3
Opportunities and Grand Challenges

OVERVIEW

The present chapter describes opportunities¹ and Grand Challenges capitalizing on emerging capabilities in high energy density (HED) science, as illustrated by recent breakthroughs summarized in Chapter 2. The committee develops the following three broad themes in the following pages, mirrored in Figure 3-1: (1) the thermonuclear regime at which densities and temperatures are high enough to sustain nuclear fusion; (2) the lower-temperature high-density range of warm dense matter, including quantum matter; and (3) more extreme, relativistic conditions, involving particle production and use of fusion as a basis for probing matter. Experiments and theory are intertwined in all three instances, with implications for disciplines ranging from astrophysics and chemistry to condensed-matter, materials, and plasma physics.

GRAND CHALLENGES AND OPPORTUNITIES FOR HIGH ENERGY DENSITY SCIENCE

Discoveries in HED science that transform the fabric of society materialize when breakthroughs in laboratory and computational technologies can test and put

___________________

¹ Rather than the inherently negative “gaps” noted in the statement of task, the committee chose to use “opportunities” with the intent that the National Nuclear Security Administration (NNSA) and the high energy density (HED) science researchers may use these as guideposts.

to practical use the creative insights provided by theory. Recent advances in experiments, simulation, and theory allow HED research to make major new contributions to science and technology, now and in the near future. The following listing is illustrative and will no doubt be surpassed by new discoveries and innovations.

1. Laboratory-based nuclear fusion. How can burning fusion plasmas be controlled and harnessed for society’s energy, security, and technology needs? Fundamental HED science is essential to the development of the technologies and processes required for controlling nuclear fusion in the laboratory, taking current experiments that are documenting the onset of nuclear ignition to the point of fully exploiting the output of nuclear reactions. More effective means of achieving fusion will offer a unique platform for characterizing new states of matter through experiments, simulation, and theory. (See also Appendix A for more detail on ignition.)
2. Next-generation laboratory astrophysics. Can extreme astrophysical phenomena evident from observations or predicted by theory be reproduced in the laboratory? HED science can leverage astrophysical observations

1. to address major questions about the evolution of the universe, including the following: What is the nature of matter in the deep interiors of dead stars (“compact” astrophysical objects) throughout the universe? Can the background of space and time (“vacuum continuum”) be broken using sufficiently intense photon densities that are now becoming available? Can we develop a quantum gravity laboratory and measure the properties of black holes (“Hawking radiation” and black-hole thermodynamics)? Can we emulate and understand cosmic accelerators? A key challenge for both theory and simulations is to quantitatively relate properties and processes at atomic, laboratory, planetary, and astrophysical scales of distance and time.

3. Quantum materials. What are the HED quantum states of matter that could lead to new classes of materials for energy transport, storage, and quantum information science? The discovery of room-temperature superconductivity, novel electronic phases, and predictions of superconducting superfluids at HED conditions point to new materials and phenomena that could be stabilized at everyday conditions, thereby revolutionizing technology and society. A concerted effort is required, integrating experiments and advanced simulations, including artificial intelligence and machine learning for both quantum systems and multicomponent chemistry.
4. New chemistry. Will the discovery of exotic atomic and electronic structures of matter and materials at HED conditions lead to a new chemistry of elements at conditions that occur throughout much of the cosmos? Experiment and theory indicate that chemical interactions at very high pressures can arise from core—and not just valence—electrons of atoms. The implications of this “kiloelectronvolt” chemistry, in contrast to the “electronvolt” chemistry of ordinary conditions, span the creation of new materials to understanding the nature of planets and other astrophysical objects.
5. Evolution of planets and conditions for life. Can we understand the conditions under which life forms and the signatures of planets on which life could emerge? HED science is revealing the violent impact processes by which planets form, with impact sterilization frustrating the early emergence of life; how planetary interiors and surfaces evolve; and how magnetic fields can be produced, shielding the planet’s surface from the charged particles and ionizing radiation emitted by the host star. HED experiments and simulations can provide the necessary validation of material properties used in interpreting the results from astronomical observations of planets and their atmospheres, including inferences of planetary formation, evolu-

1. tion, and current state. Impact processing of pre-biotic molecules also set the stage for rapid—perhaps even multiple—emergence of conditions that lead to life.

6. Cross-cutting science and the multi-scale nature of HED science. How can multi-scale theory, simulations, and experiments predict the behavior of macroscale objects and processes? HED science cuts across a number of fields and connects vastly different scales of energy, distance, and time—from atomic to astrophysical. A new generation of experiments and modeling, including simulation and theory, is beginning to define the linkages between these different scales, helping to characterize the stability of inertial confinement fusion (ICF) implosions; translating microscopic viscosity estimates to magnetic dynamo processes in planets; defining the strength of bulk matter; and correlating between kinetic, thermal, plasma-wave, Coulomb, and nuclear energy scales in the warm dense matter of low-mass stars.
7. Cross-cutting technology developments.
   1. Table-top photon and particle sources as benchtop microscopes. Many key questions in HED science can be addressed using current and emerging technologies, including compact X-ray-free electron laser (XFEL)-like sources. These provide experimentalists with nanometer spatial and femtosecond temporal resolution, thereby allowing quantitative characterization of the hot spot and confining-fuel densities inside ICF implosions, phase transition and chemical kinetics of ultra-compressed matter, new quantum electrodynamical (QED) states, and the structural complexity of new states of matter (e.g., electride solids and fluids).
   2. High-repetition-rate problem solvers. Evolving today’s single-shot experiments, analysis, and simulations toward artificial intelligence–empowered experiments (high-repetition-rate intelligent hypothesis solvers rooted in computational inference engines) has the potential to massively increase the rate of scientific discovery. For example, the tabletop diagnostics (above) and high-repetition-rate drivers will enable quantitative mapping of the multi-scale (subatomic to macroscopic) evolution of matter at HED conditions, with experiments producing the big data that empower machine learning approaches to data assimilation and discovery, especially for multi-component chemical compounds. Other key technologies for this next-generation capability include development and use of the broad-band lasers for enhanced absorption and

