3
High Energy Density Laboratory Plasmas

INTRODUCTION

Imagine taking the output of the entire global power grid for a few billionths of a second and focusing it with a large laser onto the surface of a hollow capsule no bigger than the head of a pin. Next, imagine filling the capsule with isotopes of hydrogen (deuterium and tritium), then sitting back to “watch the action.” The capsule responds by imploding at velocities of up to 300 km/s, that is, at speeds approaching 0.1 percent of the speed of light! (See Figure 3.1.) At peak compression, the temperatures and densities at the center are of order 108 kelvin (10 keV) and 100 g/cm3, with pressures approaching 100 Gbar (~1016 P). These conditions mimic those found at the center of the Sun. Not surprisingly, the outcome is a “microsun,” for a very brief moment (0.1 ns) spewing forth a miniexplosion of neutrons and alpha particles from nuclear fusion. The pursuit of this “controlled astrophysics in the laboratory” is the routine business of the inertial confinement fusion (ICF) program in the United States, and it forms the focus of an enormous variety of high energy density (HED) physics research.

High energy density physics, as said earlier, is the study of the collective properties of matter under extreme conditions of temperature and density. Not surprisingly, this study of extreme science has considerable overlap with astrophysics and nuclear weapons physics, as well as inertial confinement fusion research. This chapter gives a broad survey of laboratory HED physics, starting in the next section with a list of important scientific questions that could potentially be addressed on



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3 High Energy Density Laboratory Plasmas INTRODUCTION Imagine taking the output of the entire global power grid for a few billionths of a second and focusing it with a large laser onto the surface of a hollow capsule no bigger than the head of a pin. Next, imagine filling the capsule with isotopes of hydrogen (deuterium and tritium), then sitting back to “watch the action.” The capsule responds by imploding at velocities of up to 300 km/s, that is, at speeds approaching 0.1 percent of the speed of light! (See Figure 3.1.) At peak compression, the temperatures and densities at the center are of order 108 kelvin (10 keV) and 100 g/cm3, with pressures approaching 100 Gbar (~1016 P). These conditions mimic those found at the center of the Sun. Not surprisingly, the outcome is a “microsun,” for a very brief moment (0.1 ns) spewing forth a miniexplosion of neutrons and alpha particles from nuclear fusion. The pursuit of this “controlled astrophysics in the laboratory” is the routine business of the inertial confinement fusion (ICF) program in the United States, and it forms the focus of an enormous variety of high energy density (HED) physics research. High energy density physics, as said earlier, is the study of the collective properties of matter under extreme conditions of temperature and density. Not surprisingly, this study of extreme science has considerable overlap with astrophysics and nuclear weapons physics, as well as inertial confinement fusion research. This chapter gives a broad survey of laboratory HED physics, starting in the next section with a list of important scientific questions that could potentially be addressed on

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FIGURE 3.1 X-ray pinhole camera “movie” of a directly driven inertial confinement fusion implosion on the OMEGA laser system, from the laser irradiating the shell at early times, to the formation of a hot spot. Each image has ~50-ps temporal resolution, and the total duration of the “movie” is ~3.2 ns. The initial target diameter (upper left image) is ~1 mm, and the final compressed core diameter (third image, bottom row) is <100 µm. Courtesy of the Laboratory for Laser Energetics, University of Rochester.

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HED facilities. Then various experimental facilities are described; the section on “Facilities” is devoted to a discussion of a wide range of HED physics phenomena, and areas of overlap with astrophysics and other branches of physics are pointed out. Some applications of HED physics are then described, and the final section of the chapter describes some of the opportunities for high energy density physics studies in the laboratory. KEY QUESTIONS It is now possible for experimental science to enter into a regime that has been, until now, largely the exclusive domain of theoretical and computational physics, namely, the collective behavior of matter under extreme conditions of density and temperature. Such conditions are commonplace in astrophysics, yet laboratory experimental mileposts are rare. Indeed, the report of the National Research Council’s Committee on the Physics of the Universe, Connecting Quarks with the Cosmos,1 has embraced the need for laboratory exploration of physics under extreme conditions on HED facilities. As a guiding framework for describing this experimental frontier, the Committee on High Energy Density Plasma Physics presents a list of fundamental questions that could potentially benefit from experiments on current or future HED facilities: Can thermonuclear ignition be achieved in the laboratory? Can high-yield inertial confinement fusion implosion experiments contribute to our understanding of aspects of thermonuclear supernova explosions? Can nucleosynthesis of the heavy elements (Z>50) be studied using the intense burst of 1019 neutrons from high-yield capsule implosions? Can thermonuclear ignition lead to energy production (and possibly then to hydrogen production) through inertial fusion energy? Can the transition to turbulence in compressible flows be understood? Can supersonic turbulent flows be generated? Is there a fundamentally new, first-order phase transition unique to the plasma state, the so-called plasma phase transition (PPT)? Do mixtures (e.g., He-H, C-O, and so on) undergo phase separation at sufficiently high densities? Can metallic hydrogen ever exist in the solid state, or do quantum zero-point vibrations prevent this? 1   National Research Council, Connecting Quarks with the Cosmos: Eleven Science Questions for the New Century, Committee on the Physics of the Universe, The National Academies Press, Washington, D.C., 2002.

