the structure of well-developed RT perturbations observed by Remington et al. ͑1993͒ ͑Fig. 31͒ is very similar to the elephant trunks observed in the Eagle Nebula. Although the experiment was not optimized to have scaled parameters relevant to the Eagle Nebula, it certainly has produced relevant results, somewhat by serendipity. Comparison of the parameters of the Eagle Nebula with those of this laboratory experiment is presented in Table II.
Note that the so-called "ablative stabilization" was insignificant in both the laboratory experiment and its astrophysical counterpart. The underlying qualitative explanation of this stabilization mechanism is that the Rayleigh-Taylor perturbation is localized in a layer of thickness ϳ /2 near the surface, so that if the ablation front "consumes" or burns off a layer of thickness ϳ /2 of the fluid within a time interval shorter than the instability e-folding time, a considerable reduction in the growth rate, compared to ␥ RT = ͑2g / ͒ 1/2 , occurs. In other words, ablative stabilization becomes significant when v a Ͼ ͑ a / ͒͑g /2͒ 1/2 , where v a is the velocity of the ablative flow and we ignore a numerical factor of order unity; see surveys by Lindl ͑1995͒ and Takabe et al. ͑1999͒, for more detail and further references. Using the numbers of Table II, one finds that, indeed, the ablative stabilization is unimportant for the wavelengths of interest.
For completeness, we mention that ablation front RT instability has also been studied in extensive detail in direct drive ͑Azechi et al., 1997;Knauer et al., 2000͒.

E. Issues for experiments and theory
There exist several additional effects that have to be properly factored into the theory, numerical simulations, and experiment in order to produce a more complete picture of the real photoevaporation front phenomenon.
The first effect is related to absorption of incident radiation in ablation flow. Absorption is caused from the small fraction of electrons and ions that recombine, producing neutral hydrogen atoms which absorb ionizing radiation. Depending on the specifics of the geometry, this effect may be quite substantial. Kahn ͑1958͒ argued qualitatively that absorption of incoming radiation by hydrogen atoms formed by recombination in the ablation outflow can have a stabilizing effect, because of the stronger absorption near the dimples of the surface relief compared to the bumps. Axford ͑1964͒ presented a quantitative study that showed that this stabilization mechanism is most effective for perturbations larger than the recombination length. Sysoev ͑1997͒ provided a more complete analysis. Williams ͑2002͒ confirmed it and included the effects of radiation tilt. These papers dealt with the situation of a nonaccelerated ablation front. In a more recent study by Mizuta et al. ͑2005a, 2005b͒, both effects of acceleration and radiation absorption were included. It turned out that the linear RT instability, for the characteristic parameters of the Eagle Nebula, is stabilized by radiation absorption in the ablated plasma for concave surfaces, causing a "selfannealing" effect of any small ripples in the cloud surface. On the other hand, nonlinear perturbations may continue to grow. These results are illustrated in Fig. 32. FIG. 31. Results of ͑a͒ a simulation and ͑b͒ an experiment on the ablation front Rayleigh-Taylor instability. Perturbations are viewed side-on at 4.4 ns. The ablation front corresponds to the lower side of the material. The initial wavelength was 100 m and the initial peak-to-valley variation was 4.6 m. Three nearly simultaneous gated x-ray pinhole images are juxtaposed. Due to the ϳ100 m of parallax differences between the views, the full extent of the foil is observed. Adapted from Remington et al., 1993. Figure 32͑a͒ shows the initial configuration for the simulation, and the RT-stabilized dynamics in the linear regime calculation is shown in Fig. 32͑b͒. A simulation with larger initial perturbation is shown in Fig. 32͑c͒.
Once the curvature exceeds a critical value, the RT instability "wins out" over the self-annealing effect, and ripples grow into the deep nonlinear regime, resembling pillars in the Eagle Nebula.
In the aforementioned experiment by Remington et al. ͑1993͒, the parameters of the ablation flow were such that absorption of incident radiation was insignificant. On the other hand, by a proper choice of dopants it may be possible to reach conditions where absorption of radiation in the outflow would be similar to that in the Eagle Nebula outflow. This would then open a possibility to experimentally assess the effect of absorption on both the linear and the nonlinear stage.
The second additional effect is produced by noting that the incident ionizing radiation may be tilted with respect to the surface of the ablation front. The perturbation of the ablation pressure will then be different on the two slopes of a small-amplitude sinusoidal surface wave, leading to the excitation of this wave as a traveling wave. This effect was studied for nonaccelerated clouds by Vandervoort ͑1962͒ and, more recently, by Williams ͑2002͒. Ryutov et al. ͑2003͒ have included both the effect of acceleration and the tilt and predicted that, in the nonlinear regime, an effect similar to the breaking of the waves on the ocean surface may occur. This phenomenon can be experimentally studied in an asymmetrically radiated hohlraum, where there will be an asymmetry in the radiation flux ͑Ryutov and  The third effect is related to that situation where radiation from a distant star in the location of the cloud has a narrow angular distribution. Kane has found that this may introduce new features to the development of small-scale perturbations of the ionization front ͑Kane et al., 2005͒. This effect can also be studied with the use of a hohlraum technique, by placing the target outside the hohlraum, far enough from the hole in the hohlraum wall, so that the radiation would become strongly collimated.
