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The Foundations of Plasma Science

PLASMA SCIENCE—THE ENABLING FUNDAMENTALS

Plasma is the most abundant state of visible matter in the universe. Plasma processes occur in nature, laboratories and in industrial settings over a vast range of space and time scales. Many of these plasmas are permeated by magnetic fields, which add further richness and complexity to the underlying dynamics. Despite the great diversity of plasmas, there are underlying unifying phenomena. For example, eruptive dynamics, where a quiescent plasma undergoes a sudden change in its configuration and releases large amounts of energy, is seen in disruptions of plasmas in fusion reactors (when a growing instability can destroy the ability to confine a plasma), space storms in planetary magnetospheres, solar and stellar flares, and in astrophysical explosive events like flares from the Crab Nebula, and Gamma Ray Bursts (GRBs). The time-scales for these phenomena can vary from milliseconds to several hours, and the energy liberated exhibits an enormous range, from approximately 10⁷ Joules for a fusion plasma disruption to 10⁴⁴ Joules for a GRB. (As a point of comparison, the average U.S. household uses about 10⁸ Joules of energy per day.) These eruptive phenomena are at the leading edge of plasma science and under intense study. It is widely believed that the dynamics of magnetic fields embedded in these plasmas play a crucial role in their behavior.

The basic processes that underlie a wide range of plasma phenomena, and provide cohesiveness to the field, are the subject of this chapter. This report discusses some of the foundational concepts of plasma science that cut across the subfields, and where advances in our understanding of their complexities can lead to transformational change across multiple applications spanning the entire range

of plasma science and engineering (PSE), from microelectronics to health care. It is this interdisciplinary aspect of plasma science that has been a powerful attractor of talented scientists and engineers who are engaged in a rich spectrum of activity in academia, industry, and national laboratories. The quest to understand the fundamental aspects of plasma phenomena and to develop applications for societal benefit based on that understanding is a unifying theme of this diverse community.

In many fields of science, there is a tension between curiosity-driven research and application-inspired research. PSE is not devoid of that tension. Having said that, the extreme intellectual diversity of PSE has produced a field that embraces addressing the most critical fundamental science challenges and translating that fundamental understanding into technologies that benefit society. The continuum spans researchers who primarily address fundamental plasma science concepts to researchers who are focused on plasma-enabled technologies. The committee cannot overstate in strong enough terms the importance of jointly and holistically supporting the continuum of research from the fundamental to the applied. These are not separate activities—they are part of the continuum that leads to societal benefit.

While the frontiers of fundamental plasma science continue to be strongly driven by experiments—small, medium, and large, as well as major international facilities and space missions—computer simulations are playing an increasingly important role and form the “third leg” of discovery (in addition to experiment and theory). These simulations make use of novel algorithms and software developed by applied mathematicians and computer scientists in collaboration with physical scientists and engineers using state-of-the-art computing platforms.

Research in basic plasma science is now supported by and spread across multiple federal agencies—the Department of Defense (DoD), the Department of Energy (DOE), the National Science Foundation (NSF), the National Aeronautics and Space Administration (NASA), and the National Nuclear Security Administration (NNSA). This breadth of support reflects the intellectual breadth and the interdisciplinary nature of the enterprise. However, there is a danger that in the drive to develop new plasma-based applications, the connection to and support of the underlying science will weaken. The field should keep in mind the Pasteur Quadrant,¹ a guiding principle that describes the symbiotic relationship between basic and applied research. One of the objectives of this report is to identify such issues and make recommendations for collaboration that span multiple funding agencies. (See Table 1.1 in Chapter 1.)

The committee identifies four cross-cutting strategic challenges in basic plasma science, followed by more detailed discussions of areas within PSE that address these challenges. These are not the only basic plasma sciences challenges that span the field, but exemplify unifying challenges. Computational plasma physics, which

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¹ D.E. Stokes,1997, Pasteur’s Quadrant – Basic Science and Technological Innovation, Brookings Institution Press.

underlies all of PSE, is discussed first and followed by magnetic reconnection and waves, turbulence and the dynamo effect—plasma processes that are ubiquitous in plasmas in the laboratory and nature. This is followed by a discussion of fundamental processes in the context of dusty plasmas, non-neutral and one-component plasmas, and fundamental aspects of low-temperature plasmas (LTPs). These specific examples illustrate how cross cutting challenges impact diverse areas of PSE. This is not an exhaustive list of examples. For example, some aspects of the fundamentals of plasma shock physics are discussed in Chapter 7.

STRATEGIC CHALLENGES IN FOUNDATIONAL PLASMA SCIENCE

Strategic Challenges in fundamental plasma science are cross-cutting themes that apply across the field of PSE. Although each challenge may not apply to every subfield of PSE, these challenges unify the field.

1. Understand and predict plasma behavior under extreme conditions that challenge our present models.

“Extreme conditions” in plasmas can be realized in many ways. Some of these plasmas are created with such high densities and temperatures that their thermodynamic properties cannot be addressed by current theories and computational models. In other plasmas, extreme is measured by the ratio of electrostatic energy to thermal energy—referred to as the coupling constant Γ—being much larger than unity, making them behave more like soft or solid condensed matter than a gas. For these plasmas, the traditional methods of kinetic theory, valid for values Γ much smaller than unity, break down. Other plasmas, such as planetary magnetospheres or the interplanetary medium, have mean-free-paths between collisions that are comparable to or even much larger than the system size, and are virtually collisionless. The optimum form of the fluid equations that are needed to predict their large-scale dynamics during space weather events remains an open question. Finally, in many astrophysical objects the plasma is relativistic (in realms where Einstein’s theories of special and general relativity are needed), magnetically dominated (so that magnetic field, rather than pressure forces, controls the overall dynamics), and strongly affected by radiative and quantum effects like electron-positron pair creation.

2. Quantify, and in the laboratory, control how plasma processes direct the conversion of energy from one form to another, the transfer of energy across a vast range of scales, and the transport of energy in the laboratory and nature.

Fundamental plasma processes such as magnetic reconnection, shocks, turbulence, and the dynamo effect control the conversion of energy from one form of to another—from magnetic energy to kinetic energy, from flow energy to magnetic

energy, or from gravitational energy to kinetic energy and radiation. The nature and structure of turbulence in weakly collisional or collisionless plasmas, systems in which energy from large scales is transferred to small kinetic scales where it is then dissipated, is a subject of intense research. These systems are found in nature (e.g., the flow of energy from the Sun through the solar wind) and the laboratory (e.g., high energy density plasma experiments). These processes are examples of where investigation of fundamental plasma phenomena will rapidly translate to applications in the form, for example, of efficient energy conversion in fusion reactors or plasma processing of new materials.

3. Predict self-organization of plasmas and, where needed, control that self-organization.

Plasmas permeated by electric and magnetic fields can spontaneously self-organize in spatial coordinates (3-dimensions). They can also self-organize in an expanded space, called phase space (6-dimensions), defined by three spatial and three momentum coordinates, producing coherent structures in space and organizing how particles move with respect to them. (See Figure 2.1.) Examples of self-organization in coordinate space (3D) include the dynamo effect, whereby large-scale and slowly varying magnetic fields emerge from magnetic and velocity turbulent fluctuations on much smaller spatial scales and much shorter time scales. Examples of self-organization in phase space (6D) include solitary electrostatic waves in space or laboratory experiments. Self-organization can also involve extreme states of matter, where the fundamental research challenge is to understand how the redistribution of energy, momentum, and angular momentum in physical or phase space gives rise to coherent plasma structures at all scales. Understanding these self-organized structures is critical to developing applications in which these phenomena occur, either beneficially or detrimentally—plasma propulsion, magnetrons used for plasma production of thin films, plasma-liquid interactions in health care and agriculture and beam-plasma interactions.

4. Control and predict interactions between plasmas and solids, liquids and neutral gases.

LTPs, which involve complex interactions between plasmas and solids, liquids, and gases, have revolutionized the microelectronics industry and enabled the production of high-efficiency lighting, low-cost solar cells, and bio-compatible human implants. The beneficial applications of LTPs continue to grow rapidly, stimulating research into multiphase plasma systems—plasmas which simultaneously interact with more than one phase. The plasma-material interactions in fusion plasmas, which can involve either plasma-solid or plasma-liquid interactions, are

another example of multiphase plasmas, which have critical implications for the performance and economic competitiveness of fusion reactors. Understanding the fundamental processing of plasmas sustained in or crossing multiple phases advances fundamental plasma science and is at the heart of translational research leading to technologies.

COMPUTATIONAL PLASMA PHYSICS

Computations have become as essential to plasma physics as experiments. Computations enable researchers to ask, “What if?” and provide quantitative answers. At the heart of computation is theory, which produces the fundamental

relationships (the equations) describing the plasma dynamics that are ultimately implemented in computations, and for suggesting directions of investigation. Our fundamental understanding of plasmas first emerges in these dynamical equations. However, these equations are typically not analytically solvable (particularly in multiple dimensions). Computation is the method for extending fundamental investigations beyond that which is analytically tractable and to test the predictions of analytic theory, which must often rely on approximations to the original equations. This extension of theory then seamlessly feeds the translational research that produces society-benefiting outcomes, through the use of these same computer models to, for example, optimize magnetic configurations for fusion reactors, chart coronal mass ejections from the Sun to Earth, or design plasma materials processing reactors. Experiments are the ultimate test of theory and computer simulations. However, experiments to be performed today are limited to the facilities that now exist. For example, at the time of this writing, it is not possible to carry out an experiment using a 100 Petawatt laser for a laser-plasma interaction, as such lasers do not now exist. However, it is possible to use computations to describe the dynamics of these laser-plasma interactions (LPIs). The outcomes of those computations improve our intrinsic understanding of these phenomena and, from a very practical perspective, help us design a better laser and better experiments.

Computation: Impact on Experimental Design and Diagnostics

Computation is a critical step in experimental design. Usually, no large experiment is built without some prior guidance from computation. At the very least, engineering design involves significant computation, which must be performed to ensure that the experiment will operate safely. More relevant to plasma physics, the dynamics of the system are computationally investigated within the range of known models and the wisdom of the experimental design can be evaluated. For example, will a newly designed plasma thruster achieve the desired impulse given our current understanding of the turbulent transport of momentum? Will a laser-illuminated pellet achieve a desired fusion gain given our current theories of preheating? In the best of cases, computation can be predictive, providing confidence that certain physical outcomes will be experimentally observed, and predict a range of outcomes. Computations also provide a yardstick with which experimental results can be compared and enable us to determine whether the physics underlying the experimental results is understood. If the results of computations do not agree with experiments, one possible reason is that the underlying physics may not be understood well enough to predict an experimental outcome. The degree and manner of disagreement then guide further investigations.

Another area of increasing importance is the use of computations for diagnosing experiments. Plasmas are notoriously difficult to diagnose, given that they are hot,

radiating environments in which physical probes may not be able to survive and diagnostic lasers may not be able to penetrate. In other instances, diagnostics may not be available due to short time scales or small sizes, or because the plasma is inaccessible—for example, space and astrophysical plasmas. In the study of laser-plasma acceleration of particles, the time scale of the essential interaction, involving laser pulse profile evolution, electron trapping and electron acceleration, occur over micrometers of space in less than picoseconds of time, which is extremely challenging for diagnostics. Computations can be the surrogates for diagnostics in these inaccessible regimes.

Computations are used across all of plasma science, and opportunities to leverage computations are expanding. Cloud computing, first developed for commercial use, is putting enormous computational power into the hands of researchers without their having to make the commensurate capital investment. These resources are enabling development of new state-of-the-art codes, improving the capabilities of the underlying theoretical models, integrating across physical domains, and enabling models to address large ranges in space and time.

The Computational Revolution: Where Is It Now?