1. 1. drive, high-speed diagnostics such as the pulse-dilation-drift-tube technology, and high-speed detectors based on the Pockels or Stark effect.
   3. High-intensity laser sources. Through chirped pulse amplification (CPA; see also Box 3-3 later in this chapter), light intensities of up to 10²³ W/cm², with wavelengths in the vicinity of 1 µm, are now readily available. The energy density of such light already exceeds 10¹⁷ J m^–3, surpassing by a million-fold the onset of the HED regime described in this report. In interacting with matter, this large energy density represents an enabling technology for HED applications. An important frontier of research is to extend this enabling technology; for instance, through the use of “plasma optics,” the parametric interactions of electromagnetic waves mediated by plasma. Exploiting the fact that plasma easily withstands these intensities represents an opportunity for reaching the next factor of 1,000 increase in intensity (see Figure 3-2).

To address these Grand Challenges and opportunities, as well as many of the stated goals of the National Nuclear Security Administration (NNSA) made accessible through today’s technology, the committee recommends the following:

EXTREME TEMPERATURE AND PRESSURE: NUCLEAR FUSION

Fusion powers the Sun and stars, provides heat and light to Earth and has forged all of the elements we use (and are made of) through many cycles of stellar evolution. In our Sun and in a handful of laboratories on Earth, nuclear fusion happens when two light nuclei (composed of just a few neutrons and protons) get close enough together that nuclear forces overwhelm their electrostatic repulsion. As the two nuclei fuse together to form a heavier element, a small amount of mass is released as energy, following Einstein’s famous E = mc². This is in contrast to nuclear fission, which is the splitting of a heavy nucleus into lighter elements. One of the easiest fusion processes involves isotopes of hydrogen: deuterium (a hydrogen isotope with one proton and one neutron) interacting with tritium (a hydrogen isotope with one proton and two neutrons) to form a helium nucleus (alpha particle). After the fusion event, the alpha particle and the extra neutron carry significant energy; each reaction produces millions of times more energy than the typical chemical reactions that now fuel our cars and homes.

Opportunity: Harnessing Star Power in the Laboratory

A primary challenge of sparking nuclear fusion is directly related to delivering the energy required to overcome the mutual repulsion of the positively charged nuclei that make up fusion fuel. The current strategy to initiating fusion reactions is to heat fusion fuel to temperatures exceeding a million degrees, forming a hot plasma that is confined for long enough that the energy from these initial reactions can be sustained. When a fusion plasma captures enough of its own fusion energy to maintain a steady temperature and produce significant energy yield from this self-heating, it is called a burning plasma. When it captures enough energy to heat

itself by several more millions of degrees, thereby exponentially increasing the rate of fusion reactions, it is a plasma on its way to ignition.

The second challenge of fusion is confinement: hot plasmas are hard to confine; they expand, just as hot steam does from a kettle. And because plasmas consist of charged particles, we cannot confine them easily. Because of their large size, stars confine fusion plasmas by the sheer force of gravity. On Earth, one way to confine plasmas is to use magnetic fields, the approach taken by the magnetic fusion community. Using tokomaks (e.g., like the fusion experiment ITER), stellerators, and similar devices, a low-pressure plasma with a density a millionth that of the atmosphere at Earth’s surface is heated to high temperatures and confined by stationary magnetic fields created by permanent magnets. Another way to confine a plasma is through inertial confinement, which uses an implosion to create a hot plasma with densities hundreds of times greater than familiar solid material, holding it together long enough for nuclear ignition and burn to occur. In both cases, net energy production must satisfy the Lawson criterion, a requirement that the product of the pressure (P) and confinement time (t) must be greater than about 5 MPa-seconds (50 bar-seconds).

Magnetically confined fusion experiments operate at low densities for long times, and inertial fusion experiments operate at high densities for short times; however, both must reach or exceed this simple product to produce net energy from fusion reactions. The idea of ignition is unique to inertial fusion, with fusion reactions not merely maintaining the plasma temperature over the confinement time but also leading to the runaway heating that increases the temperature and rate of fusion production, enabling efficient burn-up of the fuel.