As summarized in this section, the dynamics and evolution of photoevaporated molecular clouds is controlled by a wide variety of external parameters. Experiments carried out in the simplest setting ͑weak absorption in the blow-off plasma, no tilt͒ have demonstrated that structures strongly resembling elephant trunks can indeed be formed as a result of the ablation front Rayleigh-Taylor instability. This supports the viewpoint of astrophysicists that ablation front dynamics is key to understanding the shape and evolution of such objects. An assessment presented above shows that there is a possibility to include other effects and make scaled laboratory experiments much more realistic in reproducing the dynamics of real systems. These more sophisticated experiments will hopefully be carried out within a few years.

VIII. PLANETARY INTERIORS AND EQUATIONS OF STATE
The interior structure of the giant planets of our solar system ͑Jupiter, Saturn, Uranus, and Neptune͒ is deter- FIG. 32. Numerical simulations accounting for the absorption of the ionizing radiation in the ablation outflow. ͑a͒ The initial perturbation on the cloud surface. ͑b͒ 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. ͑c͒ The 2D simulation result showing that nonlinear perturbations can grow even in the presence of absorption. Adapted from Mizuta et al., 2005b. mined by the compressibility of their constituent matter under high pressures due to the inwardly directed force of gravity ͑Guillot, 1999; Guillot et al., 2004͒. In laboratory terms,  Characteristic isentropes for the giant planets indicate that the plasma in their interiors is both strongly coupled, with ⌫ = ͑Ze͒ 2 / aT Ͼ 1, where Z, e, a, and T correspond to ionization state, electron charge, average atomic spacing, and temperature ͑in units of energy͒, and degenerate, meaning = T / F Ͻ 1, where F is the Fermi energy ͑Van Horn, 1991͒. This is shown for Jupiter, as well as for a brown dwarf and a low-mass star, in the phase diagram of hydrogen in Fig. 33͑b͒ ͑Saumon et al., 1995, 2000͒. The compressibility of hydrogen along a high-pressure isentrope and the predicted phase separation in a He-H mixture when hydrogen transitions to a metallic state are of central interest both for the giant planets of our solar system and for models of the extrasolar planets ͑Fortney et al., 2004͒. Also shown in the pressure-temperature plot of hydrogen in Fig. 33͑b͒ are curves of ⌫ = 1 and degeneracy = 1, showing strongly coupled Fermi degenerate conditions. Given the large theoretical uncertainties, experimental data on the highpressure EOS, phase, and conductivity of hydrogen is needed, to guide the testing and refining of interior models of Jupiter and Saturn.
The giant ice planets Uranus and Neptune also have significant uncertainties in our understanding of their interior structures. They are thought to consist of a gaseous atmosphere, a rocky core, and a thick intermediate ocean of hot H 2 O ͑water͒, NH 3 ͑ammonia͒, and CH 4 ͑methane͒ in a dense liquid phase customarily referred to as "ice" ͑Hubbard, 1997; Cavazzoni et al., 1999͒. Pressures and temperatures in the ice layer range from 20 to 600 GPa and 2000 to 7000 K, respectively, as shown in Fig. 34͑a͒. Many of the observable quantities of the giant ice planets, such as gravitational moments, atmospheric composition, and magnetic field, are thought to be determined by the properties and conditions within the ice layer. There are large uncertainties in our understanding of how the magnetic fields of Neptune and Uranus are formed. In particular, experimental data are needed on the conductivity of water, methane, and ammonia at P Ͼ 100 GPa, before models of the origin of their magnetic fields can be firmed up.
The phase diagram of high-pressure water, shown in Fig. 34͑b͒, has large uncertainties. Starting at low temperature, water will be in the solid ice state, and depending on pressure, this can have several different phases ͑Cavazzoni et al., 1999͒. At high pressure P Ͼ 100 GPa, as the temperature is increased to T տ 2000 K it is thought that a transition occurs to a solid, superionic state, where oxygen atoms maintain a crystalline bodycentered-cubic ͑bcc͒ lattice structure, but protons can readily diffuse. This makes this solid-state material an ionic conductor but electronic insulator. As the temperature is further increased to T տ 3500 K, the oxygen sublattice also melts, and a two-component ionic liquid ͑molten salt͒ is formed, which again is an ionic conductor but electronic insulator. Finally, above 7000-7500 K, water is thought to become a metal, that is, the electronic band gap closes, E gap / kT Ͻ 1. Experimental data on the high-pressure EOS, phase, and conductivity of FIG. 33. The interior structure of Jupiter is sensitive to the high pressure, high density properties of hydrogen. ͑a͒ Schematic of the interior of Jupiter. Adapted from Guillot et al., 2004. ͑b͒ Phase diagram of high-pressure hydrogen. Reproduced from Saumon et al., 1995. 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 15M ᭪ , respectively. Curve d corresponds to the hydrogen envelope of a white dwarf. The heavy solid line labeled PPT represents the predicted plasma phase transition.
water are needed to allow theoretical progress to be made on interior models of Neptune and Uranus. Fortunately, experimental progress has been made on the high-pressure properties of both hydrogen and water.