Consider a full numerical solution of the plasma in a reactor of the type used for etching and deposition for microelectronics fabrication. The reactor would have a volume of 10,000 cm³ and a particle density (both positive and neutral) of 10¹⁵ cm^-3. The simulation would have 10¹⁹ particles each with 6 coordinates or 48 bytes of computer storage, for a total of 6 × 10¹⁹ degrees of freedom requiring 5 × 10⁸ Terabytes of memory for its representation. Performing one integration time step on such a system would require resources three orders of magnitude greater than available in an exascale computer (an exascale computer can perform 10¹⁸ calculations per second), and that would still be short of a useful simulation that would require millions of time steps. While the revolution in computing has brought us high fidelity simulations, it is far from being able to compute any system with exact fidelity. (In fact, the largest problems being computed today have of order 10¹¹ degrees of freedom, smaller by 8 orders of magnitude.) Nevertheless, computations do strongly impact technology development. (See Figure 2.2.)

Although computations at the outset might sound, in principle, straight forward, considerable complications are present. In practice, computations first require (like analytic calculations) a step in identifying the appropriate, approximate equations that can be represented with fidelity on existing computer hardware and that will result in calculations that can be completed in a reasonable time. A kinetic approach is used when the dynamics involves detailed changes of the particle distribution function in a 6-dimensional phase space. (Kinetics refers to theoretical or computational approaches that include the distribution of the velocities.) When such detailed knowledge is not needed, or the magnitude of the calculation is too

large, fluid approaches are used. In these methods, an average over the velocity distribution produces equations for mass, momentum, and energy conservation. Certain assumptions must be made to reduce the number of fluid moments to a manageable (less than infinity) number in order to make the problem tractable. These assumptions can introduce significant departures from the physical description provided by the original kinetic model. For example, the damping of certain waves can be very different from one type of fluid model to another. Nonetheless, the fluid equations, regardless of the simplifying assumptions, are typically easier to implement on very large computers and so are often the method of choice for analyzing the global behavior of plasmas.

Computational approaches are as varied as experiments. For example, at the kinetic level, there are particle-in-cell (PIC) and continuum approaches. In the PIC approach, the plasma is treated as a statistical ensemble of particles moving under the influence of external and self-generated electromagnetic forces. In the latter approach, the system is modeled by partial differential equations (PDEs) for particle distribution functions which move under the influence of exactly the same forces. The PIC approach may require less computer memory, but the continuum approach has less numerical noise. Noise can be reduced in particle approaches by simply using more particles or using “δf” methods which track the perturbation in the distribution of particles from a known solution. When the magnetic field in the plasma is strong, one can use the gyrokinetic approach, which assumes that the time scale of variations is long compared with the cyclotron period for charged particles orbiting around magnetic field lines, and so only the time average motion of the particle is tracked. In the case of strong magnetic fields and low-frequency dynamics one can use magnetohydrodynamics (MHD) or multifluid equations. (In MHD, continuum equations describe the dynamics of a conducting fluid under the influence of electric and magnetic fields; and the consequences of the resulting conductivity and currents on those fields.) For fluid dynamics, one can choose an algorithm that can represent thin shock waves in supersonic (or near sonic) flows. For solving systems on time scales long compared with those of the basic oscillations in the system, implicit methods are useful.

Subscale Processes and Infrastructure

Plasma physics computations rely heavily on subscale physics processes. An example of a subscale process in a magnetized plasma is the gyrokinetics approximation, which allows one to ignore time scales smaller than the ion cyclotron period and which are not important to certain types of turbulence and transport. At another level, models have been developed that provide the fluxes of particles, momentum, and energy as a function of local parameters, like density and temperature gradients. Such reduced models have continued to be developed and refined in the last decade. Significant progress has also been made in developing subscale infrastructure that involves atomic and molecular ionization. For example, electric field ionization is important for plasma generation by laser interaction and has become increasingly important with the growth of the subfield of plasma acceleration.

Development of Novel Algorithms—Theory Based

For continuum approaches (both for traditional fluid and continuum phase-space models), there have been many developments in improving algorithms and formulations such as least-squares Finite Elements and Discontinuous Galerkin.

There have also been advances in multifluid higher fidelity models (5-moment, 10-moment, 13-moment) and shock capturing methods, which are critical to understanding collisionless plasmas.

For particle PIC approaches, there have been advances in implicit methods. These methods avoid numerical instabilities that occur when the physical spacing between grid points, exceeds the Debye length. (The Debye length is the characteristic distance over which a plasma exhibits charge separation effects and does not satisfy charge neutrality.) This resolution requirement can be prohibitive for simulating practical plasmas. There have been many advances in modeling that more faithfully capture the dispersion of electromagnetic waves, providing a better model of wave-particle interactions. This particular advance is especially important for accurate modeling of plasma processes such as particle acceleration, reconnection and shocks.

Development of Novel Algorithms—Computing Based

Parallel and now massively parallel computers have become the norm for advanced computations. Computations on parallel computers simultaneously use hundreds of thousands of individual processors (or cores) to increase the size of the problem that can be addressed. Message-passing based, distributed memory methods to use these many cores became common in the past decade, and algorithms were adapted to the new computing hardware. For example, computations were rewritten to maximize computational speed while considering the time required for data to be passed between cores, and algorithms were developed for load balancing to enable efficient use of large numbers of cores. Most software was written in a fashion of asynchronous, autonomous applications on each processor, each performing its own computations, passing information to other processors and waiting on data from other processors before continuing.

In the last decade, the need to structure data and code became even more important, with the advent of Advanced Vector Instructions and Graphical Process Unit (GPU) computing. With large processor core counts, the use of threads, which is a way for a computer program to divide itself into two or more tasks, has become more important. With GPU computing, the role of asynchronous paradigms has attracted great interest. To make proper use of such devices, one must manage thousands of separate threads of computation. This is an evolving area, and many different computing paradigms are currently being investigated.

Code Availability

In plasma physics, state-of-the-art computation is available to a relatively small group of researchers. This is perhaps best illustrated by way of contrast.

Those wishing to make use of Computational Fluid Dynamics (CFD) simulations have any number of ways to engage, such as using one of the many commercial codes available, using an open-source code, or using an in-house developed code. This relatively easy accessibility to CFD codes enables a large group of users to make use of high-performance computation. Commercial codes cater to those needing ease of use, extensive documentation, and robustness. In-house development of codes is usually undertaken only by the most expert, as they must develop the most appropriate algorithms for a class of physical problems that maps well onto the available computing hardware. This must be done in a manner that produces the desired scientific and engineering results. Well-maintained, open-source codes provide a middle ground. They do not typically come with the level of documentation or support provided by commercial codes, but they do provide a resource that a person with the time to invest in learning can make use of without getting into the intricacies of code development. However, in PSE there are relatively few commercial plasma codes that provide an easy point of entry to simulations (and these come at a price). Companies are beginning to provide such software, but none have reached the level of ease of use and broad applicability as found in CFD or in the areas of stress analysis, or electromagnetics of structures, each of which are provided by large companies and have large markets. There are projects underway to provide some broad, open-source solutions for PSE. However, the breadth and applicability of these offerings varies widely.

Computation: Training the Workforce

Computational plasma education needs to cover the many methods used in plasma physics—fluid (in particular, MHD or multifluid) approaches and kinetic approaches (both continuum and PIC). For the fluid approaches, there are a wide variety of textbooks, largely due to the use of CFD across many fields. However, for the kinetic approach there are few modern textbooks. For the particle approach there are some venerable texts, but it is difficult to find textbooks that address continuum approaches to modeling plasma dynamics. This makes it difficult to introduce students to the field, especially as there have been many discoveries since the older classic texts were originally published. Indeed, the entire fields of gyrokinetics simulations, distributed memory computing algorithms, and analysis of large data sets are missing from the existing texts.

There is little motivation for writing advanced graduate textbooks. It is difficult for researchers to find the time to write textbooks when they face demands to write research papers and obtain grant funding. These barriers could be addressed by educational funding that is specific to textbook writing. There is also a need for education about how to use numerical software. As codes become more widely used and the users are no longer the developers, the users no longer have an intimate

understanding of the relevant algorithms and methods. What those users need is only a high-level understanding, but enough to know what to look for to indicate that a simulation might not being giving the proper results. In particular they need to learn about the process of code verification and validation—how to determine whether a code is working by testing it.

In part, the problem of computational plasma education reflects the broader problem of not having a dedicated plasma reviews journal in the same way that, for example, Annual Reviews of Astronomy and Astrophysics serves astronomy and astrophysics. A dedicated plasma review journal that publishes 15 to 20 major review articles annually, thus collecting the major findings in a consolidated and comprehensive format, would serve the community well, from students to seasoned researchers alike. A useful side benefit is that the authors of these articles often use them as the basis for a monograph.

The Computational Revolution: What Is to Be Done?

Subscale Methods and Data Infrastructure

Subscale methods are needed for computation in nearly every area of PSE. How can kinetic effects be represented in global simulations of large systems based on extended fluid equations (such as in the vicinity of black holes, neutron stars and planetary magnetospheres, or in fusion plasmas)? How does one characterize viscous effects at the boundaries of plasma thrusters? Can one develop models that account for the change in the velocity distribution functions in LTPs? While analytical closure models continue to be subjects of interest, there is significant interest in developing new models based on deep learning methods.

Although significant progress has been made in developing infrastructure for data, much remains to be done. For example, the development of LxCAT, a web-based, open-access platform for data needed to model LTPs, has led to greater availability of critically needed data for the LTP community. This community-driven effort is volunteer supported and, by any measure, has been successful. However, the experience has also emphasized the need for ease of accessibility to software libraries for interpolation and implementation, standards for assessing the goodness and consistency of the data, and long-term support that does not depend on the goodwill of volunteers.

Development of Algorithms—Math Based

A continuing challenge in computation is the need to resolve systems not for physics reasons but for numerical stability and convergence reasons. For example, one must resolve the plasma frequency in PIC simulations even though the evolution

of the system to the steady-state occurs on much longer time scales. One must resolve the Debye length in PIC simulations to avoid grid instability even in regions where the plasma varies on much larger spatial scales. A common remedy is to use implicit methods. However, implicit methods can be problematic. Implicit methods typically require solving large matrices, which is time consuming and, in general, such solutions over an entire domain are difficult for distributed memory computation. Research oriented towards improving this situation would be welcomed and would have substantial impact on fluid as well as kinetic approaches. Are there explicit algorithms that eliminate these instabilities? More generally, algorithms that work well in the emerging world of heterogeneous computing would be an advance.

Development of Algorithms—Computing Based

Device-based computing is the development of algorithms that are specialized or can only be used on specific architectures of types of devices. For example, computations on GPU simply need different numerical approaches than used for conventional CPUs (central processing units). The challenge of mapping algorithms onto device specific architectures will become even more important as quantum computers become available. The advent of device-based computing and computing on huge numbers of distributed cores has led to experimentation with new data structures. How does one deal with very large datasets, especially when memory is actively managed, as memory allocation and release of large amounts data remains costly.

The challenge of device-based computing has been the focus of the DOE Exascale Computing Project (ECP). While the ECP has been very successful and has been strongly endorsed by the 2018 National Academies of Sciences, Engineering, and Medicine report Strategic Plan for Burning Plasma Research,² the coverage of ECP does not include the broad reach of PSE disciplines. Optimizing device-based computing requires a much more specialized approach in matching the details of the algorithm to the computing architecture. This unfortunately works against broadly applicable codes that may use different algorithms (e.g., fluid at high pressure, kinetic at low pressure). The lack of a broader ECP-like initiative places the PSE community in a challenging situation. Computations supported by the ECP address specific targeted applications while areas not supported by the ECP may not have the resources to develop state-of-the-art device-based algorithms. Work is required at both ends of the spectrum—device-based algorithms that are more generally applicable and more resources devoted to fostering the development of device-based

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² National Academies of Sciences, Engineering, and Medicine, 2019, Final Report of the Committee on a Strategic Plan for U.S. Burning Plasma Research, The National Academies Press, Washington, DC, https://doi.org/10.17226/25331.

algorithms across the PSE community. A balanced approach that brings together software technologies with PSE applications is needed. The future promises even greater complications. To date, GPU computing has been largely performed using the CUDA framework, which works for only NVidia hardware. Standardization of GPU frameworks would lower the barrier of entry for users and suppliers.