The field of inertial fusion—unlike its cousin, magnetic confinement fusion—has strong ties to HED science. Like all HED science, it is massively multi-scale and requires designing, testing, and diagnosing plasma experiments that take fusion fuel and surrounding components from room-temperature (or cryogenic) conditions to the hot dense plasmas enabling fusion reactions. Part of this work involves finding ways to deliver the energy that can heat, compress, and control matter, which requires extensive engineering to develop suitable lasers and pulsed-power devices. A deep understanding is needed regarding how materials respond to these drivers and move through the vast temperature-density-radiation space of the HED regime. In particular, HPC is critical to accounting for the multi-scale interactions of atomic-scale properties with mesoscale and macroscale effects, such

as turbulence, hydrodynamic instabilities, and sample or driver asymmetries. Also, development of new targets, with better quality control of materials and designs, may prove essential to success. Finally, inertial fusion experiments use sophisticated diagnostic tools, including the following: imagers that characterize micron-scale features that change over sub-nanosecond time scales; neutron and X-ray spectrometers that provide detailed information about the atomic- and nuclear-scale interactions of the rapidly evolving plasmas; and radiation-hardened diagnostics for high-neutron/gamma-flux applications.

The inter-relationship of ICF and HED science is complex. ICF relies on advances in fundamental science understanding, as well as the drivers, codes, and diagnostics developed in the larger field of HED science. Different spatial and temporal scales and a variety of experimental approaches are essential, as summarized in Appendixes A and C. The prospect of limitless, safe, and clean inertial fusion energy (IFE) can be a powerful motivator for both funding and recruitment—especially in the midst of the climate crisis. But ICF also offers unique opportunities for HED science itself—the extreme temperatures, densities, and radiation fields created by an igniting plasma lead to new pressure–temperature–radiation regimes that cannot be accessed in other terrestrial environments.

Finally, inertial fusion also has deep intellectual ties to stockpile stewardship, which has enabled the United States to maintain a safe, secure, and reliable nuclear-weapons stockpile without nuclear explosion testing since 1992. Those ties have led to the present-day funding landscape in which the NNSA supports almost all of the U.S. ICF efforts, and even a significant fraction of basic HED science. While those ties have provided ICF and HED scientists with the rich intellectual legacy of the NNSA laboratories, they also can impose necessary boundaries on free and open scientific discourse (see Chapter 5 on security).

More detail about the approaches to inertial fusion currently being pursued are elaborated in Appendix A, while Appendix C summarizes key U.S. HED science facilities.

Opportunity: Opacities at Stellar Interior Conditions

Stars and their life cycle are important in nearly all areas of astrophysics. Distant galaxies are understood by way of the light from their stellar population, and stars have been instrumental in revealing the existence of dark matter and dark energy: 95 percent of the current Universe.

Experiments in progress on NIF and Z measure the opacity of oxygen at conditions relevant to white dwarfs, and to the base of the convection zone of the Sun and other main-sequence stars. Densities and temperatures can exceed 100 g/cc and 1 keV in the solar core. As there are no experimental data, only theoretical models are currently used for the opacities at these conditions.

Astrophysically relevant opacity measurements now within reach are thus important for modeling Sun-like and white-dwarf stars. Extending this density and temperature coverage will make possible extrapolation to yet more extreme conditions, such as those near the degeneracy boundary in white-dwarf stars. Oxygen opacity is a dominant issue for carbon-rich white dwarfs, and such experimental benchmarks will have a significant impact on stellar and white-dwarf modeling.

Hydrodynamics and Turbulence in HED Plasma

Hydrodynamic turbulence is a universal phenomenon. It occurs at ambient conditions in high Reynolds-number flows, and is also present in compressible plasma phenomena such as supernova explosions. Turbulence is caused by the unbounded and protracted growth of hydrodynamic instabilities, such as the Richtmyer-Meshkov (RM) and Rayleigh-Taylor (RT) instabilities. RT instabilities, including the transition from weakly nonlinear to highly nonlinear regimes, have been explored at HED facilities. In astrophysical settings, supernova remnants can experience RT instability, producing structure at the interface between the stellar ejecta and the circumstellar matter. Recent results from HED experiments reveal how large energy fluxes, which are present in supernovae, can affect this structure.

Relativistic Plasmas and Magnetic Fields

The transition from collisionless to collisional plasma flows holds significant potential for revealing the evolution from kinetic to thermodynamic behavior in matter. Astrophysical collisionless shocks are among the most powerful particle accelerators in the universe.

Supernova remnant shocks are observed to amplify magnetic fields, and accelerate electrons and protons to highly relativistic speeds. In diffusive-shock acceleration, relativistic particles are accelerated by repeated shock crossings, a process requiring a separate mechanism that pre-accelerates particles to enable shock crossing. This is known as the “injection problem” and remains one of the most important puzzles in shock acceleration. Electrons can be effectively accelerated by small-scale turbulence produced within the shock transition (first-order Fermi process), helping to overcome the injection problem. Controlled HED laboratory experiments can now characterize the physics underlying cosmic accelerators.

Galaxy clusters are filled with hot, diffuse X-ray emitting plasma, with a stochastically tangled magnetic field whose energy is close to equipartition with the turbulent motions. In the cluster cores, the temperatures remain anomalously high compared to what might be expected considering that the radiative cooling time is short relative to the Hubble time. While feedback from the central active galactic nuclei (AGN) is believed to provide most of the heating, there has been a long debate as to whether conduction of heat from the bulk to the galaxy cluster core can help the core reach the observed temperatures. Interestingly, evidence of very sharp temperature gradients implies a high degree of suppression of thermal conduction. HED experiments are now beginning to address the problem of thermal conduction in a magnetized and turbulent plasma.