A summary of recent experimental measurements of the shock-driven EOS of D 2 at ϳ1 Mbar pressures is given in Fig. 35͑a͒ ͑Knudson et al., 2004͒. Achieving ϳMbar pressures in these cryogenic hydrogen experiments is very difficult. The results from four different techniques are shown in Fig. 35͑a͒, corresponding to experiments done on a gas gun ͑Holmes et al., 1995͒, the Sandia Z facility ͑Knudson et al., 2003͒, a spherically convergent, high-explosive-driven experiment ͑Belov et al., 2002Boriskov et al., 2005;Trunin et al., 2005͒, andthe Nova laser ͑Collins et al., 1998͒. The gas gun, Z, and high-explosive results all more or less agree with each other. The gas gun and Z experiments both used the impedance matching technique that measures the EOS of D 2 relative to an assumed known EOS of Al. The Nova experiment was the only measurement in this set of four experiments that was absolute, that is, the compressibility of D 2 was measured directly as opposed to being inferred by comparison with the EOS of a reference material. This experiment showed enhanced compressibility, not evident in the other experiments. The reason for the difference between the Nova laser mea-surements and all the rest of the measurements is still under debate. A new set of relative measurements done on the Omega laser favors an EOS of D 2 that is less compressible than the Nova data ͑Boehly et al., 2004͒, however, the situation is still far from settled ͑Mostovych et al., 2001;Nellis, 2002͒. To conclude this ongoing debate, it seems likely that a new set of absolute measurements will be necessary. There are a number of models of the EOS of high-pressure hydrogen being compared with these data, as shown in Fig. 35͑a͒. The tabular SESAME EOS and ab initio models generally are in agreement with the stiffer EOS data from Z. The linear mixing models and the Saumon-Chabrier-Van Horn model generally favor a softer EOS, that is, higher compressibility. First measurements have also been made of shock compressing hydrogen precompressed in a diamond anvil cell ͑DAC͒, allowing denser states to be experimentally accessed ͑Loubeyre et al., 2004͒. FIG. 34. ͑Color͒ The interior structure of Neptune is sensitive to the high pressure properties of water. ͑a͒ Schematic of the interior of Neptune. Reproduced from Hubbard, 1997. ͑b͒ Phase diagram of high-pressure water. Adapted from Cavazzoni et al., 1999. FIG. 35. Models used to predict the interior structure of Jupiter are tested with strong shock experiments. ͑a͒ Summary plot of recent high-pressure shock Hugoniot measurements of D 2 . Adapted from Knudson et al., 2004. ͑b͒ Plot showing the sensitivity of calculations of the interior of Jupiter to the models of the high-pressure EOS of hydrogen. Adapted from Saumon and Guillot, 2004. Different curves correspond to the following models. LM-A: Modified Ross linear mixing model. LM-H4: Linear mixing, with D 4 chains, D 2 molecules, and a D + + e − fluid metal. LM-SOCP: Ross linear mixing model, only with the one component plasma ͑OCP͒ replaced with a screened OCP for the metallic ͑atomic͒ 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 Ͻ 0.2 Mbar.
The impact on the predicted structure of the interior of Jupiter for the different EOS models is shown in Fig.  35͑b͒ ͑Saumon and  . This figure shows the mass of the core of Jupiter versus the mass of high-Z elements mixed throughout the planet, predicted using five different models of high-pressure EOS of D 2 . Models that did not reproduce the global gravitational moments of Jupiter, as determined by satellite fly-by missions, were eliminated from these comparisons. The results in Fig. 35͑b͒ show that the interior structure of Jupiter is surprisingly sensitive to the details of the highpressure EOS of hydrogen. Hence there is considerable impact and scientific interest in concluding the experimental debate on the EOS of D 2 .
There are new experimental results measuring the EOS and conductivity of high-pressure water ͑Celliers et Koenig et al., 2004͒ relevant to the interior of Neptune. In these measurements, the principle Hugoniot of water was measured by the impedance matching technique at an Al-H 2 O interface, as shown in Fig. 36͑a͒ ͑Celliers et al., 2004͒. Also, the reflectivity of highpressure water at the shock front was measured, as shown in Fig. 36͑b͒, from which the electronic conductivity e was inferred with the aid of a Drude model. This model, thus calibrated, was used to estimate e along the isentrope of Neptune, as shown in Fig. 36͑c͒. This compared with measurements of the total dc conductivity of water dc done with singly shocked ͑Nellis et al., 1988͒ and reverberating shocks on a gas gun ͑Chau et al., 2001͒ suggest that the electronic conductivity contributes roughly equally with ionic conductivity at 5000 K along the isentrope of Neptune, and will begin to dominate at higher temperatures. This will have significant implications for future models of the interior of Nepture, and, in particular, on models of the formation of its magnetic field.
Also, new dynamic measurements address the EOS and high-pressure melt transition in Fe ͑Benuzzi- Mounaix et al., 2002;Nguyen and Holmes, 2004͒, relevant to the inner-core, outer-core boundary region of the interior of Earth. A key issue here is resolving the discrepancy between the highpressure melt temperature detected dynamically in shock experiments and static measurements in a diamond-anvil cell ͑DAC͒. Additional experiments and research will likely be required to conclude this debate.

IX. COMPACT OBJECT ACCRETION DISKS AND PHOTOIONIZED PLASMAS
Photoionized plasmas are encountered in a wide variety of situations in astrophysics, namely, wherever gas is bathed in a strong radiative flux. Examples include emission nebulae that result from the photoionization of a diffuse gas cloud by ultraviolet photons from a hot "exciting" star ͑Osterbrock, 1989͒, line emission induced by continuum radiation from strong shocks, and x-raycontinuum-pumped line emission from accretion disks around compact objects such as neutron stars, black holes, or white dwarfs ͑e.g., Ballantyne et al., 2002͒. Such pumping by continuum x rays occurs in x-ray binaries, discussed further below, as well as in active galactic nuclei, not discussed here ͑Krolik, 1999͒.