Legacy codes refer to well established, often extremely complex, computer models that have served the community well, but often do not have state-of-the-art algorithms. A major challenge is bringing legacy plasma codes up to the state-of-the-art in computational standards while not compromising their physics robustness. This will require deliberate and careful selection. One criterion might be whether the code to be upgraded will be readily available and widely used. Public-private partnerships could leverage the expertise in the private sector where, for example, in exchange for making codes widely available, commercial plasma code developers could be funded to make their codes more performant. With the increasing complexity of computation, it is increasingly difficult for small teams to have the expertise and personnel needed to write or adapt codes for the wide range of available architectures. This implies that research codes will remain confined to small teams, which will not have the resources to port them to multiple devices.

With quantum computing on the horizon, device-based computing becomes a more important strategic discussion. How can such computing devices be used in computational plasma physics? The Fusion Energy Sciences Roundtable on Quantum Information Science (QIS) has identified two priority research opportunities: “using QIS to do plasma science” and “using plasma science to advance QIS.” Following this report, DOE-FES has solicited proposals and made awards that make a promising beginning. There is significant enthusiasm and excitement in the plasma science community about participating in the quantum computing frontier, which will have an impact across all computational sciences.

Verification and Validation and Uncertainty Quantification

Verification and Validation (V&V) are a critical part of computation, as they provide confidence in the computational results. (Verification refers to making certain that the computations solving the equations properly. Validation refers to the computations accurately modeling the physics.) In PSE, as in other fields, standard problems with established results exist against which codes can be compared. In plasma physics, some successful computational examples are the Geospace Environmental Modeling (GEM) reconnection challenge, and the Cyclone Base Case that is a standard set of tokamak conditions intended to compare computations of micro-turbulence. Validation studies tend to be more selective since they depend greatly on the availability of time on experimental facilities and the required coordination and interaction with teams of modelers. The adoption of computations

for complex plasma systems would be aided greatly by a more extensive set of validation cases with sufficient (and accurate enough) diagnostics data to provide stringent tests of codes. With experimental costs in some areas of PSE significantly increasing, accurate validation of computational models is especially needed so that computer simulations can be more reliable in their predictive capabilities.

As computations address frontier areas where fundamental data (e.g., opacities, cross sections, materials properties) and validating experimental data may not be available, uncertainty quantification becomes more important. How do needed assumptions or estimates of fundamental data, or methods propagate through a full simulation? There is not a vigorous culture of making such uncertainty quantification in PSE computations, particularly for large simulations for which a limited number of runs can be made. Developing strategies for uncertainty quantification in general, and for large codes in particular, would benefit the field.

MAGNETIC RECONNECTION: TAPPING THE ENERGY OF MAGNETIC FIELDS

Magnetic reconnection is a fundamental process whereby magnetic fields reconfigure topologically (sometimes viewed as “breaking” and “reconnecting”) and in the process release energy. Magnetic reconnection underlies many explosive and disruptive plasma phenomena over a wide variety of plasmas in both nature and in the laboratory and plays a pivotal role in electron and ion heating, nonthermal particle acceleration to high energies, and magnetic flux and energy transport.

In heliophysics, magnetic reconnection plays a key role in a wide range of phenomena, including solar flares, coronal mass ejections, coronal heating, solar wind dissipation, interaction of interplanetary plasma with Earth and other planetary magnetospheres, dynamics of planetary magnetospheres such as storms and substorms, and the interaction of the heliospheric boundaries with the interstellar medium. Magnetic reconnection is critical to solar and planetary dynamo processes. Without magnetic reconnection, magnetic fields advected by the plasma will become horribly tangled up and no large-scale order can emerge. In astrophysics, the importance of magnetic reconnection has been recognized for star formation in molecular clouds, stellar flares, explosive phenomena in magnetars and pulsars, and cosmic-ray acceleration. Magnetic reconnection is thought to occur in both coronae and interiors of magnetized accretion disks in proto-stellar systems and X-ray binaries, as well as in interstellar medium turbulence. Magnetic reconnection is believed to occur in the centers of Active Galactic Nuclei (AGN), where matter is accreted onto supermassive black holes. On even larger scales, magnetic reconnection may be important in extragalactic radio jets and lobes as they propagate and relax, and even in galaxy clusters. In laboratory fusion plasmas, magnetic reconnection occurs during the sawtooth oscillations in the temperature profile seen in

the tokamak core, the growth of nonlinear instabilities that cause disruptions, and self-organization phenomena in reversed-field pinches and compact tori.

While magnetic reconnection is a fundamental process in plasma physics that is worth understanding in its own right, such understanding has very practical implications and is critical to our ability to control thermonuclear plasmas for producing fusion energy and predicting space weather, to name two examples. In magnetic confinement devices such as tokamaks, major disruptions can occur due to the nonlinear interaction of reconnecting instabilities, which need to be controlled and mitigated. Extreme space weather events producing storms and substorms are thought to be powered, at least in part, by magnetic reconnection. These events can disrupt or damage the electrical power grid, can cause major interference with communication networks, damage spacecraft and be a danger to astronauts. Space weather is discussed further in detail in Chapter 7.

Achievements of the Last Decade in Magnetic Reconnection

During the last decade, thanks to space missions, laboratory experiments, analytical theory and sophisticated computer simulations, our understanding of magnetic connection has advanced greatly. These accomplishments include the following:

• An improved theoretical understanding of the plasmoid instability (an instability of thin current sheets) has been achieved, and has led to the prediction of a new regime of fast reconnection in which the reconnection rate deviates from the classical Sweet-Parker theory and becomes independent of the resistivity of the plasma when the resistivity is below a critical threshold. (See Figure 2.3.)
• The instruments aboard the multisatellite mission MMS (Magnetosphere Multiscale Mission) have produced data of unprecedented spatial and temporal resolution of the reconnection layer in the magnetosphere around Earth down to electron micro-scale (skin depth). These datasets, while confirming several theories of laminar reconnection, are producing new challenges on the interplay between reconnection and turbulence. The Fermi Gamma-ray Space Telescope, which observes the entire sky, has provided remarkable data on gamma-ray spectra from solar flares, which provides insights into the energetics of magnetic reconnection.
• The use of sophisticated diagnostic tools (e.g., electron cyclotron emission (ECE)) on tokamaks such as KSTAR, have provided deeper understanding of sawtooth reconnection events, bringing into question our past understanding, and posing new challenges for theory and simulation.
• High-energy-density plasma experiments at high-power laser facilities such as Omega at the Laboratory for Laser Energetics (LLE) at the University of Rochester and the National Ignition Facility at the Lawrence Livermore

Laboratory (LLNL) have provided new data for testing the predictions of theory and simulations of magnetic reconnection, often co-existing with shocks and turbulence. These data have been extended to include magnetized plasmas, having self-generated Biermann magnetic fields as well as externally imposed magnetic fields.

• New laboratory experiments at the Facility for Laboratory Reconnection Experiments (FLARE) at the Princeton Plasma Physics Laboratory (PPPL) and the Terrestrial Reconnection Experiment (TREX) at the University of Wisconsin-Madison have exceeded the capabilities of earlier experiments such as the Magnetic Reconnection Experiment (MRX) at PPPL and the Versatile Toroidal Facility (VTF) at MIT in size and scope. These new facilities provide an excellent complement to space missions by enabling the exploration of new regimes of reconnection through reproducible experiments and detailed diagnostics.

Current and Future Science Challenges and Opportunities

In spite of significant progress in the science of magnetic reconnection, major scientific challenges remain to be resolved. These challenges are discussed in the context of the Strategic Challenges posed earlier in this chapter.

Challenge 1: Understand and predict plasma behavior under extreme conditions that challenge our present models.

While our theoretical understanding of reconnection in collisional nonrelativistic laminar plasmas is reasonably mature, there are significant gaps in our understanding of reconnection in weakly collisional and collisionless plasmas, both nonrelativistic and relativistic. For collisionless plasmas, there are many numerical simulation results. However, analytical theory for such systems is much less developed, which has made it difficult to infer scaling laws for a broad range of realistic plasma parameters and system sizes. This also applies to the role of collisionless reconnection in compact astrophysical objects where electrons and positrons are formed and constitute a plasma (also called pair-plasma). Experiments in high-power laser facilities have the potential to address relativistic, radiative, and pair-plasma regimes.

Extreme-scale computing will be a valuable tool for addressing the highLundquist-number (S) regime where plasmas have a very high conductivity. However, the computational cost to resolve the thin layers (boundary layers) and follow the system evolution on the Alfvén time (i.e., the system size divided by Alfvén wave speed) increases as S^3/2 for 3-dimensional explicit simulations. For S~10⁶, these requirements can quickly surpass the capabilities of a petascale computer. These limitations require a strategic approach to produce reliable scalings in the high-S regime, which can then be used to better extrapolate to conditions of interest to astrophysics. In weakly collisional or collisionless regimes, the structure of reconnection layers involves both ion and electron kinetic scales. As summarized in Figure 2.4, the space and time scales associated with both electrons and ions impose a daunting level of scale separation both in space and time that is difficult to address in computations.

Challenge 2: Quantify and, in the laboratory control, how plasma processes direct the conversion of energy from one form to another, the transfer of energy across a vast range of scales, and the transport of energy in the laboratory and nature.

Magnetic reconnection controls the conversion of magnetic energy to the energy of particles in the form of plasma flows and heating or accelerating particles to very high energies. The rates at which such conversions occur can be large. Reconnection involves coupling between the largest scale size of the system down

to the orders of magnitude smaller kinetic ion and electron dissipation scales. Recent results suggest that plasmoid dynamics may couple these multiple scales efficiently. (A plasmoid is a structure that looks like a cat’s eyes within which magnetic fields lie on nested surfaces, as seen in Figure 2.3.) Key questions include how the number and size of plasmoids scale with the system-size and plasma parameters, and how the reconnection process responds to turbulent fluctuations which span an enormous range of spatial scales. Two-fluid effects and kinetic transport physics are thought to speed reconnection while the effects of micro-turbulence on reconnection are not well understood. (In the two-fluid model, one uses separate fluid equations for electrons and ions.) The latter effect is a particularly important area to investigate as space observations suggest that that reconnection occurs in a bath of turbulence.

Determining the mechanisms for acceleration of particles to high energies and the apportionment of energy between different species are among the most important challenges in space and astrophysical plasmas. Magnetic reconnection, shocks, and turbulence are widely discussed as possible mechanisms. In planetary magnetospheres, energetic particles in the radiation belts (observed, for example, by the Van Allen Probe mission) are significantly affected by space weather events. In our Milky Way galaxy, cosmic rays represent only one-billionth of the interstellar particles but carry as much energy as the galaxy’s thermal plasma for reasons that are not fully understood.

Challenge 3: Predict self-organization of plasmas and, where needed, control that self-organization.

Magnetic reconnection releases energy that was formerly trapped in magnetic field lines, converting that energy to other forms, such as the flow of a plasma or highly energetic charged particles. These other forms of energy can be degraded by collisions and turbulence, resulting in states of lower energy, heating, and increased entropy. In this process, self-organization can occur. The classic Taylor theory of plasma relaxation is based on a nonideal plasma containing multiple reconnecting instabilities. These instabilities relax to a unique final state of minimum energy subject to global constraints that are approximately preserved by the dynamics. This process is thought to occur in laboratory and astrophysical plasmas, but the Taylor state is not always realized. What are the constraints that prevent systems from doing so?

Advances in computational plasma physics have enabled understanding of coherent, self-organized structures in both configuration space in fluid simulations as well as structures such as “phase-space holes” predicted by fully kinetic simulations. In the latter case, there is not yet an underlying theoretical framework that accounts for the simulation results. Observational tests of theories have produced interesting results, but much more work is needed to provide a truly predictive capability for magnetic reconnection.