Opportunity: HED Astrophysics: Advances in Nuclear Science

The incipient conditions for HED are those at which external forces overwhelm the typical chemical forces for matter on Earth. Atomic pressures (~E_h/a_B³ ~30 TPa = 3 × 10¹³ Pa) are conditions at which external forces overpower the intrinsic forces holding core electrons in atoms, thus changing the nature of atoms themselves. Nuclear pressures are those at which external forces overwhelm the nuclear forces, such as in neutron stars with pressures >10³⁰ Pa. Such conditions are beyond current HED facilities, but during the past decade, HED facilities have explored nuclear properties by coupling hot plasma and nuclear processes in the laboratory.

For example, cross-sections of nuclear processes measured using accelerators must be corrected for screening effects, which are dominant at collision energies relevant to nuclear processes in stellar environments, supernovae and big-bang nucleosynthesis (BBN). Laser-driven implosion experiments have been used to measure light-ion fusion cross-sections relevant to stellar and Big Bang nuclear synthesis conditions in a plasma environment. Measurements of fusion product spectra from such systems are of sufficient quality to constrain ab initio theory. Measurements of elastic scattering and 2H(n,2n)1H charged-particle breakup take advantage of the diagnostic advances in HED science to measure fundamental

nuclear processes with high precision. In fact, nuclear-plasma interactions may create populations of excited isomers in HED environments, changing the effective nuclear reaction rates.

WARM DENSE MATTER

Warm dense matter (WDM) exists at key transitions in the relative dominance of thermal energy; electron (Fermi, Coulomb, and plasmon) energies; chemical bonding energies; atomic or quantum energies; and, in many practical examples, a wide spectrum of hydrodynamic energies, from turbulent to viscous to advective (see Figure 3-1). This confluence of energy scales (1) connects processes having widely differing scales of length or time, thus requiring a multi-scale approach and (2) challenges traditional hydrodynamic or thermodynamic approximations of condensed-matter and plasma physics.

In WDM, with ionized atoms (plasmas) near solid density at temperatures below 10² eV, existing models tend to vary widely in their predictions for material properties, and these uncertainties are carried forward into theories, simulations, and diagnostics of experiments, as well as nature’s complex, multi-scale HED systems. Creating conditions suitable for reliably characterizing laboratory experiments and material properties in this regime is a Grand Challenge.

Non-Equilibrium Models and Analysis

The vast majority of existing models and measurements assume that materials are in local thermodynamic equilibrium (LTE), meaning that time-varying and, in some cases, direction-dependent effects are not taken into account. In real plasmas, however, ions, electrons, and especially radiation are rarely characterized by identical temperatures.

In the HED regime, for example, electrons initially absorb laser- or X-ray energy, which must then be transferred to the many thousand-fold heavier ions as thermodynamic equilibrium is approached; this takes time, often much more than is available in experiments. At high temperatures, the energy of an equilibrated radiation field dwarfs the energy in ions and electrons at the same temperature, so local thermodynamic equilibrium is rarely achieved above temperatures of ~100 eV. Time-dependent modeling is thus an important aspect of understanding matter at high energy densities.

Additionally, many plasmas have non-thermal ion, electron, and radiation fields that can only be understood with energy-dependent treatments of transport. For example, non-thermal “hot” electrons can be created by laser-plasma interactions, by photoionization and Auger processes under X-ray irradiation, and by acceleration across gaps in pulsed-power plasmas. In such plasmas, the “tempera-

ture” effectively becomes direction dependent, so one can no longer use a scalar temperature to model interactions but must instead follow the evolution of energy-dependent distributions. Therefore, active diagnostics such as radiography, X-ray diffraction, X-ray absorption, Thomson scattering, fluorescence, or bombardment with particle beams are required. In addition to such measurements, high-quality models will help provide detailed information about ionic, electronic, and radiative properties and their evolution.

Opportunity: Benchmark Warm Dense Matter Experiments

While WDM is profoundly difficult to model, it is possible to produce and characterize using today’s technology. The primary laboratory challenges are in ensuring spatial uniformity across the sample, independently diagnosing the plasma conditions (including any departures from thermal equilibrium) and making precision measurements of the properties of interest. Measurements are challenging because WDM is generally opaque to optical diagnostics and has low self-emission. Therefore, active diagnostics such as radiography, X-ray diffraction, X-ray absorption, and fluorescence, or bombardment with particle beams are required, and these measurements can be difficult to interpret without high-quality models that provide detailed information about ionic, electronic, and radiative properties and their evolution.

XFELs offer a particularly appealing platform, given these diagnostic needs, and have the potential to connect strongly to data analytics and machine learning, given the enormous quantities of data that could be generated. This opens the door to new experimental capabilities—for example, characterizing the complexity of atoms’ inner-shell heating that leads to profound non-equilibrium effects that challenge our best models.