Here we focus primarily on the photoionized plasma conditions generating line emission from x-ray binaries, which are neutron stars or stellar-mass black holes in orbit with a stellar companion. These typically fall into two categories, divided by the mass of the stellar com- FIG. 36. The high-pressure properties of water are probed with strong shock experiments. ͑a͒ Plot of the measured EOS of water along the principle Hugoniot, at pressures up to ϳ1000 GPa. ͑b͒ Measurements of the reflectivity of shocked water vs shock velocity and shock pressure. ͑c͒ Analysis of the decomposition of the dc conductivity of water at high pressure along the isentrope appropriate for the interior of Nepture. Adapted from Celliers et al., 2004. panion: low-mass x-ray binaries ͑LMXB͒, where the companion mass is less than about ͑1-2͒M ᭪ ͑solar masses͒; and high-mass x-ray binaries ͑HMXB͒, where the companion star is typically several tens of solar masses. The line emission from LMXBs is mostly thought to arise in an irradiated accretion disk ͓as illustrated schematically in Fig. 37͑a͒ ͑Jimenez-Garate et al., 2002͔͒. In HMXBs, much line emission can be produced by photopumping of a wind issuing from the companion ͓illustrated schematically in Fig. 37͑b͒ ͑Willingale et al., 1985͔͒.
An example of an accreting compact object is Cygnus X-3 ͑Bonnet-Bidaut and Chardin, 1988͒, an object whose companion likely started out life as a massive star ͑although its mass today is highly uncertain͒ and the nature of whose compact object remains controversial ͑e.g., Lommen et al., 2005͒. A sample Chandra x-ray spectrum from Cyg X-3 is shown in Fig. 37͑c͒ ͑Paerels et al., 2000͒. The energy source "pumping" the emission lines is believed to be the hard x-ray continuum emanating from the accreting compact object. The simplest interpretation of Cyg X-3 is that the x-ray emission is from plasma in photoionization equilibrium ͑Liedahl and Paerels, 1996͒. Particularly striking in Fig. 37͑c͒ are the radiative recombination continuum ͑RRC͒ peaks. The widths of these RRC peaks give a very good determination of T e in the plasma, which is too small to produce the observed ionization states by collisional ionization. Different peaks correspond to different levels of ionization, and their widths typically suggest different temperatures of their emitting regions. Global shifts of the identified peaks in the photoionized plasma spectra are produced by variations in the collective plasma flow velocity. Hence, through the combined observations of ͗Z͘, RRC peak widths, and shifts in various line positions, the overall dynamics of the plasma in the vicinity of the accreting compact object can start to be mapped out.
To illustrate the basics of photoionized plasmas ͓following the nomenclature of Liedahl ͑1999͔͒, we assume steady-state ionization balance, and write ␤ i n i + n e C i n i = n e ␣ i+1 n i+1 + n e 2 ␣ 3,i+1 n i+1 , ͑9.1͒ where n e , n i , ␤ i , and C i represent electron density ͑cm −3 ͒, ion density of charge state i ͑cm −3 ͒, the photoionization rate ͑s −1 ͒ of charge state i, and the collisional ionization rate coefficient ͑cm 3 s −1 ͒ of i, respectively. The coefficients ␣ i+1 and ␣ 3,i+1 are for charge state i + 1 the twobody recombination rate coefficient ͑cm 3 s −1 ͒, including radiative recombination and dielectronic recombination, and the three-body recombination coefficient ͑cm 6 s −1 ͒, respectively. Three-body recombination is the inverse process of electron collisional ionization, and is generally important only at high densities, n e Ͼ 10 16 cm −3 . For the case of x-ray binaries, which is the example we discuss here, typically n e ␣ 3,i+1 ␣ i+1 , that is, three-body recombination is negligible relative to two-body recombination ͑Jimenez-Garate et al., 2002͒, so we assume ␣ 3,i+1 ϳ 0. The situation with ␤ i = 0 represents collisional ionization equilibrium ͑CIE͒, also referred to as coronal equilibrium, where radiative recombination is balanced by collisional ionization by electrons, and ionization by radiation is negligible. The CIE ionization balance is written as FIG. 37. Models of accreting compact objects, such as neutron stars or black holes, and an x-ray spectrum from such an object. ͑a͒ Accretion disk model for low-mass x-ray binaries. Adapted from Jimenez-Garate et al., 2002. ͑b͒ Stellar wind model for high-mass x-ray binaries. Adapted from Willingale et al., 1985. ͑c͒ 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 ϳ10 kpc, and has a binary orbital period of 4.79 hr. Adapted from Paerels et al., 2000. ͩ n i+1 In contrast, the situation with n e C i ␤ i can be referred to as photoionization equilibrium ͑PIE͒. The photoionization rate for a point source of ionizing continuum at a distance r from the location of interest can be written ͑Liedahl, 1999͒ ␤ i = L x i / r 2 , where L x is the x-ray luminosity ͑ergs/s͒ from the accreting compact object, and the coefficient i having units of cm 2 / erg is defined by Here i is the ionization potential out of charge state i and f ͑͒ is the spectral shape function, normalized so that ͐df ͑͒ = 1, where the integral is over x-ray energy . The PIE ionization balance is then written as in which we have defined the ionization parameter as L x / n e r 2 ͑with units of erg cm/ s͒ which is one of several similar definitions in the astrophysical literature. Note that while the ratio of ionization state populations in CIE depends only on a ratio of coefficients, the ratio in PIE depends on a ratio of coefficients and in addition on .