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Can laboratory experiments help to discriminate among competing models of planetary interiors and planetary formation? Can experiments help establish whether the core of Jupiter is solid or liquid? Is convection not possible in Jupiter’s metallic hydrogen layer, and what are the consequences for Jupiter’s interior? Can intense bursts of thermal electron-positron plasmas be created and studied in the laboratory? Can relativistic jets and shocks be generated from such an electron-positron fireball relevant to gamma-ray burst models? Are the dynamics of such relativistic jets and shocks fundamentally different from those of their nonrelativistic counterparts? Can conditions of radiation-dominated matter be created in the laboratory? Can conditions relevant to radiation-dominated black-hole or neutron star accretion disks be generated and probed? At low densities, can an equilibrium photoionized plasma be created in the density-independent, radiation-dominated regime? At high densities, can conditions be created in which radiation pressure dominates particle pressure? Are there new dynamics for this case, such as a photon bubble instability? Can macroscopic assemblies of fully degenerate matter (degenerate electrons and degenerate ions) be created, and their thermal and mechanical properties measured? Can plasma transport coefficients be determined under such conditions of extreme degeneracy, where continuum lowering dominates opacities and quantum effects dominate the plasma? Can the equation of state of bulk nuclear matter be determined in the laboratory? Can the conditions of “core bounce” (i.e., the nuclear rebound) in core-collapse supernovae be experimentally reproduced? Can the structure of neutron star interiors be experimentally accessed? Can a phase transition to the quark-gluon plasma be inferred? Can the properties of a quark-gluon plasma be determined? Can sufficiently high densities be created in the laboratory to allow pycnonuclear fusion reactions (genuine cold fusion) to be observed? Can nuclear reactions under highly screened conditions in dense plasmas relevant to the cores of massive stars be studied in the laboratory? Can macroscopic assemblies of relativistically degenerate matter (Fermi temperature, ΘFermi>mec2) be created in the laboratory, and their equations of state be determined? Can the boundary between a stable white dwarf core and one that will unstably collapse to a neutron star be verified in the laboratory? Can a radiatively collapsed shock be created in the laboratory? Would new thin-shell instabilities be created as a result? Can strong magnetohydrodynamic (MHD) shocks be created? Can a collisionless shock be created, or

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its mechanism be inferred? Can shock-induced particle acceleration be demonstrated? Can astrophysical jet formation and jet collimation mechanisms be elucidated with laboratory experiments? Can ultrastrong magnetic fields, B>1 gigagauss, be experimentally created and their effect on the surrounding plasma be studied? Can magnetic fields relevant to the atmosphere of neutron stars be created, and aspects of the complex radiative MHD processes be experimentally reproduced? Can the so-called radiation-bubble instability be replicated? FACILITIES Experimental facilities available for high energy density research include high-energy (relatively long-pulse) lasers, high power (very short pulse) lasers, pulsed-power devices, high-current particle beam accelerators, and combinations of these. New facilities planned or under construction will extend still further the range of high energy density conditions achievable. Tables 3.1 through 3.5 list a variety of HED facilities currently in operation, under construction, or in the serious planning stages. Figure 3.2 is an illustration of the National Ignition Facility (NIF) currently under construction at Lawrence Livermore National Laboratory. When completed, it will produce ~2 MJ of laser energy and will be the flagship high energy density facility in the United States. TABLE 3.1 Three Currently Operating High Energy Density Facilities That Provide the Highest Energy Densities to Experimental Targets Existing OMEGA (University of Rochester— Laboratory of Laser Energetics) Z-machine (Sandia National Laboratories) Atlas (Los Alamos National Laboratory; To Be Moved to Nevada Test Site) Type Laser Pulsed power X-ray source Pulsed power Photon energy 3.5 eV 20 MA as Z-pinch driver 50–250 eV (BB)a 30 MA as Z-pinch driver Pulse length 0.1–4 ns (longer with pulse stacking) ~100-ns rise time 5–15 ns 4.5-µs rise time Spot size 0.1–3 mm N/A ~1-mm cylinder N/A E/pulse 30 kJ 16 MJ stored energy 1.8 MJ 24 MJ stored energy Repetition rate 1 per hr A few per day 1 per day <1 per day Peak intensity ~1×1016 W/cm2 N/A X ray: 1×1014 W/cm2 N/A aBB indicates that the given photon energies refer to typical hohlraum temperatures that are achieved.

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TABLE 3.2 High Energy Density Facilities, Including Those Typically Associated with Particle Physics Existing ICF-Class Lasers TW-Class Lasers TW Pulsed-Power System Electron Linac (SLAC) RHIC Energy/photon or particle 1.5 eV 1.5 eV 0.1–10 MeV; 1–5 MA as Z-pinch driver 50 GeV 100 GeV/amu (for Au: 20 TeV/ion) Pulse length 0.1–10 ns 30–100 fs 50–250 ns 5 ps ~500 ps Spot size 50–1000 µm 5 µm ~0.1 cm (e−) ~1 cm ions 3 µm 120–240 µm Energy/pulse Up to 3 kJ 1–10 J 20–100 kJ 150 J 3 kJ/bunch Repetition rate 8–10 per day 10 Hz, a few per hour 1–10 per day 100 Hz Bunches collide at 50 MHz Typical peak intensity (W/cm2) 1×1015 W/cm2 1×1020 W/cm2 Application dependent ~1×1020 W/cm2 ~6×1016 W/cm2 NOTE: This table includes the large number of laser systems that can achieve HED conditions. While the laser systems are not listed individually, a number of systems nationwide can be used for HED studies. TABLE 3.3 High Energy Density Facilities Currently Under Construction or Contemplated in the Near Future Facility PW-Class Lasers NIF Z-R (x ray) LHC Energy/particle 1.5 eV 3.6 eV; 600 eV BBa for ICF 100–250 eV (BB)a 7 TeV Pulse length 0.5 ps 0.2–20 ns (longer with pulse stacking) 10 ns 0.25 ns (1 bunch) Spot size 5 µm 0.2–5 mm 1-mm cylinder 16 µm E/pulse 0.5~5 kJ 1.8 MJ >3 MJ 334 MJ in 2.8×103 bunches Repetition rate Up to 2 per hr 2 per day 1 per day 4×107 Hz Peak intensity 1×1021 W/cm2 2×1015 W/cm2 4×1014 W/cm2 1×1019 W/cm2 NOTE: Somewhat lower peak intensities than those listed, in the 1012 W/cm2 range with a ~1-mm target, are planned for the electron beam facility Dual Axis Radiographic Hydrodynamic Test (DARHT) (not listed); similar intensities are planned for future proton drivers as well. aBB means that the given photon energies refer to typical hohlraum temperatures that are expected for ICF experiments. Table 3.1 shows characteristic parameters for three of the largest currently operating, high energy density facilities: the OMEGA laser; the fast, magnetic pinch Z-machine; and the relatively slow pulsed-power facility Atlas. All three of these facilities were built primarily for high energy density plasma studies relevant to nuclear weapons science, including inertial confinement fusion, but the National