WAVES, TURBULENCE, AND THE DYNAMO EFFECT

The rich variety of waves exhibited by plasmas is fundamental to a wide range of phenomena in laboratory, space and astrophysical settings. Plasma waves can transport energy and momentum, produce heating of electrons and ions, and energize and scatter particles. Plasmas are often far from thermal equilibrium and instabilities can arise as a result, converting plasma energy into waves. Turbulence, often driven by unstable waves, is ubiquitous in plasmas and is widely cited as the dominant mechanism for heating and transport of particles, energy and momentum in many settings. Instabilities, waves and turbulence also play a role in the plasma dynamo, processes by which magnetic fields are generated and amplified both on small and large spatial scales with lifetimes that can vary widely depending on the plasma medium.

Relevance and Benefits

Waves and instabilities are the first type of dynamics that nearly all forms of collisionless or weakly collisional plasmas experience. Such collective dynamics result from nearly all ways of describing plasmas—at the 3D macroscopic level by fluid equations (MHD and multifluid), and at the 6D microscopic level by the

kinetic equations. Thanks to decades of close collaboration in PSE between theory and experiment, our understanding of linear (or small-amplitude) waves and wave-particle interactions is quite mature. As waves and instabilities grow in amplitude and interact with each other and with particles, nonlinear effects become very important. These nonlinear processes can produce turbulence, dissipation, heating, and particle acceleration, and a variety of coherent structures. Nonlinear effects in nature are wide-ranging—momentum transport in accretion disks around compact astrophysical objects such as black holes and neutron stars; heating of the solar and stellar atmospheres and of the stellar winds (consisting of high-speed particles) that flow out from the Sun and other stars; particle acceleration that produce the Northern lights during substorms in Earth’s (or other planetary) magnetospheres; energetic cosmic rays that pervade the universe; and the rich spectrum of waves that accelerate and expel energetic particles from the Van Allen radiation belts. These nonlinear effects can also dominate in laboratory plasmas—laser-induced plasma waves that can accelerate particle beams, expelling energetic particles from fusion plasmas; and wave-driven currents that offer the potential benefit of enabling a fusion plasma to operate in steady state. The possibilities are nearly endless.

Studies of the dynamo effect address the question of why the universe is magnetized? There are two classes of dynamos. “Small-scale” dynamos amplify magnetic energy but produce negligible magnetic flux because the averaging of fluctuations over space and time leads to near-perfect cancellations. “Large-scale” dynamos produce large-scale magnetic field structures with nonzero magnetic flux. Beautiful in its regularity, the Sun’s magnetic field and its 11-year cycle is an example of large-scale dynamo. (See Figure 2.5.) The spontaneous emergence of large-scale

magnetic fields from disordered small-scale velocity and magnetic field fluctuations is counter-intuitive. However, understanding this behavior is likely required to predict the long-term dynamics of magnetic fields that govern everything from the space climate to the launching of powerful jets during neutron star merger events.

Advances in Waves, Turbulence, and Dynamos

During the last decade, there has been tremendous progress in our understanding of waves, turbulence and dynamos in both laboratory plasmas and plasmas in nature, aided by theory, simulation and experimental observations. A few highlights of that progress include the following:

• Plasma in the universe is often magnetized and turbulent. Plasma fluctuations in space can span a huge range of scales, from hundreds of parsecs (1 parsec is 3.26 light years) to hundreds of kilometers. Observations of the solar wind and the interstellar medium (ISM) reveal qualitatively similar scaling laws for magnetic, velocity, and density fluctuations, which extend down to the ion gyro-radius. (See Figure 2.6.) At large scales, MHD provides a good description of plasma dynamics. The plasma beta (the dimensionless ratio of the plasma pressure to the magnetic energy density) in space and astrophysical plasmas is often close to or greater than unity, which distinguishes these plasmas from plasmas in the Sun’s atmosphere or laboratory that are confined by magnetic fields and typically have small beta values (including fusion plasmas). Typically, space and astrophysical plasmas are large-scale highly supersonic flows, such as solar and stellar winds, which have large flow Mach numbers but nonetheless can have small turbulent Mach numbers. At small scales, at or below the ion gyro-radius, plasma dynamics become much richer, as two-fluid, and kinetic effects become important. These scales are harder to address analytically. However, two-fluid, gyro-kinetic and kinetic plasma simulations have produced promising results in addressing these small scales, such as suggesting scaling laws that bridge different energy dissipation mechanisms. These simulations have also shed light on the role of anisotropic pressure-driven instabilities that self-regulate the nature and structure of turbulence and magnetic reconnection processes.
• Weak MHD turbulence is dominated by Alfvén waves that weakly interact with each other. The practical application of this finding is limited in nature where turbulence is typically strong. However, weak MHD turbulence can be addressed analytically and serves as a test bed for fundamental studies of the theory of MHD turbulence and energy cascades. This understanding sets the stage for the stronger turbulence seen in nature and the laboratory.

Describing strong turbulence using MHD assumes that there is a balance between linear wave propagation and nonlinear interactions. However, this assumption is not based on a rigorous analytical treatment. As a result, good physical models, numerical simulations and targeted laboratory experiments (such as at the Large Plasma Device (LAPD) at the University of California, Los Angeles) are critical to developing better understanding of turbulence. A fundamental property of strong MHD turbulence is its inherent local anisotropy. Small-scale fluctuations are progressively more anisotropic as the scale length decreases. The balance between linear and nonlinear interaction times is postulated to be preserved independently of scale length in collisionless plasmas, which is called the critical

balance condition. The validity of the critical balance postulate in kinetic turbulence is being investigated with interesting results.

• Interaction of turbulence with nonuniform plasmas represents a difficult problem. Methods for investigating turbulence in spatially nonuniform plasmas has been an active area of research, especially for fusion plasmas and the interplanetary medium. Turbulence in such plasmas does not seem to directly conform to the classical Kolmogorov-like picture of turbulence whereby energy cascades from driven large scales to small scales until the energy thermalizes. What seems to occur instead is that turbulence saturates by channeling energy into stable modes that exist at the same spatial scales as the instability that drives the turbulence. Multiscale analysis of inhomogeneous turbulence has produced transport equations that need to be tested against experimental observations. This leads to extremely demanding computational problems, approaching or exceeding the exascale. For example, multiscale, multiphysics, whole-device models for fusion plasmas based on gyrokinetic theory, needed to address inhomogeneous turbulence, need the power of state-of-the-art computing hardware. Fortunately, both computer simulations and theory are well positioned to make progress on these topics, which can have a strong impact on applications as diverse as coronal heating, evolution of the solar wind as it expands from the Sun, space weather, cosmic ray propagation and galactic turbulence.
• Coherent structures are sustained nonlinear perturbations which are localized in space and time. On the other hand, waves are localized in wavenumber or frequency—meaning that they typically have a well-defined wavelength or frequency. Examples are solitons, ion or electron phase-space holes, or double layers (see Figure 2.7), which are now widely observed in nature through progress in observational techniques. (A phase space hole is a region of coordinates and velocities that are devoid of an electron or ion.) Such coherent structures, observed in space and laboratory experiments, occur over a wide range of spatial scales, ranging from Debye to Alfvénic lengths. Coherent structures can be electrostatic as well as electromagnetic, and are thought to be a nonlinear end state of some forms of turbulence.
• With the advent of high-power lasers and pulsed-power devices, some astrophysical environments can now be reproduced in the laboratory. This is the realm of high energy density plasma physics. This capability has led to the study of astrophysical processes in scaled laboratory experiments, including magnetic reconnection, collisionless magnetized shocks, Weibel-mediated shocks, the generation of magnetic seeds at shocks by the Biermann effect, and the small-scale turbulent dynamo. In conjunction with new capabilities in high-performance computing, these developments have set the stage to achieve significant scientific advances.

Current and Future Science Challenges and Opportunities

Challenge 1: Understand and be able to predict plasma behavior under extreme conditions that challenge our present models.

Waves and turbulence in weakly collisional, high-beta plasmas is poorly understood, despite recent advances in analytical theory and simulation. An intriguing aspect of this state of matter is the relevance of the magnetic field. Although the magnetic field (in the absence of reconnection) is not the dominant source of energy, it does influence the transport properties of the plasma by imparting directionality and new degrees of freedom, thereby influencing the large-scale dynamics. The magnetic field-induced anisotropy introduces a fundamental difference between the dynamics of magnetized plasmas and collisional plasmas or those that are unmagnetized. An unique feature of weakly collisional, magnetized, very high beta plasmas is that kinetic microinstabilities can make them unstable. (That is, small variations in the velocities can be amplified exponentially to the point of producing turbulence.) The dynamics of such plasmas are governed by complex, multiscale interactions between kinetic physics and large-scale bulk plasma motion. Strategic areas for future investigations

include: (1) identifying the most important linear kinetic instabilities; (2) determining how kinetic instabilities interact with other plasma processes, such as reconnection, heat fluxes, and particle acceleration; and (3) determining how fluid transport on large scale lengths interacts with kinetic transport on micro-scales.

Challenge 2: Quantify and, in the laboratory control, how plasma processes direct the conversion of energy from one form to another, the transfer of energy across a vast range of scales, and the transport of energy in the laboratory and nature.

In typical occurrences of turbulence, energy is transferred from large scales to small scales through a cascade process. The range of length scales in MHD turbulence has a “break-point” where the dissipation of energy becomes more rapid as the length scales get smaller. Turbulent fluctuations with scale lengths smaller than that of the break point form the dissipation range. In weakly collisional space and astrophysical plasmas, the scale lengths where this breakpoint occurs often has a two-fluid or kinetic origin (e.g., the ion skin depth or ion gyroradius). While there is clear evidence of these breakpoints in observations of plasma turbulence in the solar wind or ISM, there are no definitive theories that describe the transition. Theoretical and computational models based on two-fluid (or Hall MHD, where electron inertia is ignored) equations, gyro-kinetic equations and fully kinetic equations have been developed to compare with specific observations, with some success. The results suggest that the dissipation range may itself be multiscale (caused, for example, by secondary instabilities of fractal current and vortex sheets) with wave damping or particle heating occurring at short scale lengths. Determining the causes of such electron and ion heating is one of the critical unsolved problems in the study of space and astrophysical turbulence. Observations to be made by the Parker Solar Probe mission will provide needed insights to the source of this heating.

Even for a plasma that satisfies the MHD approximation, the large-scale dynamo problem remains unsolved—what are the mechanisms whereby magnetic fields erupt and decay? Until recently, it was generally accepted that small-scale fluctuations in the plasma can lead to catastrophic quenching of the growth of large-scale magnetic fields. However, recent theoretical work on systems with flow shear suggests that small-scale dynamos, after saturation, can drive the growth of large-scale fields. (Saturation of a dynamo occurs when an exponential growth of the magnetic field produces magnetic forces that balance those producing the turbulence.) In the kinetic regime, even less is known. Recent studies have started to explore kinetic effects on dynamos. However, our understanding of dynamos in weakly collisional and collisionless plasmas is limited. The topic is complex, simultaneously touching kinetic turbulence, collisionless reconnection, nonthermal particle acceleration, and diffusion.

Challenge 3: Predict self-organization of plasmas and, where needed, control that self-organization.

When influenced by waves, instabilities, and turbulence, self-organization in plasmas becomes even more complex, bringing forth new and unresolved questions. There appears to be no comprehensive explanation for dissipating energy in plasmas that is as successful as Taylor’s relaxation theory for MHD plasmas. In this theory, energy is minimized while magnetic helicity is kept approximately constant in a dissipative plasma, with the outcome producing a unique, force-free state as a result of self-organization. However, in MHD systems that are not particularly turbulent, there is a tendency to relax into states that have more free energy than Taylor states (as seems to be true for quasi-steady states in fusion plasmas). A unifying principle to describe such states remain elusive. The picture is even more incomplete for kinetic plasmas that self-organize to form coherent structures. Scientific questions that remain unanswered include: How and under what conditions will plasmas self-organize? What are the natural processes that produce the nonlinear instabilities that may produce self-organization? Once formed, what role does self-organization play in defining plasma transport coefficients such as electrical or thermal conductivity or diffusivity? Are the processes responsible for self-organization also responsible for significant particle acceleration in reconnection sites, in the solar corona and wind, and in astrophysical objects? To what extent does self-organization generate or scatter traveling plasma waves, such as Alfvén waves or whistler waves? How long do self-organized structures last? What are the mechanisms that cause them to break up or dissipate? How can we control or mitigate disruptions in magnetic fusion plasmas, which are examples of self-organization?