Whereas several advanced X-ray sources exist, many are based on traditional accelerator technologies (such as XFELs like the Linac Coherent Light Source [LCLS] or modern synchrotrons like the Advanced Photon Source) requiring significant size and cost, which limit their applications in HED experiments. There has been significant effort to put mid-scale compression capabilities (100 J to 1 KJ lasers) at these light sources, but less effort has been spent on developing new light source technologies that could potentially be used at today’s large compression facilities (NIF, Z, Omega). This is a significant gap because these are the only facilities capable of generating the most extreme HED conditions, including matter at atomic scale pressures and dense plasmas with significant fusion yield. Several plasma-based approaches of producing kiloelectronvolt to megaelectronvolt X-ray photons with high-intensity lasers can potentially provide alternative approaches for generating sufficient X-ray fluences, pulsewidths, and so on for HED science experiments. Recent developments in ultrashort pulse lasers now offer unprec-

edented control over the trajectory of a laser intensity peak, and the distance over which it is sustained, opening to door to even more advanced HED probes (see, e.g., Figure 3-3).

Opportunity: Extended High-Accuracy Models

State-of-the-art models for WDM include density functional theory (DFT), which is considered most accurate at low temperatures, and path-integral Monte Carlo (PIMC) models, which are most reliable at high temperatures. Both can access the WDM regime, but it is not clear how results from these two different approaches can be compared.

Extending these models—or developing new models that can use experiments, PIMC and DFT as touchstones—is an important frontier for HED science. As an example, recent DFT calculations have predicted observable effects of mixing valence electronic structure in compressed transition-metal alloys, an exotic effect that would signal extreme densities forcing overlap of valence states and enabling exploration of profound coupling between electrons and photons in WDM.

This is a particularly important challenge because many material properties are interrelated. For example, electron-ion collisions determine such diverse properties as electrical and thermal conductivities, stopping power, and line broadening. Models that enforce these relationships and use them to constrain observables for comparison with data can enormously increase the impact of any single, high-precision measurement.

Opportunity: Hydrodynamic Properties

In comparison with matter in other HED regimes, warm dense plasmas are characterized by relatively high densities and low temperatures. This leads to interesting macroscopic fluid properties. For example, WDM is cold enough and practical time scales can be short enough for the plasma to be effectively inviscid. As a result, hydrodynamic turbulence can be easily generated and tends to persist. The energy contained in random hydrodynamic flows might then even be large compared to the thermal energy content.

Under compression, there are then interesting questions to ask. If a blob of plasma laden with turbulent energy is compressed to a smaller volume (see Figure 3-4), how much energy is required to compress it, and how is that energy partitioned between heating and turbulent motions? This partitioning of energy is important because it affects the rate of nuclear fusion. Nuclear fusion happens only when there is large relative velocity between the reactants, which is measured by temperature, not turbulent fluid motion in which neighboring particles tend to have small relative velocities.

The next interesting effect occurs because the viscosity of plasma is proportional to T^5/2, making it sensitive to temperature, in contrast with ideal neutral gas, which is insensitive to temperature. This sensitivity leads to a positive feedback effect. The viscous dissipation of turbulent kinetic energy makes the plasma hotter,

which makes it more viscous, in turn leading to faster dissipation. This positive feedback results in what has been theoretically predicted as a “sudden dissipation effect.” The sudden dissipation, with sudden increase in temperature, could result in a sudden onset of nuclear fusion or intense radiation. An important opportunity lies in experimentally verifying this and related hydrodynamic effects in WDM.

Opportunity: Focused Multi-Scale Experiments and Modeling

Beyond the time-dependent, energy-dependent, and pressure-dependent microscale physics discussed above, the fundamentally multi-scale nature of HED science brings opportunities for focused experiments and multi-physics simulations and models that can clarify how microscale properties affect mesoscale behavior. Interesting questions include the following: How do changes in thermal conductivity affect the development of hydrodynamic instabilities? How does interdiffusion couple with turbulence and spallation that lead to material mixing across interfaces? How do rotational or turbulent velocity fields behave under compression or intense irradiation?

Here, retaining diverse experimental approaches is especially important for ensuring robust progress. Planar experiments can be driven by both lasers and pulsed power, while cylindrical and spherical geometries are most natural for pulsed power and lasers, respectively. As the system geometry can have a profound impact on mesoscale phenomena, maintaining a diversity of platforms is important for reliably transferring understanding from focused multi-scale experiments to more complex, whole-experiment systems. High-precision diagnostics of mesoscale experiments are key to extracting this understanding and have benefitted

from coordinated efforts across the community to develop high-resolution instruments. In particular, XFELs like those at the LCLS Matter at Extreme Conditions end-station are among the most powerful diagnostic tools available for meso-scale imaging and X-ray diagnostics. Moreover, there is significant potential for plasma-based X-ray “lasers,” generated with compact laser pumps these would change dramatically the characterization capabilities for compression facilities.

Modeling and Simulation

Advances in the field of HED science rely on a close coupling of experiment, theory, and simulation. Typically, “theory” refers to the governing equations of a particular system. For example, DFT is one of the primary atomistic theories used by HED scientists to describe compressed matter and WDM. In the complex, multi-scale systems of HED science, few theoretical frameworks can be directly implemented using “analytic models”; instead, a majority of modeling is done using computationally intensive simulations.