In terms of the ionization parameter ͑ignoring threebody recombination͒, one can write Eq. ͑9.1͒ as

͑9.4͒
This allows one to see easily the CIE limit, where =0, and the PIE limit, where is very large. One can also see why photoionized plasmas are often described as "overionized," since their ionization is always larger ͑and is sometimes much larger͒ than the ionization of a CIE plasma at the same electron temperature T e . The emission spectrum from a photoionized plasma having large includes prominent recombination lines, produced when electrons radiatively recombine with an ion, reducing its charge state. Recombination lines are thermally broadened to higher energy because the electron that joins the ion may have a range of initial energies. Thus the amount of broadening increases with and is a diagnostic of T e . The recombination lines from a strongly photoionized plasma are narrow compared to those from collisionally ionized plasmas, because the charge states ͑and thus transition energies͒ are far larger than those that would be produced by thermal electrons without the radiation. The narrowness of the recombination lines is one signature of a photoionized plasma. There are also other differences in the emission spectra of photoionized ͑as opposed to collisionally ionized͒ plasmas ͑Liedahl et al., 2001͒. In regions of PIE, highly ionized ions are observed by UV and x-ray satellites over the range =10-10 4 ergs cm/ s. Below that range, recombination lines fall at energies below the x-ray band and are not observed by x-ray satellites. Above that range, most ions are fully stripped and neither freebound nor bound-bound transitions are observed.
Photoionized plasma codes that calculate ionization balance and predict emission spectra are essential for interpreting spectral data from astrophysics and from the laboratory. Most of the different codes in wide use have similar overall structures and approaches ͑Ferland et Liedahl et al., 2001͒. These models do not assume an equilibrium ͑LTE͒ distribution of ionization or of excited states and they may or may not assume a Planckian radiation spectrum. The level of ionization is determined by balancing all ionization and recombination processes. Ionization processes include photo, Auger, and collisional ionization and charge transfer. Recombination processes include radiative, dielectronic, three-body recombination, and charge transfer. Free electrons are typically assumed to have a Maxwellian velocity distribution. These models typically solve equations for the line and continuum radiative transfer simultaneously, and thus evolve the radiation spectrum and predict the detailed emission spectra. The charge state fractions, atomic excitations, and emission spectra are computed in some kind of "detailed level accounting" methodology, evolving the dominant rates into and out of each energy level. The various models treat the atomic structure and detailed level accounting at various levels of sophistication and detail. Examples follow of codes currently in wide use that calculate spectral emissions from photoionized plasmas.
GALAXY is a collisional-radiative code that calculates the steady-state ionization balance within the plasma, given density, temperature, and incident radiation field as input ͑Rose, 1998; Foord et al., 2004Foord et al., , 2006Rose et al., 2004͒. Collisional and radiative excitation and ionization as well as autoionization and all reverse processes are included. Screened hydrogenic rates for both collisional and radiative processes are assumed, and Hartree-Dirac-Slater ͑HDS͒ cross sections are used for photoionization. The GALAXY code employs an average-ofconfiguration approximation for electronic states with a principal quantum number n Յ 5 and configuration averages for higher n.
NIMP is a non-LTE, average-atom model ͑Djaoui and Rose, 1992;Rose et al., 2004͒. It follows the time evolution of principal quantum shell occupancies, averaged over the distribution of ionic states. As a result, the shell occupancies are noninteger. By following the shell populations in time, the number of differential equations is reduced in comparison with what is needed for a model that follows individual ionic states. A fundamental approximation made is that there is no statistical correlation between electrons occupying different shells. NIMP includes photoexcitation and photionization, as well as their inverse rates, using simple Kramers photoionization cross sections, convolved with the intensity of the ambient radiation field. NIMP employs a time-dependent model, that is, it does not assume steady-state conditions.
FLYCHK is a collisional-radiative model that calculates non-LTE, non-steady-state ionization distributions, given inputs of density, temperature, and radiative flux ͑Chung et al., 2003͒. It uses highly accurate atomic data for ions with an open K shell and for Li-like ions. Their populations are calculated from rate equations including all relevant collisional and radiative processes. The kinetics of other ions with an open L shell or M shell are included by assuming a hydrogenic model for selected ions, for which transitions out of and into excited states are calculated, and ground states for the remaining ions. Alternatively, a screened hydrogenic model for all ions, including ions with an open K shell, can be selected. In this case, ground-state and excited-state configurations are considered in the calculation of all rates. FLYCHK is capable of performing calculations for steady-state or time-dependent cases, and for collisionally dominated as well as radiation-dominated cases. This code, and its predecessor FLY, were developed originally to model ionization balance and kinetics in high power laser experiments. They have been compared against a wide variety of laboratory data over the past two decades.