DUSTY PLASMAS: FROM COMETS TO FUSION REACTORS

In a dusty plasma (sometimes referred to as a “complex plasma”), the typical plasma components of ions, electrons, and neutral atoms are joined by a fourth component: solid, charged particulate matter or “dust.” These dust grains are often nanometer- to micrometer-size objects that acquire charge either through the direct collection of electrons and ions from the surrounding plasma or through other processes that can lead to charging (such as the photoelectric effect resulting from UV and VUV illumination or ionizing radiation). In space and astrophysical environments, dust grains can acquire either a net positive or a net negative charge, depending upon the conditions of the local space environment. In either case, the dust grain charge is the key property that couples the particles to the surrounding plasma and governs the resulting dynamics of the four-component dusty plasma. An equally important property that distinguishes a dusty plasma is the possible influence of gravity. In most other plasma systems, the gravitational force effectively plays no role in the dynamics of the plasma because the electrical, magnetic and fluid

forces are all large compared to gravity. However, for dust grains of several microns in size and whose mass can be millions to billions of times larger than the ions and electrons, gravity can play a dominating role in the behavior of the dust component.

Relevance and Benefits

Dusty plasmas are ubiquitous and appear in a variety of contexts in science as well as technology. In the laboratory, a dust particle of the size of a few microns can attract 10,000 electrons or more at room temperature. Dusty plasmas are often described by the coupling constant Γ, which is the ratio of the average electrostatic energy to the average kinetic energy. For plasmas with these large, heavily charged particles, Γ can be much larger that unity enabling such plasmas to behave as though they were liquids or solids. The large size of the dust particles enables them to be tracked and illuminated with lasers, providing novel tools to study and diagnose strongly coupled plasma dynamics. Dusty plasmas have been used to experimentally and theoretically investigate fundamental properties of soft condensed matter such as the phase transition from the liquid to the solid state, defect formation, and melting produced by waves and instabilities.

Dusty plasma research is highly interdisciplinary. It is strongly relevant to studies of astrophysical objects, particularly star-forming regions and the ISM, as well as cometary tails and planetary rings. Charged dust is found on numerous airless bodies throughout the solar system—from comets to meteors to moons, and can pose both a danger (e.g., due to contamination of space systems) and a benefit (e.g., as surfaces where water and other volatile material could be trapped) for human exploration of the Moon and Mars. Controlling dust-particle interactions with the plasma and the growth of particles in reactive plasmas form the basis for understanding and actively manipulating dust particles for industrial applications in a variety of LTPs (Chapter 5).

Within the United States, the dusty plasma community is supported by NSF, DOE, and NASA with researchers distributed across institutions that range from predominantly undergraduate institutions to PhD granting institutions to national laboratories. Maintaining a healthy and active U.S. research community remains a challenge.

Progress and Achievements

There has been substantial progress in understanding the physical properties of dusty plasmas over the past decade. Some highlights include the following (see Figure 2.8):

• Anisotropic and nonreciprocal interactions: These studies investigate systems in which the action-reaction symmetry (well-known from Newton’s second law) can be broken for mesoscopic particles when their effective interactions

are mediated by a nonequilibrium environment. Dusty plasmas have provided an ideal medium in which to explore the role of symmetry-breaking.

• Binary mixtures and nonequilibrium phase transitions: Most laboratory studies of dusty plasma focus on particles that have the same size, composition and mass—that is, they are monodisperse. For the same plasma conditions, these particles will acquire the same charge enabling a simpler description of the plasma. Between monodisperse and the fully polydisperse systems (particles that have different shapes, masses and compositions) that are found in nature, recent studies have focused on binary dusty plasmas consisting of two different

• monodisperse dust particle species. These binary mixtures have enabled investigation of a variety of phenomena including the dynamics of demixing and the formation of lanes as a pattern, relevant for many applications.

• Atomistic modeling of fluids: The physics of undercooled liquids (i.e., liquids having temperature below their usual freezing point), especially near the glass transition, is a challenging topic in fluid physics. Since dusty plasmas enable visualization of kinetic phenomena on a particle-by-particle basis, it is possible to investigate critical phenomena in statistical mechanics such as the dependence of the structural glass transition on the number of spatial dimensions.
• Precision monitoring of particle size evolution: The dust-particle mass, surface potential, and charge all depend critically upon the size and shape of the particle. Although it is generally assumed that in experiments, the dust grain size generally remains constant, recent in situ measurements of particles reveal that this is not always the case due to plasma-surface interactions. In the next decade, diagnostics that can provide real-time, independent measurements of the particle size and charge are a critical need.

Current and Future Science Challenges and Opportunities

Dusty plasma research is connected to the four Strategic Challenges previously discussed.

Challenge 1: Understand and be able to predict plasma behavior under extreme conditions that challenge our present models.

Strongly coupled dusty plasmas are inherently an “extreme” plasma state, characterized by values of the coupling constant greater than unity. The presence of the dust particles enables direct visualization of plasma phenomena at the single-particle and collective scales simultaneously—enabling unprecedented measurements of the time and space evolution of a plasma component through the direct reconstruction of the distribution function. Dusty plasmas therefore provide an excellent model system upon which to test models of statistical physics, plasma physics, and soft-condensed matter.

The large mass of the dust particles—compared to that of electrons, ions and neutrals—and the resulting very small charge-to-mass ratio, means that dusty plasmas can be studied in regimes that are beyond those of typical laboratory LTP systems. With gravity often a dominant force in laboratory dusty plasmas, moving to microgravity environments is a method to study the smaller scale, inter-particle forces. In another regime, very large magnetic fields (or very small particle sizes) are required to investigate the properties of magnetized dust. In both microgravity

and magnetic field studies of dusty plasmas, the last decade has seen technological developments that will enable new advances.

The leading efforts for microgravity studies of dusty plasmas is centered on the “Plasmakristall” (PK) series of experiments on the International Space Station (ISS). PK-4 is the current ISS experiment with the focus on fluid-like dusty plasma behavior. PK-5 (also known as “Ekoplasma”) is under development. Without a dedicated U.S. microgravity facility, partnership in the PK-4 and PK-5 consortia are essential to accessing microgravity conditions. The long-term future of the ISS as a research platform, support of the national agencies (in the United States and abroad), and developing a distributed, possibly multiagency, support for hardware development are all critical challenges facing the future of microgravity dusty plasma research in the next decade.

The last decade has also seen substantial progress in magnetized dusty plasma experiments, made possible by a reduction in technology costs, improvements in experimental design as well as knowledge of plasma operations to ensure plasma stability. For some time, high magnetic field facilities have been operated in Japan, Russia, and Europe, but within the last 5 years, a multiuser, collaborative research facility, the Magnetized Dusty Plasma Experiment (MDPX) has begun operating at Auburn University in the United States. (See Figure 2.9.) For the next decade, understanding the extended study of steady-state, LTP, and dusty plasma regimes at high magnetic field is a critical goal.

Challenge 2: Quantify and, in the laboratory control, how plasma processes direct the conversion of energy from one form to another, the transfer of energy across a vast range of scales, and the transport of energy in the laboratory and nature.

Dusty plasmas are a thermodynamically open, nonequilibrium system in which energy flows freely between the electrons and ions (at the microscopic scale) to the dust particles (at the mesoscopic scale). In spite of the large-scale separation between the dust particles and the surrounding plasma particles, there is a continuous exchange of energy between the microscopic and mesoscopic scales. An important emerging area of dusty plasma science concerns the deliberate growth of nanoparticles (dimensions of a few to tens of nm) to microparticles (a few to tens of microns) through the chemical energy conversion processes in reactive plasmas. By leveraging inter-particles forces and plasma chemistry, technologically important nanoparticles with unique particles can be produced. (See Chapter 5 for more details.)

Challenge 3: Predict self-organization of plasmas and, where needed, control that self-organization.

Dusty plasmas can be “tuned” via the Coulomb coupling parameter to exhibit self-organized behavior ranging from solid-like to gas-like, while the particles remain suspended in the plasma. In the presence of a magnetic field, this ordering can

undergo significant modifications in ways that are not well understood. Dusty plasmas containing nano- to micro-particles exhibit tendencies to form a wide variety of self-organized and imposed-structures, such as voids. An example of a “probe-induced” void is, shown in Figure 2.10. While progress has been made in providing plausible theoretical models for void formation, a comprehensive theoretical framework for predicting self-organized structure formation in dusty plasmas remains elusive.

Challenge 4: Control and predict the interactions between plasmas and solids, liquids and neutral gases.

Dusty plasmas are the embodiment of a plasma system that defines the challenge of controlling plasma surface interactions. Dust particles are charged solid matter that are embedded in a plasma environment. All of the fundamental properties of a dusty plasma are defined by the interaction between solid particles and plasmas. A key mission for dusty plasma research is to achieve control over these interactions. Some future challenges include:

• Determining the dust particle charge. The most fundamental parameter for a dusty plasma is the charge on the particle. While a number of techniques are used to make charge measurements (e.g., two-particle collisions and/or resonant oscillations), these measurements give the charge-to-mass ratio, and an assumed particle mass is then used to determine charge. A future challenge is the development of noninvasive, nonperturbative techniques that independently determine the particle mass and charge. This is particularly important for chemically reactive dusty plasmas in which the particles grow (or erode), meaning that their size, mass and charge can be functions of position and time.

• Tuning of plasma-dust grain interactions for precision control of trajectories and growth of nano- and micro-particles. In the bulk plasma, the dust particle interaction with the plasma is isotropic. These interactions produce self-organized structures, for example, single or multiple layers of hexagonal lattices. However, when particles interact with anisotropic ion fluxes, as can occur in and near sheaths, the self-organization structures take on different forms, such as linear strings. This qualitative change in self-organized structures is due to the production of local space charge through altered dust-dust and dust-plasma interactions triggered by anisotropic ion fluxes. Correspondingly, in strongly magnetized plasmas, where ion and electron motion is limited by their gyromotion, experiments show that the magnetic field may also impose a directional order to the dust particles. A strategic challenge is to actively control dust-plasma and dust-dust interactions. This capability allows the preparation of the dust particle state in the plasma, and then the use dust particles as microscopic diagnostics to provide information about the state of the plasmas and to control the properties of the plasma. Achieving this goal requires the development of plasma chambers with variable internal geometries and multielectrodes to manipulate plasma density and the electron temperature, using controlled mixtures of particle sizes, or using shaped magnetic geometries, and associated sheath and presheath structures, to manipulate the dust particles.

Dusty Plasma Facilities on Earth and in the International Space Station

The development of dusty plasma research has been dominated by “table top” experiments. This is likely to be the dominant mode of exploration for the foreseeable future. The greatest need for current experiments is the development of new diagnostic tools that can provide real-time, spatially resolved measurements of both the plasma and the dust particles. Key unresolved questions that may be addressed by a next generation of diagnostics would include: (a) noninvasive, real-time measurements the dust grain charge; (b) confirmation of the ion flow dynamics and the formation of the ion wake field in the vicinity of dust particles; and (c) the development of new image analysis tools—possibly leveraging new developments in machine learning—to rapidly process and identify the full three-dimensional motion of particles, particularly in cases where multiple synchronized cameras are used or using new types of light wave (e.g., plenoptic) cameras.

Two areas in which larger collaborative teams have advanced dusty plasma research are the study of dusty plasmas under microgravity conditions and in magnetized plasmas. The next decade will hopefully see the continued operation of the PK-4 microgravity facility on the ISS followed by a successor instrument, PK-5 (Ekoplasma). The United States should consider supporting researchers to

pursue microgravity studies as well as supporting the development of experimental hardware for those facilities.