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TABLE 3.4 Possible Future High Energy Density Facilities Future 0.1 Exawatt-Class Lasers ZX (x ray) HIF NLC LCLS (e−) LCLS X rays (coherent) Energy/particle 1.5 eV 40 MA; up to 280 eV BB for ICF 5 GeV 250 GeV 14 GeV 8 keV Pulse length 100 fs-1 ps 10 ns (x rays) 10 ns 370 fs 230 fs 230 fs Spot size 100 µm N/A 3 mm 250×3 nm 28 µm (as FEL driver) 0.1–100 µm E/pulse 20 kJ >6 MJ 1–10 MJ 300 J 12 J 2 mJ Repitition rate 2 per day 0.5 per day 10 Hz 190 pulses at 120 Hz 120 Hz 120 Hz Peak intensity >1×1021 W/cm2 >1×1015 W/cm2 1×1015 W/cm2 7×1024 W/cm2 5×1017 W/cm2 >1×1019 W/cm2 NOTE: The facilities listed will significantly expand the range of HED conditions available terrestrially, although significant technological development may be required to achieve these parameters. TABLE 3.5 Examples of Current and Future International High Energy Density Facilities Facility Type of Facility Country GSI PW PW-class laser+ion storage ring Germany MAGPIE TW pulsed power Great Britain Vulcan+PW ICF-class+PW-class Great Britain LULI PW-class lasers France LIL First stage of ignition class France Laser Megajoule Ignition-class laser France Gekko+PW ICF-class+PW-class lasers Japan NOTE: The approximate parameters for the various types of facilities can be found in Tables 3.1 through 3.4. Several facilities will have a combination of longer-pulse lasers and ultrahigh-power (petawatt) lasers. Nuclear Security Administration, which operates them, makes a portion of their time available for fundamental high energy density physics research. Table 3.2 shows other existing HED facilities. These include ICF-class lasers not listed in Table 3.1, high-intensity (terawatt [TW]) laser and pulsed-power systems typically found in universities, and particle physics facilities that can achieve HED conditions (often in combination with other HED technologies). Many of these smaller laser systems can be operated at a significantly higher repetition rate than is possible with high-energy laser systems. These high-average-power systems can perform hundreds or thousands of experiments, allowing detailed data to be

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FIGURE 3.2 Rendering of the ~2-MJ National Ignition Facility (NIF) that is currently under construction at Lawrence Livermore National Laboratory, showing the location of various components and support facilities. When completed, the NIF will be the nation’s highest-power MJ-class high energy density physics facility, built primarily for weapons-relevant high energy density physics research, including inertial confinement fusion. Up to 15 percent of the laser time is planned to be available for basic science experiments. Courtesy of Lawrence Livermore National Laboratory. obtained. High-average-power laser systems will also be required for laser-drive inertial fusion energy. Tables 3.3 and 3.4 list future high energy density facilities, either under construction or being discussed, though significant technological advances may be required to build these advanced systems, which will extend the range of high energy density conditions available for experiments. The National Ignition Facility will be the flagship high energy density facility in the United States. Similar development of high energy density facilities is occurring outside the United States.

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Table 3.5 lists some of these facilities. The LMJ laser facility, under construction in France, will have capabilities similar to those of the NIF. Active foreign research efforts under way and the availability of an increasing suite of international facilities will continue to allow active international collaborations to be pursued. In fact, a number of the experimental results shown in the subsequent sections (particularly in Figures 3.7, 3.9, and 3.10) are the results of international efforts and collaborations involving U.S. researchers collaborating on international facilities or foreign researchers collaborating on U.S. facilities. HIGH ENERGY DENSITY PHYSICS PHENOMENA This section describes a number of physics phenomena of wide scientific interest that are unique to HED conditions. The density-temperature phase diagram for hydrogen, shown in Figure 3.3, provides a convenient roadmap through the most important HED regimes. The upper left-hand side of the figure corresponds to extremely high densities and low temperatures where quantum-mechanical degeneracy pressure dominates. The lower right-hand side corresponds to regimes of extremely high temperature and low densities, where radiation effects dominate. Intermediate between these two extremes, radiation, particle, and degeneracy pressures can all contribute to the plasma dynamics. A key distinguishing feature of the HED facilities is that macroscopic volumes of matter can be placed in these extreme conditions for laboratory study. High Energy Density Materials Properties When an object (solid, liquid, or gas) is subjected to an increase in external pressure, p, it tends to compress according to p=−β (ΔV/V), where β is its bulk modulus, and (ΔV/V) is the compression. Solids typically have β≈1 Mbar; hence, very high pressures are needed to compress a solid. When p/β≪1, the material compression is negligible, and its response is well described by elasticity theory. In the HED regime, however, p/β≥1 by definition. Here, the response of matter is no longer a gentle perturbation, but rather a significant, perhaps even violent, compression or deformation. At sufficiently high pressures and densities, molecules can dissociate and atoms can ionize, each of which affects the compressibility and deformation. Solids can undergo phase transitions to reach lower collective energy states and twinning transitions, in response to sufficient applied shear stresses. New techniques for studying the time-resolved response of materials to extreme pressures and applied stresses have been developed in recent years. An illustrative selection of examples is described below.