Typically, “simulation” refers to a numerical implementation of a theory, or collection of theories, in a computer code. These codes can access a variety of scales or combinations of scales (e.g., a radiation-hydrodynamics code may model an entire fusion experiment, relying on constitutive data from atomic-scale simulation). A simulation based on DFT might model a handful of atoms with high theoretical fidelity, for instance, whereas a molecular dynamics simulation with empirical potentials might model thousands of atoms at a lower theoretical fidelity. Moreover, there remain challenges in radiation-hydrodynamics, extended magnetohydrodynamics (MHD), hohlraum modeling, laser-plasma intercations (LPIs), and ultra-short pulsed laser (USPL) simulations, as well as Vlasov and Focker-Planck non-equilibrium transport analyses that are ready for significant advances. Exascale computational resources are expected to allow unprecedented modeling of systems with many degrees of freedom and across many scales.²

Since HED experiments are typically tiny and short-lived compared to everyday length and time scales, the data obtained are usually noisy and can be difficult to interpret. Simulations are used extensively to (1) design experiments and make

___________________

² A separate, congressionally mandated, and ongoing National Academies activity has been organized on the topic of “post-exascale” computing.

predictions, (2) analyze and interpret measurements, and (3) facilitate mutual testing of theory and experiments.

Understanding the reliability of simulation predictions is therefore a key facet of HED science, especially for complex systems requiring high fidelity across many length and time scales, (1) when non-equilibrium or non-local processes are significant, (2) when there is limited accuracy in existing simulations, or (3) when there is limited resolution in experimental measurements. Hence, simulation is crucial to the future of HED science, and increasing efforts in theory, simulation, and machine learning at universities and national laboratories is key to progress.

The scope of traditional HED science funding can also be broadened to support the discovery of new materials (e.g., hydride superconductors) and other new states of matter, to refine and test the predictions of both atomistic and multi-scale simulations, to extend predictive capabilities and synthetic diagnostics that enable direct comparisons to experimental observables, to explore improvements that can access more complex composition spaces, and to provide long-term support aimed at improving the underlying theory.

Future Computational Environment (Hardware and Software)

The full potential of multi-physics simulations is just starting to be realized through development, deployment, and maintenance of both theory and software. Compared with condensed-matter and plasma physics—for example, HED science is a relatively young scientific enterprise spread across different countries and institutions, some of which are in classified environments.

There is therefore an opportunity to build up a robust software community that is sensitive to the restrictions attendant to security, attuned to progress in the wider community, and aware of the great benefits of open collaboration and broad developer and user bases. Recognizing all of these factors, experience in other research communities (e.g., condensed matter) shows that open development of community codes can revolutionize the field. HED science is ripe for benefitting from similar advances.

At the same time, it is vital to maintain a balance between investments in software relative to hardware, to avoid researchers being unable to profit from spectacular new hardware capabilities. The NNSA has had success in co-development of codes and hardware, and this experience would be valuable in informing strategic

planning for high-performance computing in basic science applied to HED science. Where possible, new codes would ideally be optimized for future heterogeneous hardware. A broad developer base that includes experts with training in modern computing architectures could enormously benefit the field.

___________________

³ See MICCo, “Computational Materials Science Centers and Projects Around the World,” http://miccom-center.org/centers.

Machine Learning and Data Science

As has happened in many other areas of science and technology, machine learning and data science are poised to lead to great advances in HED science. For example, ML-optimization of interatomic potentials developed by computationally intensive simulations can facilitate rapid progress in calculating properties of many-body systems under conditions of extreme density and temperature. At the mesoscale, machine learning can help constrain subscale models for turbulence and mix. At the experimental scale, it can help refine target design, and more accurately determine experimental controls. There have even been initial successes in applying these techniques to ICF implosions and burn.

To date, machine learning has mostly been applied to microphysics for systems with short-range forces. However, many HED science systems have important long-range interactions. There is a need to include long-range forces and to develop efficient software to model those systems at the mesoscale to approach and validate many-body systems and phase transitions such as metal-insulator transitions, lattice fracture, and electrides.

Optimizing experiments at high-repetition-rate facilities can provide a robust data set for machine learning, thereby supporting the development of feedback loops between theory, computation, and experiments. Strong initial efforts for integrated data collection, curation, and processing are now under way at Stanford University’s LCLS, as an example. In particular, the committee encourages the following:

• Establishing databases as well procedures for data mining of large sets of measurements to investigate trends in structure–function relations, and for data processing and interpretation.
• Integrating theory and computation, key to establishing feedback loops between predictions and measurements, and to advance understanding. It is essential to define physical models to obtain robust comparisons.
• Applying machine learning for HED science, as next-generation facilities will need to produce, collect, analyze, and process data at much higher repetition rates than ever, incorporating the available data from experiments and simulation into computational models. It is essential to define physical models, from atomistic to continuum, including first principles and kinetic theory, to obtain robust comparisons.

While machine learning is a promising technology in the areas outlined above, it should not be concluded that this will replace the traditional approaches that have been needed for solving coupled, nonlinear, differential equations. Machine learning will supplement rather than replace these technologies.

Benchmarking

Benchmarking, in general, refers to establishing an independent standard that can be relied on to characterize the accuracy of any given model or experiment. Scientific communities tend to be most familiar with experimental benchmarks, for which carefully calibrated, high-precision measurements of a material property (e.g., pressure, conductivity, or opacity) with rigorous uncertainty quantification are combined with independent measurements of the material state (e.g., density and temperature). These benchmarks may be few and far between; an example on the way to an experimental benchmark is the iron opacity data described above.