In exploring dusty plasmas in magnetized plasmas and magnetized dusty plasmas, the last decade has seen the development of several experimental platforms—many involving superconducting magnet systems. All these laboratories are generally extensions of the “tabletop”-scale groups but requiring substantially more personnel and diagnostic infrastructure than a single PI laboratory. The MDPX device at Auburn University is the first facility in the United States specifically designed for supporting external users. Since beginning operations in 2014, researchers from the United States, South Korea, India, Germany, and France have conducted studies ranging from dust charging effects and particle growth to materials processing to calibrations of fusion diagnostics at magnetic fields up to 3 Tesla. For both microgravity and high magnetic field studies, partnerships are critical—both through leveraging federal agencies partnerships (see Table 1.1 in Chapter 1) and promoting national and international partnerships within the community to grow the field.

NON-NEUTRAL AND SINGLE-COMPONENT PLASMAS: CONFINED IN THERMAL EQUILIBRIUM FOR DAYS

The classic definition of a plasma is an ionized gas composed of negative and positively charged particles that, on average, is electrically neutral. The classic plasma can only be non-neutral over very short times (defined by the plasma frequency), very short lengths (defined by the Debye length) or near the boundaries of the plasma where large electric and magnetic fields are applied (defined by the sheath thickness). Most properties of classic plasmas result from being composed of discrete negative and positive charges, attempting to assume on the average an electrically neutral state.

In non-neutral plasmas, particle species with only a single sign of charge predominate—that is, the plasma is intentionally out of charge balance. Often, only a single particle species appears in the plasma (a single-component plasma). A few examples of non-neutral plasmas produced in the laboratory are pure electron plasmas and pure positron plasmas (both of which are single-component plasmas), electron-anti-proton plasmas, and ion plasmas consisting of one or more species of positive ions. Since the natural response of collections of charge particles with a net charge density is to produce forces that reduce the charge density, creating non-neutral plasmas requires specialized experimental techniques.

Non-neutral plasmas have useful properties not shared by neutral or quasi-neutral plasmas. One important advantage is the existence in non-neutral plasmas of a confined thermal equilibrium state using only static electric and magnetic fields (the “Penning-Malmberg trap” configuration). In contrast, there is no confined

thermal equilibrium for classical neutral plasmas in static fields, which is the fundamental reason why neutral plasma confinement is such a difficult problem. (See Figure 2.11.) In non-neutral plasmas, the existence of a confined thermal equilibrium state enables plasma confinement for long times (up to hours, days or even weeks), enables experiments with an exceptionally high level of reproducibility and accuracy, and enables precision industrial plasma applications.

A second feature of non-neutral plasmas is the ability to access extreme strongly coupled and strongly magnetized states of matter. Unlike neutral plasmas, non-neutral plasmas can be cooled to cryogenic temperatures without electron-ion recombination (whose rates greatly increase as the temperature decreases), because there is no oppositely signed charge species with which to recombine. This enables the study of novel strongly coupled and strongly magnetized plasma states in thermal equilibrium (such as pure ion liquids and crystals), which is not possible in any other classical plasma system. The combination of strong magnetic fields (required in Penning-Malmberg trap confinement) and cryogenic temperatures produces novel strongly magnetized and quantum plasma states with nonideal Γ-factors that can be similar to those in the environment of highly magnetized neutron stars and white dwarfs.

Relevance and Benefits

Non-neutral plasmas were among the first plasmas studied or employed in industrial applications. Electron beams used in vacuum tubes, and later in

high-intensity radiation sources such as magnetrons, gyrotrons, and traveling wave tubes are a form of non-neutral plasmas. Understanding collective non-neutral plasma dynamics and radiative interactions is essential to the continuing development of these radiation sources, as well as other vacuum electronics applications in both the nonrelativistic and relativistic regimes of operation.

The Penning trap configuration used in non-neutral plasma confinement is also used to stably confine charged particles for fundamental atomic physics studies, such as measurements of the g-factors (a measure of the magnetic moment and angular momentum) of elementary particles, as well as for high-resolution cyclotron mass spectrometry. Such Penning mass spectrometers are found in laboratories world-wide. The last decade has seen the development of new science involving low-energy non-neutral antimatter plasmas (i.e., positron plasmas or antiproton plasmas) at energies ranging from 100 eV to less than 10^-3 eV. Much of this progress has been driven by the development of new plasma-based techniques to accumulate, manipulate, and deliver antiparticles for specific applications.

The ability to precisely control and manipulate cryogenic non-neutral plasma crystals has made them attractive systems for use in quantum information studies, which have blossomed over the last decade. Pure ion crystals consisting of up to several hundred trapped ions are now used to form lattices of quantum q-bits whose interactions and entangled states can be controlled and manipulated using lasers and microwave signals. These non-neutral plasma crystals are among the most promising technologies for quantum computation and quantum simulation.

More generally speaking, the research in this area of fundamental plasma physics has strong interdisciplinary connections, contributing to and borrowing from the wider world of plasma physics, atomic physics, fluid dynamics, astrophysics, soft condensed matter physics, and statistical physics. Using results from non-neutral plasmas, fundamental questions are being addressed in all of these broader areas.

The U.S. non-neutral plasma community collaborates with many international groups on a variety of projects. Perhaps the largest international collaborative effort is the CERN (European Organization for Nuclear Research) based effort to produce and study trapped cold antimatter such as antihydrogen (made of a positive positron and a negative anti-positron). Another international collaboration involves the production and magnetic confinement of a neutral positron-electron plasma. The U.S. non-neutral plasma community is also active in the world-wide efforts to trap charged particles for a variety of purposes, including spectroscopy of trapped high atomic number ions, metrology, quantum information studies, and high-resolution mass spectrometry of trapped radionuclides.

Progress and Achievements

In the past decade, non-neutral plasmas have continued to provide a rich source of fundamental physics advances across several areas. Below are a few highlights of recent work.

• Laser-cooled cryogenic pure ion plasmas have been a productive testbed for theories of plasma transport properties over the years. Recently they were employed to experimentally determine, for the first time, the Salpeter enhancement to nuclear reaction rates in plasmas for 0 < Γ< 20. (The rates of nuclear reactions are enhanced by a surrounding plasma that leads to the lowering many-body Coulomb barriers.) This enhancement is predicted to increase the rate of nuclear reactions in astrophysical plasmas by orders of magnitude for Γ >1, but has not until now been observed in experiments. The experiments supported the Salpeter theory while challenging competing dynamical screening theories.
• The dynamics of 2-dimensional (2D) inviscid incompressible fluids have been studied in non-neutral plasma experiments with Reynolds numbers as high as 10⁵. These experiments enabled precise control and characterization of nonequilibrium and even turbulent 2D flows. Recent studies have focused on vortices driven by external time-dependent shear flows, characterizing several novel effects including vortex stripping.
• Neoclassical transport in magnetized plasmas is a form of cross-magnetic field transport of particles, momentum, and energy that is enhanced by symmetry-breaking magnetic and electric field “errors.” Such errors are inherent in many plasma experiments. This transport can induce damaging losses of energetic particles in fusion devices. Non-neutral plasmas provide an excellent testbed for neoclassical transport studies since these plasmas can be confined without the turbulent fluctuations that mask the effect in conventional plasmas, and controlled symmetry-breaking fields can be applied. Recent theory and experimental work have led to breakthroughs in understanding neoclassical transport in fusion plasmas.
• Antihydrogen atoms created through the controlled mixing of cryogenic non-neutral antiproton and positron plasmas, have been trapped and studied. Directly measuring differences, if any, between matter and antimatter atoms may help us understand why the universe is made up almost entirely of matter when both matter and antimatter should have been produced in equal amounts in the Big Bang.
• Quantum simulation of spin models can provide insight into problems that are difficult to study with classical computers. Trapped ions have recently been shown to be a practical system for carrying out such simulations.

Experiments have studied the quantum spin dynamics in a 2D ion crystal consisting of several hundred ions in a Penning trap geometry. Good agreement with ab initio theory lays the groundwork for simulations of more complex interactions (e.g., transverse-field Ising models with variable-range interactions) that are generally intractable with classical methods.

Workforce Development

From the point of view of student education and workforce development, most non-neutral plasma experiments are table top or few-investigator devices compatible with university laboratories. As such they provide excellent training opportunities for experimental physicists by providing hands-on experiences. The overlap of non-neutral plasmas with atomic physics, condensed matter physics, astrophysics, and fluid dynamics makes this area attractive to both theory and experimental students with a range of interests and backgrounds. Undergraduates with minimal background in plasma physics can gain useful research experience.

Current and Future Science Challenges and Opportunities

Challenge 1: Understand and be able to predict plasma behavior under extreme conditions that challenge our present models.

Non-neutral plasmas can be cooled into the cryogenic regime of strong coupling, having Γ >> 1. Strong magnetic fields can be applied, such that the cyclotron radius of all species is smaller than even the distance of closest approach between particles. (This magnetization regime is difficult to achieve in “hot” neutral plasmas, requiring ultra-large magnetic fields exceeding 10⁹-10¹⁰ Gauss.) Being able to sustain non-neutral plasmas under these extreme conditions poses science challenges: (a) What are classical and quantum nonequilibrium transport coefficients in strongly coupled and strongly magnetized plasma (particle diffusion, thermal conduction, viscosity, collision rates)? (b) Progress in understanding the dynamics of defect formation and growth has been achieved in 1D plasma crystals confined in a linear Paul trap. (See Figure 2.12.) In this area bordering plasma and soft condensed matter physics, how do defects form and propagate in 2D and 3D plasma crystals?

Challenge 2: Quantify and, in the laboratory, control how plasma processes direct the conversion of energy from one form to another, the transfer of energy across a vast range of scales, and the transport of energy in the laboratory and nature.

The most fundamental energy and momentum transfer mechanisms in a magnetized plasma, collisional heat conduction and viscosity, are not fully understood.

Recent experimental and theoretical work in non-neutral plasmas has shown that classical cross-magnetic field thermal conductivity and shear viscosity applies only to plasmas for which the plasma frequency is large compared to the cyclotron frequency. For plasmas where this is not the case (i.e., plasmas in strong magnetic fields), the classical “Braginskii” coefficients (with transport coefficients to account for the effects of magnetic fields) may be incorrect by orders of magnitude. In fact, transport coefficients (thermal diffusivity and kinematic viscosity) are independent of magnetic field in this regime. The classical coefficients neglect transport induced by weakly damped waves carrying energy and momentum across the magnetic field. It has been predicted that such long-range wave-induced transport will dominate thermal conduction and viscosity in any quiescent plasma of sufficient size. Investigations of fundamental transport coefficients in non-neutral plasmas hold the promise of providing data required to develop theories of cross-magnetic field transport applicable to several problems in PSE.

Challenge 3: Predict self-organization of plasmas and, where needed, control that self-organization.

One of the phenomena most difficult to explain in nature is the appearance of order out of disorder. Turbulent hot plasmas are arguably one of the most disordered “high entropy” states of matter that can be achieved; and yet it is possible for ordered states to appear spontaneously in such systems. One way this can occur involves a “backward flow” (inverse cascade) of energy from fine scales in the turbulence to larger scales, through the merger of nearly 2D vortical structures into ever-larger size scales. One example is the appearance of “vortex crystals” from decaying 2D plasma turbulence, first documented in pure electron plasma experiments. (See Figure 2.13.) A similar inverse cascade is responsible for Earth’s jet stream and the H-mode that appears in fusion reactors, both of which are self-organized large-scale flows arising from a finer-scale incoherent turbulent background. Recently, vortex crystal states have been observed in the atmosphere of Jupiter, having formed spontaneously from the driven turbulence of Jupiter’s atmosphere. Advances in our understanding of inverse cascade produced self-organization from non-neutral

plasma experiments and theory will have wide applicability, from fusion plasmas to atmospheric dynamics for earth and planets.

Challenge 4: Control and predict the interactions between plasmas and solids, liquids and neutral gases.