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FIGURE 3.3 Phase diagram for hydrogen in temperature-density space showing the great complexity of even the simplest molecule. Courtesy of H.M.Van Horn, University of Rochester, now at National Science Foundation. High-Pressure Equation of State The equation of state (EOS) of a material can be experimentally determined by applying a known external pressure to a sample and measuring its volumetric response (compression). If the applied pressure is in the form of a shock, the material response is determined through the Rankine-Hugoniot relations. Modern HED drivers are also capable of delivering shaped pressure pulses that enable isentropic compression experiments, or other off-Hugoniot conditions. High energy density facilities are particularly well suited for EOS studies at high compression, because of the very high pressures possible. A high-energy laser can be used to launch a strong-shock wave by ablation pressure. Pulsed-power devices can launch “flyer plates” with which to shock a sample by impact, or they can produce isentropic compression by

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applying a tailored magnetic pressure pulse directly to the surface of a conducting sample. Alternatively, by appropriate pulse shaping, compressions to higher density at a given peak pressure can also be achieved, thereby probing off-Hugoniot regimes. Gas guns, explosively driven flyer plates, and electromagnetic launchers can also be used to launch shock waves in materials for compression studies. In addition, static techniques such as diamond anvil cells can be used to generate moderately high pressures in materials. Hydrogen is the simplest and most ubiquitous element in the universe, and its EOS is critical to planetary structure and planetary formation models, as well as to the performance of inertial confinement fusion capsule implosions and stockpile stewardship. Yet it has an impressively complicated phase diagram, as shown in Figure 3.3. The EOS measurements of hydrogen over the past decade have yielded several surprises. For example, the theoretically predicted plasma phase transition has yet to be experimentally observed. With the recent availability of large high energy density experimental systems (first the Nova laser, and now OMEGA, Z, and NIKE), multimegabar EOS measurements have become possible in liquid hydrogen. As high energy density systems continue to move to higher energies (e.g., the NIF), the parameter space accessible to experiments will be greatly expanded. As mentioned in Chapter 2, new results could significantly impact models of planetary structure and possibly planetary formation models, and they could also affect the modeling of inertial confinement fusion implosions. It should also be noted that in measurements relevant to planetary interiors, the experimental results should be directly applicable, without any scaling (see Figure 1.1 in Chapter 1), provided they are made at the correct density, temperature, and equilibrium states. Measurements of reflectivity and conductivity of shocked hydrogen allow observation of the dielectric-to-metallic transition. The temperature in the shock-compressed material can be determined by various spectroscopic techniques. Taken together, these measurements provide powerful tests of models of the properties of dense, degenerate plasmas. To have significant impact on models of planetary interiors, the accuracy of the experimental measurements needs to approach 1 percent in density, 20 percent in temperature, and factors of 2 in solubility and transport coefficients. Theories and simulations of the EOS of dense, strongly coupled, Fermi-degenerate plasmas are a very active area of ongoing research. Semiempirical models, such as the “chemical picture,” typically use effective pair potentials fit to experimental data. Ab initio simulations using molecular dynamics or Monte Carlo models attempt to calculate the plasma conditions from first principles. Most of these models assume equilibrium conditions. Given that experiments on HED facilities can have rather brief time scales, a few nanoseconds, or sometimes even less, there may be a need for kinetic theories to explicitly calculate the evolution to

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In one example, the magnetized target plasma is a field-reversed plasma configuration (FRC) that is produced within a solid, cylindrical conductor. That conductor can be imploded by a high current on a microsecond time scale. The intent is that a stable plasma configuration, the FRC, can benefit from the enormous pressures that can be exerted by a high current without being driven unstable if the current is carried by a collapsing metal conductor instead of the plasma itself. If the inner surface of the imploding conductor remains solid, it will also remain stable. The plasma pressure that can be achieved can substantially exceed the applied magnetic-field pressure as follows. The external magnetic pressure drives the liner inward, converting the magnetic-field energy into kinetic energy of the liner. The liner accelerates inward until the compression of the FRC is sufficient to produce a back-pressure that approximately equals the drive pressure, at which time the liner begins to slow down. It comes to a halt only after all of its inward kinetic energy has been converted to magnetic plus thermal energy of the FRC, taking into account energy loss due to magnetic-field diffusion into the liner. Estimates using reasonable choices of physical parameters, including magnetic and particle diffusion coefficients, suggest that a 30-MA-current driver, such as the Atlas facility, could achieve 1-cm-radius, several-centimeters-long plasmas at 1 Mbar (1011 P). This corresponds to a density of 6×1019/cm3 at 10-keV temperature, a very interesting plasma for producing deuterium-tritium fusion reactions. Intense Ion Beams (Heavy and Light) Intense ion beams can be produced using pulsed-power accelerators or using conventional accelerator technology. The former case is limited to 10 to 20 MeV by the nature of the technology, and high power density is achieved by focusing a beam that might be produced at the mega-ampere level. Intensities achieved using PBFA II Particle Beam Accelerator at Sandia National Laboratories, Albuquerque, before it was converted to the Z-machine exceeded 1012 W/cm2. Heavy ion beams can be generated from conventional ion sources at the ~1-MeV and ~1-A level for about a few microseconds. The power density can then be increased by merging separately generated heavy ion beams, acceleration to the gigaelectronvolt level, and axial bunching. It is expected to be possible to produce beams at 1 to 10 GeV and 104 A for ~10 ns and to focus them to ~1015 W/cm2, as is required for inertial confinement fusion, but the proof-of-principle experiments for this are still in the planning stage (as discussed earlier in this chapter). Because the range of ions at the few megaelectronvolts per nucleon energy level is in the micron range, intense ion beams can be used for many of the same materials science applications for which nanosecond lasers are used, including generating ablation plasmas and driving shock waves into solid materials. Ions have