CLOUDY is a steady-state, photoionized-plasma code developed to analyze and interpret spectral observations of astrophysical plasmas. It has been in use in the astrophysics community for ϳ25 years ͑Ferland et al., 1998͒. More recently, it has started to come into use to calculate ionization balance in laboratory experiments on high-energy-density facilities, such as Z pinches and lasers ͑Foord et al., 2006͒. CLOUDY is a large-scale, spectral-synthesis code designed to simulate the heating and cooling within an astrophysical plasma of a given density and then to predict the emitted spectrum. It relies on atomic databases to allow accurate comparisons with spectral emission data. CLOUDY calculates both the ionization balance and electron temperature by a detailed energy accounting of all relevant heating and cooling processes in the plasma, such as from collisional excitation followed by radiative cooling. With input of density, species concentrations, and incident x-ray flux, CLOUDY will calculate emission spectra and the plasma T e . The other models above assume T e is given as input.
There are other photoionized plasma codes that have not yet been applied to the experiments discussed below. One example is the XSTAR code ͑Kallman et al., 1996Bautista and Kallman, 2001;Kallman and Bautista, 2001;Boroson et al., 2003͒, which calculates a steady-state model of a spherical gas cloud with a radiation source at its center. The input parameters include the source spectrum, the gas composition and density, and ionization parameters. XSTAR then finds as a function of radius the electron temperature, the atomic level populations, and the emitted spectrum that escapes the cloud. XSTAR has been applied ͑Boroson et al., 2003͒ to HMXBs. Another example is the code TITAN ͑Dumont et al., 2000;Collin et al., 2004͒, which makes similar assumptions to those of XSTAR and also includes Comptonization and emphasizes an accurate treatment of radiative line transfer.
To test and validate the models used to interpret astrophysical photoionized plasma spectra, such as that shown in Fig. 37͑c͒, experimental data from photoionized plasmas in relevant regimes are required. It was recognized recently that relevant conditions could be created in the laboratory using the intense burst of x rays coming from the Z-pinch at the SNLA Z facility Heeter et al., 2001; 2003͒. An experiment was developed to measure the x-ray spectra from a photoionized plasma under approximately scaled conditions. As discussed above, the figure of merit is the ionization parameter = L x / n e r 2 . The goal was to reproduce, in a scaled sense, the photoionization conditions found in the x-ray binary Cyg X-3, where =10 2 -10 3 erg cm/ s.
In the experiments radiation from the pinch was generated by coupling a 20-MA, 100-ns rise time current pulse into a 2-cm-diameter, 1-cm-length, cylindrical wire array, producing plasma that implodes at hundreds of km/s and then stagnates, causing intense x-ray emission. This created an 8-ns full width at half maximum x-ray source with a spectrum close to that of a black body with a temperature T r of 165 eV. The x-ray flux from the pinch is spectrally measured with the combination of an absolutely calibrated transmission grating spectrometer, an array of filtered x-ray detectors ͑XRDs͒, and an array of filtered photoconducting detectors ͑PCDs͒. The result is shown in Fig. 38͑a͒. For comparison, a peaknormalized T r = 165 eV black-body radiation spectrum is also shown ͑Foord et al., 2004͒. This x-ray burst at peak power is preceded by a period of lower radiation flux. A sample was designed so that the early, lower radiation flux would produce a large, slowly evolving plasma through which the later, intense radiation could penetrate. The charge-state distribution in the sample, the density in the sample, and absolute radiative flux as a function of energy were measured independently. The pinch also produces a quasicontinuum x-ray source at the energies required to produce a useful absorption spectrum. A typical absorption spectrum from an Fe sample, located a distance of 1.5-1.6 cm from the pinch, is shown in Fig. 38͑b͒ ͑Foord et al., 2004͒. In this experiment, reaches a value near 25 ergs cm/ s at the peak of the radiation pulse, and the observed time-integrated absorption spectrum is believed to correspond to ϳ 20. The measured electron density is n e ϳ 2 ϫ 10 19 cm −3 . Also, calculations show that electrons and ions equilibrate rapidly, so the ion temperature T i can be taken to equal T e ͑Foord et al., 2004, 2006͒. The code CLOUDY, when allowed to calculate the electron temperature and run with a model consistent with the measured saturation of the Fe resonance lines, finds T e = 150 eV.
A number of photoionized plasma models have now been compared with these results, as shown in Figs. 38͑c͒ and 38͑d͒. In Fig. 38͑c͒ ͑Foord et al., 2004, 2006͒ we show the results for steady-state simulations using fixed T e and n e . The radiation field has a spectrum and energy density consistent with those produced by the pinch in the experiment, but is implemented in the simulations as an isotropic field. The conditions used correspond to = 20. Results from the model GALAXY are shown as a function of temperature from 30 to 210 eV. The experimental data are shown by the circular symbols with error bars. At the density of the experiment ϳ2 ϫ 10 19 cm −3 calculations show that as T e is lowered below ϳ50 eV, three-body recombination becomes important, and ͗Z͘ starts to decrease. From 70 to 210 eV, however, additional increases in temperature have little effect, because three-body recombination has become small and thermal electrons have insufficient energy to ionize ions that were produced by photoionization. Simulations from the models FLYCHK ͑Chung et al., 2003͒ run with T e = 150 eV and CLOUDY ͑Ferland et al., 1998͒ are also shown. It is interesting to note that FLYCHK and GALAXY predict broader distributions than CLOUDY ͑and the data͒, shown in Fig. 38͑c͒. For temperatures in the range T e = 70-210 eV, GALAXY predicts FIG. 38. The results from experiments on the Z facility test models of photoionized plasmas. ͑a͒ Z-pinch x-ray flux spectral measurement at peak power with an XRD array ͑stepped lines͒, a transmission grating spectrometer ͑solid circles͒, and a PCD array ͑solid squares͒. Shown for comparison is a peak-normalized T r = 165 eV black-body spectrum. Adapted from Foord et al., 2004. ͑b͒ 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 Foord et al., 2004. ͑c͒ Calculations of the ionization distribution from the photoionized plasma models GALAXY, CLOUDY, and FLYCHK compared with observations. Adapted from Foord et al., 2004. ͑d͒ Calculations of the ionization distribution from the photoionized plasma models NIMP and GALAXY, compared with that observed in the experiment of ͑a͒. Adapted from Rose et al., 2004. ͑e͒ 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 ͑a͒. Adapted from Phillips et al., 2001. a width of full width at half maximum of 1.6-1.7, compared to 1.2 for CLOUDY. Differences in the widths are likely due to differences in the specific rates that couple the Fe 15+ , Fe 16+ , Fe 17+ , and Fe 18+ ions ͑Foord et al., 2004͒. For example, dielectric recombination and autoionization are treated somewhat differently in each code, which could effect ͗Z͘ and the ionization distribution width ͑Foord et Rose et al., 2004͒. The fact that CLOUDY calculates T e and the charge state selfconsistently may be relevant to its better agreement with the data ͑Foord et al., 2006͒. More extensive comparisons with data would be needed, however, before such a conclusion could be firmed up. Properly treating radiative transfer in the major cooling lines, which are at least partially optically thick, is also important for getting more realistic models. This is an area where considerable work still needs to be done ͑Van Hoof, 2005͒.