Non-neutral plasmas are typically confined away from contact with liquids and solids. An exception to this rule is in the use of low-energy monoenergetic antimatter beams as a probe of solid materials, and for use in studies of the interaction of antimatter with individual neutral atoms. These studies rely on ongoing advances in positron plasma control and confinement. Non-neutral plasma-gas interactions are also of importance in a number of other contexts. For example, the collisional drag between the plasma and background neutral gas can limit the plasma confinement time, heat (or cool) the plasma and cause deleterious effects such as decoherence in quantum information studies. This particular process is for the most part well-understood. However, the chemical reactions that can occur between plasma charges and background gases are not well understood. These reactions, such as charge-exchange collisions and charged molecule formation and break-up, are of interest in a number of contexts including the reactions occurring in low temperature molecular clouds in interstellar space. Some of these reactions are predicted to have timescales of hours or days depending sensitively on the plasma temperature and density, and are therefore very difficult to measure by standard means. However, in a non-neutral plasma where the charges are confined for days or weeks, such measurements are possible. The appearance of new charged ion species could be measured in situ using the newly developed method of ion cyclotron thermal mass spectroscopy, or in some special cases by means of laser fluorescence diagnostics. This is another example of where fundamental studies of non-neutral plasmas have impact well beyond the laboratory and, in this case, to interstellar astronomy.

PLASMA INTERACTIONS WITH LIQUIDS, SOLIDS, AND GASES

Fundamental plasma research is often focused on the physics of waves and instabilities, which are properties of the bulk plasma far from boundaries. In fact, in these studies the edge effects produced by boundaries in laboratory plasmas are undesirable. However, laboratory plasmas are intrinsically bounded and the bounding interface can have a huge impact on the plasma properties. Although plasma boundary interactions may be undesirable in the context of studying bulk properties, plasma-boundary interactions are the basis of nearly all plasma materials processing, plasma based biomedical applications and plasma enhanced environmental stewardship. The fabrication processes used in the optics, solid-state

lighting and microelectronics industries are based on plasma-boundary interactions. The importance of solid interfaces in plasmas can even be extended to space plasmas where the presence of dust provides a plasma-solid interface.

The science challenges more closely aligned with technologies using plasmas are discussed in Chapter 5. From a fundamental perspective, why are plasma-interfacial interactions so important and why can they have a dominant impact on plasma behavior? Plasma-interfacial interactions can be highly complex due to the possible strong coupling between plasma properties and the interfacing material surface properties. This coupling can be due to different mechanisms depending on plasma and interface properties:

• Surfaces can act as electron sources upon ion or energetic species impact, surface heating or high interfacial electric fields induced by the plasma.
• Surface charging of dielectric interfaces can lead to enhanced or decreased electric fields near surfaces even leading to the possible extinction or generation of plasmas.
• Liquids have generally smaller energy barriers for species transfer at the interface and can therefore have a much more pronounced influence on the plasma state. Evaporation of the liquid phase induced by the plasma can dramatically change the gas composition near the plasma-liquid interface and so change plasma properties.
• The surfaces of liquids and soft matter can deform upon plasma exposure. These deformations can cause increasingly inhomogeneous electric fields and plasma self-organization.
• In reactive plasmas, the surface properties can be changed during plasma exposure leading to a continuous change in plasma-surface interactions.

The complex interaction of plasmas with solids and liquids leads to many interesting scientific questions including what happens to the structure and nonequilibrium properties of the plasma-solid/liquid interface during plasma exposure, and the transport mechanisms of charged and reactive species across the plasma-solid/liquid interface. The study of these interfacial processing involves in addition to plasma science solid state physics, material science, and chemistry, and is a highly interdisciplinary subfield of plasma science.

A significant part of the plasma physics community is concerned with studying collective phenomena in plasmas generated at very low pressure and in noble gases to reduce or even eliminate collisional effects. Nonetheless in many plasmas of interest, both atomic and molecular gases are present at significant densities or intentionally introduced. This leads to a rich spectrum of collisional processes and the generation of a multitude of species and chemical reactions. These studies have provided the foundation of many plasma-based applications and rely heavily on

atomic and molecular physics. As collisional effects strongly impact the distribution of electron energies, reactions directly impact the plasma dynamics and electron kinetics leading to new plasma phenomena. An example is the recently discovered ultrafast gas heating mechanism in atmospheric pressure air plasmas due to rapidly dissociating, electronically excited molecules. Many of these collisional interactions lead to new plasma phenomena enabled by the enhanced complexity of collisional plasmas.

Variations in gas composition and densities can also have a strong effect on plasma dynamics and properties. An example of the use of changes in gas composition to control plasma generation is the so-called cold atmospheric pressure plasma jet, shown in Figure 2.14.

Relevance and Benefits

Plasma-material interactions have relevance to a number of areas:

Magnetic fusion: In fusion reactors, about 20 percent of the energy produced cannot be captured to produce electricity and is instead exhausted in the form of heat and plasma particles in the divertor area. The huge particle and energy flux, due to the high power density in fusion plasmas leads to unique plasma-material interactions making it a key challenge on the path to the development of fusion for sustainable electrical power generation. Plasma-material interactions, which include interactions between plasmas with solids as well as liquid interfaces at boundaries, is a very important area of research, with significant implications for the performance of fusion reactors. (See Chapter 6.)

Plasma-material synthesis and processing: Many plasma interactions with solid surfaces have been exploited for societal benefiting applications ranging from semiconductor processing and synthesis of nanostructured materials with unique properties to arc welding and the development of plasma-based medical applications. Plasma-material interactions are utilized as a key enabling technology in the semiconductor industry, a top 10 industry in the United States, serving a roughly $2 trillion electronics market. (See Chapter 5.)

Dusty (space) plasmas: Dusty plasmas are the embodiment of plasma-surface interactions as the highly dispersed solid phase leads to an exceptionally large surface-to-volume ratio. A better understanding of dusty plasmas will contribute to our understanding of star-forming regions as well as comets and planetary rings. Dust particles are also believed to play a key role in molecule formation in space as studied in astrochemistry.

Plasma-liquid interaction: In addition to its importance in magnetic fusion reactors where liquid walls are being investigated, plasma-liquid interactions have a vast array of applications ranging from water treatment to wound healing and material and chemical synthesis. In the last decade an extreme type of multiphase plasmas has emerged, which can be seen as an equivalent of dusty plasmas, though with the dust replaced by liquid droplets or aerosols having sizes of a few microns to a millimeter. The “plasma-aerosol,” a dynamic suspension of liquid droplets dispersed in a gas, encompasses a wide range of scenarios that can involve single microscopic droplets up to full sprays and jets while the plasmas themselves vary from nonequilibrium low temperature to thermal plasmas. Plasma aerosols enhance the transfer of activation energy from plasma to the liquid thanks to the large surface-to-volume ratio and the production of species in close proximity of the

droplet surface. Demonstrated and potential benefits include on-demand delivery of designed micro/nanomaterials and delivery of short-lived species synthesis of high value chemicals, drugs and nanomaterials. Enhancing transfer of reactivity from plasma to aerosols will enable on-demand, point-of-use and energy efficient production and delivery of chemical activity for fertilizer production, sterilization and indoor agriculture.

Progress and Achievements

There has been impressive progress in understanding of the interaction of plasmas with gases, liquids and solids over the past decade.

• LTP research has increasingly extended plasma-surface interactions studies from solid materials to liquids and soft matter. While our understanding is still limited, major advances in modeling and diagnostics have been made. This has led, for example, to improved understanding of the role of solvated electrons and H radicals in plasma-liquid interactions and the role of plasma-produced species on plasma interactions with living matter. An example is the role of plasma-produced O₂(¹∆), a very long lived electronically excited state of the oxygen molecule, in the oxidation of capsid proteins of virus and the potential role of O₂(¹∆) selectivity of plasma-treatment of cancer.
• A detailed understanding of the influence of metal vapor in thermal plasmas, particularly in welding arcs, has been developed. Three-dimensional time-dependents models and spatially resolved time-dependent measurements have clarified the mechanisms driving metal vapor transport, and the influence of metal vapor on arc properties.
• The last 10 years have seen a move to more advanced control of power delivery and plasma kinetics leading to control of plasma-surface interactions at length scales of a single atom, an example being atomic layer etching. This process has been enabled by an increased knowledge of the underpinning plasma processes by a combination of modeling and diagnostics.
• The implementation of advanced diagnostics has enabled a broader understanding of the interaction of plasmas with polymers, including the role of UV photons and the effect of plasma-produced radicals on surface modification and etching.
• Boronization (or an equivalent, such as lithiumization), is the plasma deposition of a thin boron (or lithium) containing film on the inner walls of the fusion reactor chamber through the injection of boron into the plasma. Boronization has been used successfully in tokamaks for many years as a means of controlling impurities, oxygen in particular. However, the

• boronization process is poorly understood and undoubtedly less than optimal. Lithium micro-granule injection, often dubbed powder or aerosol injection, has been successfully investigated in fusion research demonstrating improvements in terms of wall conditioning and opening access to high performance scenarios.

• Multiple existing experiments are studying tungsten for first walls for fusion reactors in preparation for its use in ITER. However, the occurrence of melting in these experiments has been greater than expected. The extrapolation of tungsten erosion estimates to DEMO (the follow-on fusion reactor to ITER) indicate unacceptably short lifetimes for the plasma facing components. Concerns such as these have served to increase interest in the use of liquids as plasma facing materials. A flowing liquid surface would be melted by design and erosion and redeposition would have no long-term effects. However, how liquid films survive real fusion machine environments is still unclear and a subject of much debate.

Current and Future Science Challenges and Opportunities

In view of the huge potential benefits of the interaction of plasmas with liquids and solids summarized above, research is supported by a broad set of programs and divisions within NSF, DOE, and DoD that support materials or plasma research. While these diverse funding sources are in some respects a strength of the field, it has unfortunately led to a silo effect between studies focusing on plasma physics and on synthesis/material processing from a materials perspective. A key challenge in the next decade is to bring together experts in plasma science, materials research and chemistry to tackle the major science challenges highlighted below. This will require coordinated initiatives between materials-focused and plasma-focused programs in federal agencies enabling advances in the science and technology of both fields, as recommended in Chapter 5.

Challenge 1: Understand and be able to predict plasma behavior under extreme conditions that challenge our present models.

Materials for plasma-facing components are often exposed to enormous fluxes of energetic particles and energy corresponding to extreme conditions that are far from the conditions under which material properties have been studied. Similarly, extreme nonequilibrium plasma conditions can be achieved at the interface between LTPs and solids/liquids due to huge fluxes of energetic species at near room temperature. Our current understanding of these unique conditions is extremely limited and requires the development of detailed in situ diagnostics complemented with modeling efforts if our understanding is to improve.

Major efforts have also been devoted to study plasma generation in liquids requiring much higher electric fields than in their respective gases/vapors due to the significantly higher density of liquids. Recently, mechanisms have been formulated to explain plasma generation in liquid water without the need for bubble generation, complemented with experimental work reporting plasma produced pressures up to 1 GPa. This research is closely tied to many unresolved questions of the change in structure and properties of liquids under extreme conditions (such as high electric fields, pressure and temperature) and its ability to create extreme plasma conditions.

Another example of such a new scientific frontier are atmospheric pressure microplasmas that can lead to relatively high power density LTPs having microscopic dimensions. In some cases, LTP plasma densities can approach values typical of fusion plasmas (10¹⁴-10¹⁷ cm^-3). While the electron temperature is of the order of a few electronvolts, the large surface to volume ratio leads to significant losses. This combination results in relatively low neutral gas and ion temperatures of about 0.1 eV. The interfacial region between the bulk plasma and the solid surface consists of a plasma sheath with dimensions ranging from a micron to tens of microns in which an intense electric field induces Fermi level shifts near the solid interface. These conditions can result in field emission of electrons and field ionization in some cases. The interaction of relatively dense and cold plasma with solid-state materials is a largely unexplored topic. The coupling between plasmas and surface increases for higher-pressure plasmas, and challenges remain in resolving the huge spatial gradients in species densities near interfaces.