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an advantage in that they are absorbed in the volume of a material, penetrating to a depth that is determined by the target material and their energy, whereas a laser interacts with the surface of a solid target and depends on the state of the plasma on the surface. The beams themselves are high energy density plasmas in their own right. Intense light ion beams must be very close to charge neutral or they cannot propagate, and so they are essentially neutral plasmas moving at high speed in the laboratory frame. A proton beam at 4 MeV and 1 MA/cm2 represents an energy density of about 3×108 J/m3, although it is largely in directed kinetic energy rather than thermal energy. In a heavy ion beam entering an inertial confinement fusion target chamber, the kinetic energy of the individual ions may be high enough that charge neutrality is not a necessity for propagation. In that case, the kinetic energy density and the energy densities in the electric and magnetic fields are large. For lead ions at 1 GeV and 100 kA focused to 1 cm2, the kinetic energy density is ~1010 J/m3. Intense ion beams and their associated self-magnetic fields can also be used in magnetic confinement fusion to generate favorable magnetic confinement configurations. High-Energy Electron Beams Similar to ion beams, electron beams can be produced using pulsed-power generators or conventional accelerators. Because the space-charge limit is much higher for electrons than ions in an accelerating gap (by the square root of the ion-to-electron mass ratio), pulsed-power generators can produce electron beams reaching 106 A/cm2 or even more in a 1-MV accelerating gap with self-focusing caused by anode plasma production. Such beams exceed the so-called Alfvén current limit and cannot propagate in vacuum. Because of their large electrostatic and magnetic energy densities, they must be charge and current neutralized. Intense electron beams can, in principle, be used to deliver energy some distance away from the source if their self-fields are neutralized. In an intense electron beam (e.g., 1 MA at 1 to 20 MeV), the self-fields assure that there is as much or more kinetic energy in transverse motion as there is in the direction of propagation. Surface ablation (and shock wave generation) can easily be achieved in solid density materials by focused intense electron beams. High energy density electron beams can also be produced by conventional accelerator technologies, such as the 50-GeV electron beam produced at the Stanford Linear Accelerator Center. The interaction of these beams with plasmas is described in Chapter 4.

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X-ray Lasers X-ray lasers provide an example of using one type of high energy density system to produce another that can then be used in high energy density experiments. Energy deposited in a plasma by a laser or pulsed-power source leads to a population inversion resulting in x-ray lasing at wavelengths as short as ~40 Å. Because of their short wavelength, soft x-ray lasers have a significantly higher critical electron density (see the subsection above on “Laser-Produced Plasmas”) than conventional visible or UV lasers have, and they can propagate through high-density plasmas. They can also be used to volumetrically heat solid materials and high-density plasmas. Recent developments in soft x-ray laser research have been directed toward utilizing higher-power technology to reduce the pumping source size to tabletop dimensions. Collisional excitation schemes have been very successful and have been adopted worldwide. These include fast capillary discharges and picosecond laser-driven transient schemes. These x-ray lasers operate in the high-efficiency saturation regime with typical pulse durations in the picosecond to nanosecond regime, output energies of tens to hundreds of microjoules, and high repetition rates (a few hertz to 1 shot every few minutes). These x-ray sources have peak powers and brightnesses higher than those of present-day synchrotrons but much lower repetitions rates. They have been used for many applications, including the interferometry of millimeter-scale dense plasmas, characterization of optics, and imaging of biological samples. Future directions include the development of ultrafast x-ray laser schemes operating below 50 Å and the determination of material properties under extreme conditions. The main advantages of these x-ray lasers are their scalability to shorter wavelengths with higher output energy that would allow them to be developed as unique diagnostic tools for picosecond interferometry of other high energy density conditions such as those that the NIF will generate. Gas Guns and Diamond Anvils A fundamental goal of geophysics is a basic understanding of the structure and dynamics of Earth’s interior in general and of the generation of Earth’s magnetic field in particular. Somewhere embedded in the churning, twisting flow patterns of the core-mantle system lies the cause for the dramatic reversals of the dipole geomagnetic field, as shown in paleomagnetic reversal records. The energy source for this dynamo is a combination of heat flow out of the solid inner core and the enhanced rotation rate of the inner core compared to the mantle, which is separated from the inner core by a liquid outer core. The result of this inner turmoil at Earth’s surface is as dramatic as the turmoil itself: plate tectonics, earthquakes, volcanoes, and—perhaps triggered by the magnetic-field reversals—possible global climate changes.

