9
Theoretical and Computational Plasma Physics

INTRODUCTION AND BACKGROUND

Plasma physics is the study of collective processes in many-body charged-particle systems. Like the fields of condensed matter physics and molecular biology, plasma physics is founded on well-known principles at the microscopic level. In the case of plasma physics, the description is based on the Liouville equation or kinetic equations for the electron and ion distribution functions in a multidimensional phase space and Maxwell's equations, whose sources are self-consistent moments of the distribution functions. The plasma state is distinguished by the existence of a vast number of collective motions over a very wide range of spatial and temporal scales. The interaction of these collective motions often leads to turbulence or coherent patterns and structures. Indeed, coherent patterns frequently may coexist with turbulence. A priori theoretical prediction of plasma behavior has enjoyed only limited success. Therefore, experiments are critical to the identification of fundamental processes in a plasma, such as the evolution of coherent structures arising from nonlinear interactions. These, in turn, form the intellectual building blocks for understanding the evolution of yet more complex processes.

The history of plasma science is as diverse as the subject itself. In Chapter 8 above, early work in laboratory plasma science is described, beginning with the work of Faraday in the 1830s on the chemical transformation of the elements and continuing with Langmuir's work on gas discharges in the 1920s and research on electron beams and beam-type microwave devices in the 1940s and 1950s. Within a decade of Langmuir's work, the discovery that radio waves reflect from



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Plasma Science: From Fundamental Research to Technological Applications 9 Theoretical and Computational Plasma Physics INTRODUCTION AND BACKGROUND Plasma physics is the study of collective processes in many-body charged-particle systems. Like the fields of condensed matter physics and molecular biology, plasma physics is founded on well-known principles at the microscopic level. In the case of plasma physics, the description is based on the Liouville equation or kinetic equations for the electron and ion distribution functions in a multidimensional phase space and Maxwell's equations, whose sources are self-consistent moments of the distribution functions. The plasma state is distinguished by the existence of a vast number of collective motions over a very wide range of spatial and temporal scales. The interaction of these collective motions often leads to turbulence or coherent patterns and structures. Indeed, coherent patterns frequently may coexist with turbulence. A priori theoretical prediction of plasma behavior has enjoyed only limited success. Therefore, experiments are critical to the identification of fundamental processes in a plasma, such as the evolution of coherent structures arising from nonlinear interactions. These, in turn, form the intellectual building blocks for understanding the evolution of yet more complex processes. The history of plasma science is as diverse as the subject itself. In Chapter 8 above, early work in laboratory plasma science is described, beginning with the work of Faraday in the 1830s on the chemical transformation of the elements and continuing with Langmuir's work on gas discharges in the 1920s and research on electron beams and beam-type microwave devices in the 1940s and 1950s. Within a decade of Langmuir's work, the discovery that radio waves reflect from

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Plasma Science: From Fundamental Research to Technological Applications the ionosphere established the existence of the space plasma that surrounds the Earth. A new era in plasma physics began with the international development of efforts to achieve controlled thermonuclear fusion in the 1950s and with the space program, which began with the launching of Sputnik in 1957. For the past 30 years, space, fusion, and the development of advanced weapons systems have been the main drivers for plasma science. Early in the space and fusion programs, a rich variety of fundamental configurations and phenomena were investigated, but as a rule, nonlinear processes—although fascinating scientifically—proved to be a detriment to the achievement of fusion plasma conditions in the laboratory. As a consequence, fusion research evolved to focus on systems with the least complexity consistent with programmatic goals. Inertial fusion research evolved in directions that either minimized nonlinear laser-plasma interactions or optimized particle-beam drivers. Magnetic fusion research concentrated on the tokamak approach, the most stable axisymmetric confinement configuration. The principal difficulty encountered in fusion and in defense applications has been the inability to predict the nonlinear behavior of plasmas to an accuracy required by engineering considerations. A successful example of such a prediction is illustrated in Figure 9.1. In the exploration of space plasmas, it was not possible to reduce the natural complexity of the magnetic field geometry through engineering design. Spacecraft data have identified many key nonlinear phenomena: collisionless shocks, bursty and steady magnetic reconnection, double layers, current sheets, dynamo generation of magnetic fields, and the overall structure of magnetospheric plasmas, which are high-mirror-ratio magnetic confinement configurations. Up until now, because spacecraft obtain local data, only the rudimentary aspects of these processes have been measured. While the discoveries of plasma phenomena in the space environment are remarkably varied, their abstractions into basic plasma processes subject to investigation by computational simulation, laboratory experiments, and analytical theory have lagged because support, especially for laboratory experimentation, has ''practically vanished" in the words of the Brinkman report, Physics Through the 1990s.1 Notable exceptions exist, of course, and these are presented later in this chapter. The next decade could promise a fundamental reversal of this paradigm, provided the resources for basic plasma experimentation described in Chapter 8 become available. One can anticipate that plasma phenomena discovered through spacecraft and astronomical observations, as well as fusion research, will play an important role in motivating laboratory experimentation. Moreover, the theo- 1   National Research Council, Plasmas and Fluids, in the series Physics Through the 1990s, National Academy Press, Washington, D.C., 1986.