Additional comparisons of the predicted versus experimentally observed ionization distribution for this plasma are shown in Fig. 38͑d͒ ͑Rose et al., 2004͒, for calculations with the average-atom model NIMP ͑Rose et al., 2004͒, making the assumptions described in the previous paragraph regarding n e , T e , and the magnitude and spectrum of the radiation field. Calculations are shown without and with inclusion of the radiation field. Without radiation, the observed ionization state would be underpredicted. In other words, photoionized plasmas exhibit ͗Z͘ which is significantly greater than the result in collisional regimes at the same T e . Also included in the comparison are predictions from GALAXY ͑Rose, 1998͒ presented for the same conditions. It is interesting that the average atom model NIMP, which is a much simpler model, does a better job at reproducing the measured ionization distribution than GALAXY, which includes much more detailed atomic physics. This suggests that refinements may be needed in the transition rates used by GALAXY to populate the Fe 16+ , Fe 17+ , and Fe 18+ ions, in particular, in the dielectronic recombination and autoionization processes ͑Foord et al., 2006͒. NIMP, on the other hand, follows the time evolution of principal quantum shell occupancies, averaged over the distribution of ionic states. This class of model has been used widely over the past three decades, and has been extensively and successfully calibrated against laser experiments, which may contribute to the better agreement with data shown in Fig. 38͑d͒. It may also be that "coverage" is more important than "accuracy" for capturing the average charge state distribution of the plasma ͑Rose et al., 2004͒. Even though the atomic data used in NIMP are not as detailed or as accurate as in GALAXY, NIMP includes all possible energy levels and transition pathways in an average sense. This may, in fact, be more important for calculating the average ionization state. If, on the other hand, one is trying to match an individual spectral line position or shape, then accuracy is more important, and GALAXY would be superior to NIMP. An evaluation of the predicted effect of density on ͗Z͘ is shown explicitly in Fig. 38͑e͒. This figure shows the results of GALAXY calculations ͑Phillips et al., 2001͒ for the average ionization of Fe, over a wide range of elec-tron density n e ͑cm −3 ͒. The calculations assumed that T e = 100 eV, that the radiation spectrum was Planckian with T r = 200 eV, and adjusted the radiation flux to maintain = 10 ergs cm/ s. This shows that, for the conditions roughly similar to those achieved in the experiment at the Z facility, the electron density needs to stay below n e Ͻ 10 19 cm −3 for collisional effects ͑three-body recombination, collisional ionization͒ to be negligible in the ionization balance.

X. OUTLOOK FOR THE FUTURE
There are a multitude of new facilities on the horizon that will enhance the ability to pursue HED laboratory astrophysics. These include high-energy, long pulse lasers and magnetic pinch facilities; high-energy, short pulse lasers; and ultrashort pulse lasers. In the category of high-energy HED facilities, the NIF ͑at LLNL͒ ͑Hogan et Miller, 2004;Moses, 2004͒ andLMJ ͑at CEA in Bordeaux, France͒ ͑Andre, 1999;Cavailler et al., 2004͒ lasers will each deliver about ϳ2 MJ of laser energy, once they are complete. The LIL laser in Bordeaux, France, will be an eight-beam demonstration facility for LMJ, and should achieve at full performance over 60 kJ of 3 light ͑Di-Nicola et al., 2004͒. The ZR magnetic pinch facility ͑at SNLA͒ will deliver a fast risetime pulse of 30 MA current to implode a cylindrical wire array, generating over ϳ2 MJ of x rays ͑Matzen et al., 2005͒. The Omega-EP facility ͑Stoeckl et al., 2006͒ will include two 2.5-kJ PW lasers, which can be focused either into a stand-alone chamber or into the Omega 60-beam chamber, synchronized with the 30 kJ, 60-beam Omega laser, enabling new regimes of high intensity laser-matter interaction studies ͑Sangster, 2004͒. The LULI laser facility is being upgraded to have four beams: one 1-kJ, 1-long pulse beam, one PW beam, and two 100-J probe beams ͑Koenig et al., 2004͒. The Gekko-12 laser facility at Osaka University will be upgraded so that the 12-beam, 10-kJ-long pulse Gekko will be augmented by a high-energy ͑up to ϳ10 kJ͒ petawatt beam for fast ignition studies ͑Miyanaga et al., 2004͒. The Helen laser at AWE in the UK will be upgraded into Orion, which will be ten 1/2-kJ 2 beams, plus two 1/2-kJ petawatt lasers. And the Vulcan petawatt is just starting routine operation at ϳ500 J in ϳ1/2 ps ͑Danson et al., 2004͒. There are also a number of ultrashort pulse ͑Շ1 ps͒, moderate-energy lasers operating or under development, such as the Texas Petawatt at the University of Texas at Austin ͑Gaul et al., 2005͒, and the Leopard laser at the University of Nevada at Reno. The Zebra magnetic pinch machine, also at the University of Nevada at Reno, is being developed, and will be combined with the Leopard laser, to form the Nevada Terawatt Facility ͑Erlandson et al., 2004͒. All of these facilities will eventually be equipped with an array of timeresolved diagnostics, for carrying out unique HED experiments.