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Much progress has been made in understanding Earth’s interior magnetorotational dynamics. With the advent of supercomputers, three-dimensional MHD models have begun to reproduce some of the dynamics thought to exist deep below our feet. These simulations have even predicted magnetic-field reversals. Such large-scale three-dimensional MHD code simulations, however, can only be as reliable as the input information, such as the material properties—material strength, phase, melt point, viscosity, and conductivity—at very high pressures (0.1 to 3.6 Mbar), high temperatures (1000 to 6000 K), and high densities. This leads to the obvious question: How can the properties of the relevant materials be ascertained at such extreme conditions? The answers to questions such as these come from high-pressure laboratory experiments. There are several experimental avenues to such high-pressure conditions. The first, the diamond anvil cell, is the “workhorse” for establishing the phase diagrams of materials at pressures up to several megabars. These devices are essentially a high-tech device that compresses thin samples (10 to 100 µm) between two flat diamond anvil surfaces. When combined with a bright source of x rays in the kiloelectronvolt energy range, such as that supplied by a synchrotron light source, this setup is an extremely powerful tool for determining the phases of materials. Experiments on diamond anvil cells are static, with strain rates of <10−6 s−1. Alternate experimental approaches include gas guns or powder guns. These devices are essentially a large-scale gun barrel. When detonated, a macroscopic “bullet” or sabot is accelerated out the end, impacting a sample, causing shock compression. This allows the equation of state of the shock-compressed sample to be determined with high accuracy, making gas guns a workhorse for dynamic or Hugoniot equation-of-state measurements. Pressures accessible by gas gun experiments can also reach several megabars. High explosives are a variation on this theme of dynamic experiments. This technique is not as widely used as gas guns are, owing to lower precision. However, high-explosive-driven integral experiments are possible in a wide variety of geometries. Typical pressures achievable are several hundred kilobars. Diagnostics for High Energy Density Laboratory Systems As the technologies to produce high energy density conditions have evolved, so have the abilities to diagnose and understand these conditions. This has included development of (1) advanced diagnostics and (2) target fabrication techniques, as well as (3) advances in numerical simulation capability. These technologies form a triad, without which advances in understanding high energy density physics conditions would be severely limited. A few examples of diagnostic development are

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described in this section, and the other two legs of the triad are described in the subsequent sections. Many of the advanced diagnostic techniques have been developed as part of the inertial confinement fusion program. As described in the beginning of this chapter, short spatial and temporal scales are characteristic of ICF implosions. The need to diagnose these experiments has led to impressive developments, including time-resolved x-ray spectroscopy and imaging at picosecond time scales with multikiloelectronvolt photon energies. Diagnosis of nuclear reaction products includes detailed spectral and temporal measurements of neutron and charged particle spectra from primary, secondary, and tertiary reactions. For laser and pulsed-power facilities to be attractive to users for high energy density plasma physics experiments, or for secondary experiments using the high energy density plasmas as drivers, the facilities must have excellent diagnostic systems providing information about the plasma conditions as a function of time. The diagnostics needed by a particular user might include experiment-specific instruments as well, such as shock-breakout instruments when a shock wave is generated in a thin plate attached to a high-temperature hohlraum or by the extremely high magnetic pressure that can be produced by the Z-machine. Another diagnostic requirement for experiments involving high-optical-depth materials is imaging with very high energy backlighter x rays (tens of kiloelectronvolts to even megaelectronvolts), to be able to radiographically see through these targets. Laser Diagnostics High energy density facilities rely on a large number of diagnostics to understand the laser or pulsed-power system performance, as well as the laser target interactions or pulsed-power system-driven plasma dynamics. Because of the relatively short time scales of interest (a few nanoseconds or less), much of the emphasis has been on the development of high temporal-resolution diagnostics. These include visible and x-ray streak cameras (producing a continuous record) and time-gated imaging detectors (producing two-dimensional information snapshots). The latter can be used to make movies with ~50-ps frame times and ~50-ps resolution (an example is shown in Figure 3.1). For even better time resolution, short-pulse lasers are often used in a pump-probe scheme, in which the interaction is probed with a second laser, the arrival time of which is varied to build up a time-resolved measurement. Any pump-probe technique using ultrafast lasers is sensitive to the exact pulse shape (prepulse and intensity contrast) of the beam.

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Imaging of Target Nonuniformities The evolution of hydrodynamic instabilities is of paramount importance to understanding inertial confinement fusion and high energy density conditions in general. As energy is deposited in a plasma, shock waves can be launched and the system can be accelerated, leading to conditions in which the hydrodynamic motion is unstable. Diagnostic imaging of perturbed, high-density targets allows the evolution of these instabilities to be measured and compared with numerical simulations and theoretical predictions. Constraints are many and varied, with a goal of simultaneously resolving the space and time evolution of the perturbations with time windows, spatial amplitudes, and perturbation wavelengths that are as small as possible. Here an illustrative diagnostic example for hydrodynamic experiments typical of those performed on the OMEGA or NIKE laser is considered. The diagnostic requires the following: fields of view of more than 1 mm, perturbation amplitude modulations that range from 0.25 µm to tens of microns of solid plastic, objects with diameters of 5 µm or less, and precise time gates that are less than 50 ps. The fundamental enabling diagnostic technology that provides imaging of target mass perturbations in these regimes is x-ray backlighting. The flexibility of high energy density drivers allows part of the energy to be used to generate the probing (backlighting) x-ray radiation. Time resolution is obtained with the help of a framing or streak camera as a detector, or by using an ultrafast laser to generate a short x-ray pulse. To compensate for poor spatial resolution of available detectors, high image magnification (about 10× to 20×) is generally used, which, in turn, requires high system throughput. Experiments with thick targets (e.g., 40 to 100 µm of solid plastic) also require a high efficiency of the diagnostics and a high energy of the probing radiation. For any backlighting scheme, there are two other general requirements: (1) small size of the backlighter source and (2) filtration of imaging radiation from the self-emission of the object. The surface brightness of the backlighter must be larger than the object brightness only in the bandwidth of the spectral line being used to image the object. Examples of x-ray imaging and radiography of HED plasmas produced by lasers and pulsed-power machines are shown in Figures 3.7 through 3.10. High-energy petawatt laser systems may allow high-energy x-ray backlighting of thicker samples at higher x-ray photon energies than are possible with current long-pulse laser systems. Directed jets of protons generated when these lasers interact with matter should allow very opaque targets to be radiographically diagnosed. There are now available a range of imaging systems that couple well to the x-ray backlighting technique, and which meet many of the criteria described above. These include Kirkpatrick-Baez microscopes, gated x-ray pinhole cameras, point projection imaging, and curved-crystal monochromatic imagers.