Codes can also be used to establish theory-based benchmarks. A recent example is given by a Simons Foundation project in which the general scientific community was invited to submit their computational results for several different, clearly defined, many-body quantum systems: the Hubbard model, a hydrogen chain, and transition metal atoms and dimers. For these systems, several different theoretical approaches obtained the same results, giving confidence that those methods were indeed mutually consistent, and allowing these methods to be used for a range of other systems. In the 2 years since publication, the benchmark study has had a large impact on the electronic-structure theory community.

Standards are needed for science to advance, and the committee expects that a similar approach can also help validate research within HED science. The committee therefore recommends a theory-based benchmarking initiative focused within the HED community.

After defining a precise target benchmark, experimental and theoretical approaches can jointly publish comparisons, with data made available to the community along with full details of how the results were obtained (see Box 3-1). For code benchmarks, it is important that different methods be used for validation, and—within the same method—that different codes be used for verification (see also Box 3-2).

For experimental benchmarks, different platforms can be used to reach similar target conditions, albeit with potentially different time and length scales—for example, dynamic compression with pulsed power, diamond-anvil cells, or lasers. If agreement can be achieved, then the measured properties at the independently determined conditions can be used with confidence as a benchmark. If different results are obtained from different platforms, then the source of the disagreement could be identified. In the case of the long-standing disagreement between pulsed-power and laser-based measurements of the hydrogen equation of state, for example, both data interpretation and kinetic effects have apparently contributed to the disagreement.

Once a benchmark is established, it can be used to develop new theories and models, and to increase confidence in multi-physics predictions using models that match the benchmark. For example, benchmark data from the Simons Foundation code comparison can be used to validate the DFT functionals or to develop machine-learned potentials, and can also be used for predictions at conditions other than those benchmarked. Examples of reference data include properties of “simple” mixtures—for example, hydrogen and helium; dynamical transport properties, such as opacities or collision frequencies; and the structure factors, pressures, and compressions that inform equations of state.

Although most existing HED science benchmarks assume local thermodynamic equilibrium, the HED science community is now positioned to move toward benchmarking important non-equilibrium processes. Such processes may include reaction kinetics; unequal electron, ion, and radiation temperatures; non-thermal energy distributions; complex mixtures; and strongly correlated systems under extreme conditions. Both uncertainty quantification of multi-physics codes and theory itself can be used to determine which materials and conditions are the most important for different HED applications.

EXTREME HIGH ENERGY DENSITY SCIENCE: BEYOND WARM DENSE MATTER AND NUCLEAR FUSION

Opportunity: Frontiers in High Energy Density Radiation and Particle Acceleration

Pair Production

State-of-the-art laser intensities of 10²² W cm⁻² have energy densities on the order of 3 × 10¹⁷ J m⁻³, a million-fold greater than the onset of HED at 10¹¹ J m⁻³. Therefore, the HED radiation regime, as accessed by high-intensity lasers for example, represents an important frontier in the realm of very HED science. This intense radiation regime may be considered interesting both because of its own unique physical processes, and because it offers an enabling technology for taking matter to extreme energy densities.

The interest stems, in part, from the fact that at high intensities, light can undergo a variety of nonlinear or parametric interactions mediated by plasma, by which the energy in light at certain wavelengths may be converted into light at different wavelengths. At even higher intensities, exceeding the so-called Schwinger limit, matter-antimatter pairs may be created. A matter-antimatter plasma, comprising electrons and anti-electrons (positrons), is thought to be found in the atmospheres of pulsars and other astrophysical settings. When electrons encounter positrons, there is mutual annihilation of the electron-positron pair, releasing a large amount of radiation. Conversely, pairs of electrons and positrons are produced in the laboratory using very-high-intensity radiation sources.

To date, only small amounts of electron-positron pairs have been produced in experiments, however. An important frontier for research in HED science is to produce sufficiently many electron-positron pairs in the laboratory to observe the collective interactions of a large number of pairs such as occur in pulsar atmospheres. This quantum electrodynamics (QED) plasma regime, comprising an electron-positron plasma, features both strong-field quantum and collective plasma effects. Researchers

have a good idea of what these collective effects might be, because they expect a single positron to respond to electric and magnetic fields as if it had the electron mass but a positive charge. But until these collective effects are demonstrated in the laboratory, it is impossible to be sure there will be no surprises.

Figure 3-5 shows progress in achieving such a state of matter, from creating just a few positrons in the laboratory in 1996, to suggestions and simulations of reaching the QED plasma regime. Note that the energy densities involved are quite high. To reach the QED critical field for pair production, a 50 GeV electron-beam collides with a 10¹⁸ W/cm² laser pulse. The e-beam has energy density of about 10¹⁵ J m⁻³, and the laser has energy density of about 10¹³ J m⁻³. However, energy is frame-dependent, so in the relevant frame of the e-beam, the laser has energy density of about 10²³ J m⁻³, close to the Schwinger limit for pair production. In case (c) of Figure 3-5, where a pair plasma is simulated, the 30 GeV e-beam has a density of about 10²⁰ cm⁻³; 50 MeV pairs are created at a density of about 10²² cm⁻³, so the pair energy density is near 3 × 10¹⁸ J m⁻³.