Challenge 2: Quantify and, in the laboratory control, how plasma processes direct the conversion of energy from one form to another, the transfer of energy across a vast range of scales, and the transport of energy in the laboratory and nature.

The key distinctive feature of LTPs is that energy coupling mainly proceeds through electrons in the bulk plasma and possibly ions in the sheath regions adjacent to surfaces. This leads to highly nonequilibrium plasma kinetics. The kinetic energy of electrons is transferred to atoms and molecules by collisional processes between electrons and neutral gas atoms and molecules. These collisions can lead to the generation of tens to hundreds of possible species depending on the gas mixture and electron energy distribution (EED). The control of ion energies striking surfaces is a dominant need in customizing plasmas for materials processing. The fundamental LTP challenge involves controlling the energy distribution of electrons to channel the energy deposition into the production of ions, excited, radical and reactive species that drive the desired processes in the gas phase or at interfaces. Similarly, controlling the distribution of ion fluxes to surfaces enables control of surface processes having energy thresholds.

The ultimate LTP challenge is achieving predictive control of the plasma initiated chemical processes. This is particularly complex due to the sensitive two-way coupling between the EED and the gas composition, including the species produced through collision processes. Many plasma kinetics and chemistry models have been developed but a thorough experimental validation of models is the exception due to the large complexity of the composition of the plasma. Understanding complex molecular plasmas requires the development of validated predictive capabilities which in turn requires a large team and long-term efforts. This challenge includes developing highly controlled and accurate benchmark experiments. While recognizing the increased complexity due to the nonequilibrium nature of LTP, the community could highly benefit from establishing validated reaction sets complemented with benchmark experimental studies similar to GRI-mech used in the combustion community. This effort should be coupled to transport models and plasma-surface interaction models.

Challenge 3: Predict self-organization of plasmas and, where needed, control that self-organization.

As in many physical, chemical, and biological systems, self-organization is a common phenomenon at the interface between a plasma and a solid or liquid. While some aspects of the phenomena for specific cases are understand, currently the mechanisms responsible for self-organization in plasmas interacting with surfaces are not well understood. There is a need for the development of an overarching model explaining the large variety of often very similar self-organizing phenomena occurring over a broad range of pressures and power densities. Typically, self-organization occurs in the anode or cathode layer at the interface between a plasma and a resistive or dielectric medium, which could be a liquid. (See Figure 2.15.) When ionization fronts impinge on a dielectric surface the discharge tends to branch and develop surface ionization waves that can have self-organized patterns. There is a need to develop more comprehensive plasma models with detailed kinetics capable of predicting the occurrence of and transitions between these patterns. Detailed spatially resolved measurements other than fast imaging for model validation are also lacking. Similarly, while 3D simulations of ionization waves and streamers have been performed in the gas phase (see Chapter 5), surface ionization waves have only been very recently modeled and the intrinsic 3D phenomena of self-organization phenomena in surface ionization waves have not been addressed.

Challenge 4: Control and predict the interactions between plasmas and solids, liquids, and neutral gases.

While in situ diagnostics for surface characterization during plasma exposure are emerging, a majority of material characterization to date is based on ex situ diagnostics where the material is analyzed after plasma exposure. The lack of in situ

diagnostics adds an additional layer of complexity in the analysis and interpretation of the actual plasma-material processes. There is a strong need for the development of in situ diagnostics amenable to a harsh and complex plasma environment. This is absolutely critical as there is a lack of understanding of the basic processes underpinning many plasma-material interactions and there remains a need for model validation.

Significant progress has been made in plasma-surface interaction modeling. (See Figure 2.16.) However, comprehensive models with a two-way coupling of nonequilibrium kinetics in plasmas intersecting with interfaces address only specialized systems. The physical processes at the interface of a plasma and a solid or liquid are extremely complex, involving a large number of elementary processes in the plasma and in the solid as well as fluxes of energetic species across the interface. An accurate and unified theoretical treatment of these processes is very difficult due to the vastly different system properties on both sides of the interface: quantum versus classical behavior of electrons in the solid and plasma, respectively; as well as dramatically differing electron densities and length and time scales. Liquids provide additional challenges over solids as they can have a much more pronounced influence on the plasma state.

In many models of bounded plasmas, the surface processes are either neglected or treated using phenomenological parameters such as sticking coefficients, or sputtering rates and secondary electron emission coefficients given by simple theories. These parameters are known from measurements or fundamental, materials specific theories or computations only in specialized cases and with limited accuracy. Similarly, surface physics simulations are usually not linked self-consistently to the

plasma. As a result, the collective influence of the plasma and correlations with surface processes are usually not accounted for. Such an approach does not account for the mutual influences between plasma and solid surface, and so do not have broadly applicable predictive capabilities. Integrated modeling of the entire plasma-solid/liquid interface is needed and is a major challenge for the plasma community.

FINDINGS AND RECOMMENDATIONS

The science challenges in basic plasma physics are immense and the opportunities to translate advances in fundamental plasma science to develop applications are strategic. Addressing these challenges and leveraging these opportunities requires the availability of a dynamic theory-based workforce. As endorsed in this report, computational PSE is critical to the future of the field. As a necessary complement to the effort in computational PSE, there is a need for supporting fundamental theory and developing a workforce of the future that is schooled and expert in theory.

Finding: The theoretical PSE workforce is not large enough to meet our current needs and will become even less able to do so in the future without deliberate measures.

Recommendation: In developing their research agenda, federal agencies supporting plasma science (e.g., NSF, DOE, DoD, NASA) should make deliberate efforts to support theory.

Finding: Investigations of fundamental plasma science provide the understanding of these complex processes that underpin the behavior of plasmas across the entire realm of PSE. Studies of fundamental processes tie together seemingly disparate phenomena across the PSE discipline and provide a unifying perspective to the vast array of PSE applications.

However, basic plasma science investigations are often perceived as being separate from application-inspired research and are often funded separately. As a result, it is increasingly difficult for fundamental studies and applications to leverage each other’s efforts.

Finding: A widening gap between fundamental studies and application-inspired research impedes progress in both fundamental studies and application-inspired research and slows the rate of translational research that leads to societal benefiting technologies.

Recommendation: Federal agencies that fund plasma science and engineering should forge partnerships with other plasma-focused agencies as well as agencies focused on applications benefiting from plasmas (or programs within agencies) to close the widening gap between fundamental plasmas science research and translational research leading to applications.

This recommendation extends to partnerships between programs within a single agency (e.g., FES and BES within the DOE Office of Science). The committee specifically draws attention to the numerous examples of such partnerships listed in Table 1.1 in Chapter 1 for possible adoption of some of these potentially cutting-edge partnership projects.

Finding: There has been a general loss of broad collaborative activities within the PSE community over the last decade.

Finding: In both experimental and theoretical/computational areas, the creation of teams with the critical mass to address important and complex issues in basic plasma science are needed.

Finding: Center-type activities can provide opportunities that strengthen the overall health of the PSE community while providing important incubators for the development of the PSE workforce.

Recommendation: DOE should broaden its support of Plasma Science Centers through recurring solicitations at critical funding levels to provide both new opportunities to advance important areas of plasma science as well as to improve the impact of the plasma science community.

Partnerships with other federal agencies are encouraged, and the committee refers to Table 1.1 in Chapter 1.

Finding: While many of the basic plasma science facilities are aging, the last decade has seen important investments in several new or expanded facilities in the range of $1 million to $4 million.

Finding: Many U.S. plasma science facilities were built during the last decade with funding provided by the NSF Major Research Instrumentation program, and many of these facilities provide opportunities for external researchers to conduct collaborative experiments with the host institutions. However, the experimental facility needs of different communities that are pursuing basic plasma science can vary widely.

For example, there are important collaborative, multi-PI research activities that may require significantly larger facilities. The recent Report of a Workshop on Opportunities, Challenges, and Best Practices for Basic Plasma Science User Facilities (2019)³ makes strategic recommendations on the types of facilities that are considered important enough to a broader science community to justify significant investment of resources.

Finding: Today, facilities at a spectrum of scales and reflecting the requirements for addressing different problems at the frontiers of plasma science (in the range $1 million to $20 million) are needed.

Recommendation: NSF, DOE, NASA, and other federal agencies with an interest and programs in plasma physics should provide regular opportunities for the continued development, upgrading, and operations of experimental facilities for basic plasma science at a spectrum of scales.

There are several existing and planned laboratory user facilities that are able to address the challenges in basic plasma science described here. Currently, the primary mechanism for obtaining support for users of these facilities is through the NSF/DOE Partnership in Basic Plasma Science and Engineering (PBPSE).

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³ 3 Report of a Workshop on Opportunities, Challenges, and Best Practices for Basic Plasma Science User Facilities,” 2019, https://arxiv.org/abs/1910.09084.

While many users have been successful in obtaining this support (typically 3-year grants), there are some projects that do not require a full 3 years of funding to be executed (e.g., performing a one-time experiment to validate a model or theory).

Finding: Many potential users of these experimental facilities would benefit from small levels of support to gain experience with and obtain initial data for proof-of-concept demonstrations that are usually expected in a full proposal to PBPSE. A mechanism to provide one time-short term funding to perform these experiments would address this critical need.

Existing funding models that might be used are the National Laser User’s Facility (NLUF) program at the Laboratory for Laser Energetics at the University of Rochester and the Matter at Extreme Conditions (MEC) facility at the SLAC National Accelerator Laboratory. Coordination across existing user facilities would be beneficial in implementing this funding mechanism; a model that might be followed is that used by LaserNETUS.

Finding: In addition to a shared funding resource for user support, a network of basic plasma science facilities might also coordinate on proposal selection, users groups, and outreach activities, thereby addressing the STEM pipeline into plasma science.

Finding: A network of basic plasma user facilities that would provide opportunities for access to new and upgraded plasma science facilities needs more coordination and support than currently exists.

Recommendation: Federal agencies, particularly DOE-FES and NSF-MPS, should implement a program for one-time, short-term funding for users of basic plasma science facilities.

Recommendation: A community-wide workshop led by a partnership of DOE-FES and NSF-MPS should define the parameters and participation of such a program and network of user facilities.

For the most part, computation remains the province of experts. Most noncommercial simulation codes are primarily used by their developers and a small cohort that can be supported by direct access to the developers.

Finding: Plasma simulation is not optimally accessible to the wide range of potential users, including experimentalists and industrial users.

As more sophisticated hardware becomes available in the exascale era, codes that were developed using older technologies face an increasing technology gap and need to be ported to new architectures.

Finding: Funding agencies have not traditionally supported code usability to the extent needed to make research codes user-friendly, support users of codes, or to transition existing codes to new computing architectures.

Recommendation: Funding agencies, and in particular DOE and NSF, should support mechanisms for making computational plasma software more widely accessible to noncomputing experts, and to transition current codes to new computing architectures.

For example, these agencies should examine the role for public-private partnerships that could make easily used software available on agency computers. In this regard, to make the broadest impact, open source software being sponsored by NSF and DOE should be accessible to the nonexperts and useable on a broad range of computing architectures.

Finding: At the time of this writing, opportunities for machine learning (ML) and artificial intelligence (AI) that impact computations (and experiments) are only beginning to be realized. This is an extremely rapidly developing field. Leveraging these advances may require new approaches to computation.

Recommendation: To assure that plasma science and engineering computations take advantage of advances in machine learning and artificial intelligence, a periodic workshop should be held to share best practices, jointly sponsored by NSF, DOE, and NASA.

Finding: There is a lack of modern educational and review material in computational PSE that addresses the methods of computation and how to make effective use of computations.

The preceding finding is becoming an even greater need as more of computational plasma physics transitions to a situation where fewer but more widely accessible codes exist, each with many users who are not necessarily the developers.

Finding: With the rapid growth of interdisciplinary research in plasma physics, it is time to consider the establishment of an annual journal that reviews major developments in all areas of plasma physics, much like the Annual Reviews of Astronomy, for example.

Recommendation: Computational plasma science and engineering, supported by NSF, should include projects for writing textbooks and developing courses to train the current and next generation of computational plasma scientists, and to enable noncomputer experts to make optimal use of computations.