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Nuclear Reaction Diagnostics The increased availability of high energy density systems has significantly expanded the range of nuclear and charged particle diagnostics that are used to study them. Part of this expansion is due to the larger energy of the high energy density systems, which produce higher nuclear yields, allowing lower cross-section processes to be observed. In the past, ICF implosions were diagnosed with neutron detectors that measured the primary neutron fusion yield (e.g., D+D→He3+n or T+p) and the secondary (two-step) reaction (D+T→He4+n). As the energy coupled into the implosions has increased, a large number of lower probability reactions have begun to be detectable (e.g., the secondary reaction D+He3→He4+p). This has led to the development of a wide array of new neutron and charged particle diagnostics that can provide significantly more information about the target characteristics. The higher nuclear reaction yields associated with current and future ICF implosions lead to the opportunity to measure astrophysically relevant nuclear reaction rates under conditions that are close to those in astrophysical objects. Nuclear reaction cross-sections are typically measured in beam-target experiments with beam energies of hundreds of kiloelectronvolts or megaelectronvolts. These rates are then extrapolated to the multikiloelectronvolt temperature conditions in stars. Multikiloelectronvolt temperatures are achieved in ICF implosions. The nuclear reaction yields of solar-relevant processes can be measured, providing more accurate reaction rates for stellar processes. An example that may be possible on the OMEGA laser system is to measure the rate of 3He+3He→4He+2p reactions, if the distribution function is sufficiently Maxwellian. The NIF will extend the opportunities for measuring nuclear reaction rates relevant to stellar processes. A particularly intriguing possibility is the potential to use the bursts of 1019 neutrons from the D+T→α+n thermonuclear yield from an igniting ICF capsule to study reactions relevant to the s, p, and r astrophysical nucleosynthesis processes. For example, the neutron flux from an igniting capsule is high enough to drive 10 to 20 percent of dopant nuclei, say 89Y, into excited states via (n,n′) reactions, and trigger multiple step reactions on those excited states with lifetimes >1 ps. Special Needs for Pulsed-Power System Diagnostics The diagnostics needed to study the high energy density plasmas made in pulsed-power systems are essentially the same as those used in comparable laser-based experiments, with the additional need to operate in a high-radiation environment. For example, the bremsstrahlung background at the Z-machine can be 106 rads/s as a result of “stray electrons” accelerated in the vacuum feed to the Z-pinch load. In addition, there is the electromagnetic noise generated by the machine, as well as ground motion resulting from the self-closing water switches in

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the pulsed-power system. Thus, every diagnostic instrument must be placed as far from the vacuum chamber as possible; it may have to be decoupled from the ground motion, and it must be collimated and shielded as well as possible. This said, the extremely interesting and relatively large-volume plasmas generated by the Z-machine and their many applications to high energy density science place a premium on having a large set of diagnostics in place for users. Although smaller pulsed-power machines produce less troublesome background, they also produce much smaller signals. Therefore, the same care in shielding diagnostics from background x rays and electromagnetic noise is necessary on smaller facilities as on the Z-machine. It is noteworthy that the relativistic electron beams generated by petawatt lasers and high irradiance CO2 lasers can produce large electromagnetic noise pulses that require the same attention to detail in shielding and collimation of detector channels as are required of pulsed-power experiments. Beam Diagnostics Intense electron and ion beams generate dense plasmas on surfaces if the deposited energy in a ≤1-µs pulse reaches ~1 kJ/g. Thus, any material placed in the path of such a beam will be rapidly ionized, making it difficult to measure beam properties such as current density and total beam momentum or energy. For example, small apertures in Faraday cups for intense ion beams can be completely blocked by plasma in just a few nanoseconds, and results from a pendulum that is intended to measure the impulse delivered by a beam to a target can be misinterpreted because of the large impulse due to an ablating plasma. The net result is that substantial numerical modeling is often necessary in order to elicit useful information from intense beam diagnostic systems that are straightforward to interpret at more modest energy densities. Beam propagation in a gas or plasma introduces similar problems for direct measurements because, for example, the resulting reverse current induced in the plasma or gas after breakdown can partially or completely eliminate the self-magnetic field of the beam current. Therefore, alternate diagnostic methods must be used to monitor beam properties, such as the intensity of x rays induced in a thin foil as the beam passes through it, for electrons, and nuclear reactions that yield an easily observed reaction product, for ions. Laser-based measurements, including interferometry, laser-induced fluorescence spectroscopy, and laser scattering can provide information on the background plasma and/or the beam. Advances in Target Fabrication Target fabrication is an essential enabling technology for high energy density physics. Targets have advanced enormously over the past three decades, not by