These energy densities can be compared to the HED science onset at 10¹¹ J m⁻³; ICF energy densities of about 10¹⁷ J m⁻³; or magnetic fusion energy densities of about 10⁶ J m⁻³. They are well into the HED regime, and the opportunities of this high-radiation-energy-density regime are addressed in other reports, such as that of the Brightest Light Initiative. The present report therefore focuses on HED involving matter rather than light, yet the committee emphasizes the fundamental importance of research on HED radiation fields.

Interest in the HED radiation regime additionally stems from its role as an enabling technology for future experiments. In particular, the next factor of a thousand in laser intensities can be developed in order to address the following: Is there completely new physics to explore? Can one separate out applications for different wavelengths? Are there robust fusion ignition schemes enabled by such high energy or intensity capabilities?

At present, only visible light can reach the necessary high intensities, through chirped pulse amplification (CPA). To amplify shorter-wavelength (e.g., UV) light requires free-electron lasing or plasma-based amplification methods. For the next factor of a thousand or so in laser intensity, which is required to reach the Schwinger limit to produce antimatter, one can imagine compressing and focusing to a cubic wavelength either megajoules in the optical regime or millijoules in the X-ray regime. In that case, the technology would likely rely on plasma-mediated approaches, such as illustrated in Figure 3-3.

Still, the present generation of lasers is impressive in its own right. New short-pulse kilojoule, petawatt-class lasers have recently come online and are being coupled to large-scale, long-pulse facilities. These short-pulse lasers also happen to reside in a unique laser regime: high-energy (kilojoule), multi-picosecond pulse-lengths, and large (tens of microns) focal spots, where their use in driving energetic particle beams is largely unexplored.

Target-normal sheath acceleration (TNSA) at the Advanced Radiographic Capability (ARC) laser at NIF has accelerated protons up to 18 MeV using laser pulse lengths exceeding 1 ps and quasi-relativistic (~10¹⁸ W/cm²) intensities, for instance. This is indicative of a process that sustains electron acceleration over multi-picosecond time scales and allows for proton energies to be achieved far beyond those of TNSA at such modest intensities. The characteristics of the ARC laser allow for the investigation of one-dimensional (1D)-like particle acceleration.

Astrophysics

Relativistic extragalactic jets are of high interest, as astrophysicists try to understand how these jets can be accelerated to Lorentz factors of several tens and how they can be so sharply collimated (see Figure 3-6). The answers are thought to be intimately related to the mechanisms of jet launching, which are still not under-

stood. The dynamics and creation mechanisms behind gamma-ray bursts (GRBs) are also enigmatic. One long-standing GRB model by Meszaros and Rees posits that a black hole “engine” generates a relativistic outflow with multiple internal shocks (see Figure 3-6). In the rest frame of the observer on Earth, one can see the emissions of the multiple internal shocks as well as the forward shock. Given that they are occurring in a reference frame moving relativistically toward Earth, these emissions are shifted to gamma-ray wavelengths.

These high-energy phenomena demonstrate the need for experiments to test our understanding of relativistic plasma astrophysics. Notably, relativistic electron temperatures can now be produced and measured in subrelativistic laser-plasma experiments, suggesting great promise for breakthroughs in laboratory astrophysics.⁴

Opportunity: Nuclear Reactivities in HED Matter

Astrophysically relevant nuclear reactions are just now beginning to be studied using inertial confinement fusion (ICF) implosions on NIF and Omega. These capsule implosions can be used to study plasma nuclear reactivities.

Initial studies focus on key reactions (e.g., T(t,2n)a, T(3He,np)a, and 3He(3He,2p)a), the goal being to explore thermonuclear reaction rates and fundamental nuclear physics in stellar-like plasma environments. Further goals are to push this new frontier of plasma nuclear astrophysics into unique regimes not reachable through existing platforms, with thermal ion velocity distributions, plasma screening, and low reactant energies.

HED science facilities also provide a unique capability of studying neutron-induced nuclear cross sections in an HED physics environment. In the s-process, low-lying short-lived excited states can thermally be populated in stellar plasma environments through nuclear excitation by electron capture or transition (NEEC or NEET), which may significantly alter the neutron absorption rate in branching point nuclei where such rates are comparable to their beta-decay rates, leading to altered population of predicted universal isotopic abundances. Furthermore, these processes can occur on the highly excited states produced by neutron absorption

___________________

⁴ See G.J. Williams, A. Link. M. Sherlock, et al., 2020, “Production of Relativistic Electrons at Sub-relativistic Laser Intensities,” Physical Review E 101(3):031201; G.J. Williams, A. Link. M. Sherlock, et al., 2021, “Order-of-Magnitude Increase in Laser-Target Coupling at Near-Relativistic Intensities Using Compound Parabolic Concentrators,” Physical Review E 101(3):L031201.

reactions before gamma emission, effectively “hijacking” an (n,γ) reaction midway through completion. As there are currently no existing capture-rate measurements on plasma-excited nuclei, the state-of-the-art HED science facilities are in a unique position to provide data of the underlying physics governing these processes. Exploding pushers are used as a source of high-yield, low-areal-density fusion products at the NIF to study nucleosynthesis relevant to astrophysics. Future work at still higher compression energies than those enabling kiloelectronvolt chemistry may enable the study of quantum nuclear (pycnonuclear) reactions in which the cold compression overlap of nuclear wave functions gives rise to nuclear fusion (see Figure 3-7).