The greater number of HED experimental facilities will allow the new area of HED laboratory astrophysics to be developed at a much faster pace. With the advent of the next generation of very large facilities ͑NIF, LMJ, ZR͒, key new regimes will be accessible where current facilities have fallen short. Based on the discussions given in this article, we suggest the following as potential fruitful areas for next generation HED laboratory astrophysics studies on the large facilities.
In the area of SN explosion hydrodynamics, a scaled, multilayer, spherically divergent experiment could be carried out that should transition well into the turbulent regime. Attempts at a scaled down version of such an experiment on the Omega laser came up short in the amount of energy available to drive the package. The desired hydrodynamic instabilities were initiated, but never entered the deep nonlinear regime ͑Robey et Drake et al., 2002͒. With the larger energies available on NIF and LMJ, this multilayer, divergent geometry experiment could serve as a conclusive test whether the "standard ͑spherical shock͒ model" of core-collapse SNe is correct, at least from a hydrodynamic perspective.
It should become possible to test high Mach number jet propagation and collimation over longer distances through an ambient medium, with and without the effects of radiative cooling. Experiments such as this should help answer whether astrophysical jets can remain collimated from a purely hydrodynamic or radiative-hydrodynamic perspective or whether additionally magnetic fields are required.
With the more intense bursts of x rays possible on the next generation larger facilities ͑NIF, LMJ, ZR͒, it should be possible to conduct photoionized plasma experiments in the correct regime of ionization parameter, ϳ L / n e r 2 , allowing black-hole accretion disk models to be tested under properly scaled conditions.
In the area of opacities, the larger facilities open up the possibility for measurements of opacity under conditions relevant to the core of solar-sized stars ͑ϳ1 keV, 100 g / cm 3 ͒. Also, measurements of expansion opacities, that is, opacities in a homologously expanding ball of plasma, should be possible. These are relevant to SN light curve calculations.
Another new regime will be the ability to study matter under planetary interior conditions, with quasiisentropic drives that reach 1 -10-Mbar conditions, or higher, in a well-controlled, reproducible manner. This should allow EOS determinations and measurements of phase, conductivity, and maybe even solubility of mixtures of H, He, and more complex "ices" under conditions relevant to planetary interiors. It should be possible to experimentally show, unambiguously, whether or not the plasma phase transition in hydrogen exists. It may even be possible to study properties of matter under even more extreme conditions relevant to the envelopes of white dwarf stars. White dwarfs are interesting in their own right, but also serve as "cosmochronometer" ͑Fontaine et al., 2001͒, and when accreting from a binary partner, form the initial conditions for a type-I SN.
Extended duration radiation sources will be available, which will be ideal for experimental studies of models and the dynamics of radiatively driven molecular clouds, such as the Eagle Nebula ͑Mizuta et Pound et al., 2005͒. Unique effects are predicted due to the directionality of the radiation, due to stars acting effectively as "point sources," and due to the photoevaporated plasma not necessarily being optically thin ͑Kane et Mizuta et al., 2005a Once ignition is achieved, the intense burst of D-T neutrons, generating a flux of 10 32 -10 33 neutrons/ cm 2 s, may allow excited-state reactions to occur, which are relevant to the nucleosynthesis of heavy elements, i.e., those nuclei more massive than Fe ͑Libby et al., 2004͒. It may also be possible to study thermonuclear reactions in highly screened, dense plasmas, relevant to reactions in dwarf stars. If high gain ͑G Ͼ 100͒ implosions can be produced ͑Suter et al., 2004͒, it may be possible to examine some of the physics issues surrounding the proposed deflagration-to-detonation transition, and the role of hydrodynamic mixing, relevant to type-I supernovae.
Finally, with ultrahigh intensity, short-pulse lasers it may be possible to study matter under ultraextreme conditions relevant to the vicinity and atmospheres of accreting neutron stars ͑Moon et al., 2005͒. Extreme large magnetic fields are needed in a radiation-dominated plasma. Generation of the electron-positron plasma of relevance to particle acceleration mechanisms in astrophysics has also been discussed ͑Liang et al., 2003;Wilks et al., 2005͒. Aspects of these conditions may be within reach with the combination of multiple petawatt lasers, plus the NIF, LMJ, or ZR driver.