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slow evolution but in true paradigm shifts from early low-tech endeavors to the sophisticated precision materials of today. The evolution of high energy density systems, both in energy scale and complexity, together with the evolution of diagnostic capabilities and numerical simulations, has led to a concomitant need for more sophisticated and complex targets. Sophistication and control are needed to fabricate targets capable of supporting the intellectual challenges of high energy density plasmas. The extreme complexity of today’s targets was achieved as a result of multiple breakthroughs in new technologies and materials science. A critically important step in order to create high-quality spherical shells was that of combining two processes. One process involves density-matched microencapsulation via a droplet generator to produce shells with a highly spherical outer surface. The other process involves a decomposable mandrel technique that allows the actual target shell to be coated onto the mandrel (which is then decomposed and removed). The result is a highly spherical shell with a highly uniform wall that is vital so that defects in the target do not dominate implosion dynamics. Hohlraums have likewise undergone several stepwise progressions in their manufacture, culminating with today’s precision diamond-turning machines that routinely control tolerances to a few microns on complex parts. The ultraprecision characterization of targets continues to evolve with interference microscopy that allows the diameter, wall thickness, and first mode deviations to be measured quickly with modest computing capability. An atomic force microscope traces the shell diameter providing multidimensional quantitative surface analysis for use in simulation codes. Success in the generation of large x-ray fluxes with pulsed-power devices has led to significant advances in the construction of wire arrays and more complicated targets used for equation-of-state studies. The flexibility engendered by high energy density systems has led to even more complicated targets, some that lack any symmetry, others that might be designed to enable multiple backlighting sources, and all requiring extreme precision throughout the manufacturing process. An important future goal of high energy density physics requiring advances in target fabrication is the production of energy from inertial fusion. Providing billions of precision targets at the low cost needed for energy production will require an intimate understanding of the relevant materials science and additional breakthroughs in the way targets are fabricated. Standardized efficient industrial production technologies must be combined with existing knowledge in the field. An example is the use of fluidized beds to coat hundreds of thousands of targets at once. Initial experiments indicate that one fluidized bed can supply half of the 500,000 targets per day required by a 1,000-MWe power plant. Additional quantum leaps in the way that targets are manufactured will require a continued effort from industry, national laboratories, and universities, each bringing its unique strengths to this

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highly challenging field. The high-repetition-rate (driver, targets, and so on) capabilities developed for inertial fusion energy would also be beneficial for many high energy density experiments. High-Performance Computing Computational capabilities have been revolutionized in recent years, bringing physical phenomena within the scope of numerical simulation that were out of reach only a few years ago. The Department of Energy’s Advanced Strategic Computing Initiative (ASCI) has played a major and multifaceted role in this revolution, as has the continued evolution of microprocessor and other technologies. High-performance computing today is typified by large parallel platforms with 30 gigaflops (Gflops) of sustained performance. High-speed connections enable centralized visualization systems for tasks ranging from debugging to processing of large database results. With the ability to perform highly resolved, multidimensional computations, advanced scientific computing has become an enabling tool for first-principles explorations of high energy density phenomena. Both theory and experiments now typically rely on numerical simulation that comprises an essential component of more-integrated research programs. Ultimately, inputs from theory, laboratory experiments on equations of state, dynamics, explorations of scaled phenomena, and so on, must be integrated in comprehensive computer simulation codes. These incorporate the physics, hydrodynamics, radiation, and other manifestations of high energy density phenomena, along with appropriate algorithms, and explicit or implicit models, in a software environment that must cater to the multiprocessor environment on which it runs. Numerical simulation can now rightfully be considered as an important component in high energy density science discovery. Large, multidimensional data sets for and from such simulations require preprocessing before they can serve as inputs, postprocessing to digest the results, and, not least, computer visualization. Both the input data that specify initial and boundary conditions and the output data must also be compared against a host of diagnostic data for validation and other purposes. Ideally, this is an integrated, iterative, closed-loop process, with experiment, simulation, and theory each suggesting the next step(s). The ever-increasing simulation needs of high energy density physics, discussed elsewhere in this report, suggest the need for an assessment of the necessary improvements and capabilities. Even if Moore’s law persists for the next decade or so, with DOE’s Advanced Strategic Computing Initiative continuing to drive advances at an even greater pace, a number of problems exist that simulations will not be able to completely solve. High-Reynolds-number, radiatively coupled turbulence, in either laboratory or astrophysical environments, for example, is likely to remain beyond

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the reach of direct numerical simulation—that is, through a solution of the equations of motion with no approximations—for the foreseeable future. The difficulty arises from the combination of the large required spatial and temporal dynamic range and from the three-dimensional dynamics. Considerable insights can, however, be gleaned from simulations that advance the envelope in this fashion, exploiting increases in computational power with simulations relying on the fewest approximations possible. High energy density simulation codes include advection algorithms for the simulation of shocks and also vortical- and magnetic-field-driven instabilities, equation-of-state models that extend from solid to plasma regimes, and detailed electron and radiation transport and opacity packages that can provide an adequate estimate of the energy transport for the full range of high energy density temperatures and densities. Furthermore, some of these codes model the intense electromagnetic wave/particle interaction of high-intensity beams, from plasma coronal nascence through high-density heating. While no codes include all of these effects simultaneously, relevant parts of high energy density physics problems can be simulated, yielding results with predictive value. Such simulations advance our understanding of complex phenomena, yield insights that are fundamental in interpreting and designing experiments, and provide data for new theories and models. Hardware and computation algorithm advances are required in order to continue to address these problems. Given a span of phenomena in a typical high energy density problem, simulations become tractable as more physics is modeled rather than simulated at every point in space and time. While in a way this is always the case—we rely on continuum and other approximations to simulate hydrodynamics—the complexity of high energy density problems requires an increase in the level of modeling and abstraction. Physics-based subgrid-scale and other phenomenological models that permit a reduction in the number of grid points on which the dynamics must be solved can potentially achieve this. Such models will rely on theoretical advances and special, well-characterized experiments that probe dynamics at small scales and validate the simulations that have incorporated the subgrid-scale models.