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Plasma Science: From Fundamental Research to Technological Applications FIGURE 9.1 Theoretical model of the "fishbone" oscillations observed in tokamak plasmas. This figure shows that the high-frequency modulation of the magnetic field occurs in bursts (lower trace); it also shows the induced loss of high-energy particles during each burst, by the decrease in the normalized pressure of the energetic particles, βh. (Reprinted, by permission, from L. Chen, R.B. White, and M.N. Rosenbluth, Physical Review Letters 52:1122, 1984. Copyright © 1984 by the American Physical Society.)

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Plasma Science: From Fundamental Research to Technological Applications retical and simulation capabilities developed to understand this new generation of small- to intermediate-scale laboratory experiments will set standards for modeling space and astrophysical plasmas. Technological advances promise to create fundamentally new classes of plasma experiments and to enable new diagnostics. For example, as discussed in Chapter 8, our conceptual understanding of plasma dynamics will be enriched by visualization techniques only now becoming available for plasmas. RECENT ADVANCES IN THEORETICAL AND COMPUTATIONAL PLASMA PHYSICS Fusion, space exploration, and defense applications have been the engines of high national priority that have powered fundamental advances in plasma theory and computational plasma physics. In turn, the improved understanding of basic plasma processes has led to the seminal development of important new concepts and applications. Without attempting a complete delineation of significant achievements, in this section the panel highlights selected advances in analytical and computational plasma physics during the past decade that have resulted from the interaction of plasma theory with laboratory experiments and, to some extent, with space and astrophysical plasma measurements, because similar physics manifests itself in plasma systems of vastly different physical scales. At present, laboratory experimentation is dominated by research on magnetic and inertial fusion. Smaller experimental efforts can be found in active space experiments, nonneutral plasmas, coherent radiation generation, advanced accelerator concepts, and turbulent Q-machine plasmas. Additional advances in plasma theory and computations are incorporated in the chapters of Part II covering specific plasma topics. Hamiltonian Transport Apparently dissipative processes, such as particle diffusion, can occur in conservative Hamiltonian systems whenever chaos is present. In the 1980s, advances in understanding such transport were driven largely by anomalies observed in hot, effectively collisionless, magnetically confined plasmas, in which both the particle orbits and the magnetic field line trajectories obey Hamiltonian equations. A plausible contribution to anomalous loss is the effective diffusion induced by such chaotic behavior. Recent numerical and analytical studies have shown that Hamiltonian transport rates can depend sensitively on such unexpected structures as turnstiles, devil's staircases, and stochastic webs. Moreover, the ideas have been applied to estimating the loss of energetic charged particles from magnetically confined systems, reducing the necessity for elaborate and expensive numerical calculations based on guiding-center theory.

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Plasma Science: From Fundamental Research to Technological Applications Coherent Structures and Self-Organization The theoretical discovery of solitons, long-lived coherent solutions to certain nonlinear fluid equations, arose out of plasma physics research in the 1950s. In recent years, a more general class of nonlinear structures, including both solitons and less permanent, but still robust objects (solitary waves), has been found to play a significant role in plasma evolution. Thus, large-scale turbulence is often dominated by vortical structures, analogous to fluid vortices, but depending on the interaction of the plasma with electromagnetic fields. At smaller scales, such phase-space structures as clumps or holes can critically affect plasma dissipation. The past 10 years have seen significant progress in classifying, explaining, and assessing the importance of such phenomena. Their importance in laboratory plasma confinement, nonneutral plasmas, magnetosphere evolution, and solar physics is now firmly established, although much of the difficult nonlinear physics remains to be understood. Strong Plasma Turbulence The past decade has contributed to a greater, although still incomplete, understanding of plasma turbulence. Strong turbulence theory has been applied to many microinstabilities (drift waves and ion temperature gradient, trapped-particle, microtearing, and magnetic modes in tokamak plasmas). Resonance broadening has been addressed, and the direct interaction approximation (DIA), although still heuristic and difficult to implement numerically, has been extended to provide a general form that can be used for simpler transport models. Some understanding has been developed of turbulent cascades in plasmas, of nonlinear transport mechanisms, and of the coupling of heat and particle transport. Numerical studies of solar convection have greatly improved our understanding of turbulence in stars. Gyrokinetics During the past decade there has been a refinement of gyrokinetics, the approximate theory of the motion of charged particles in strong magnetic fields, with applications to stability theory and magnetohydrodynamics. Of particular note is the successful application of this description to the numerical simulation of a class of slow instabilities, the ion temperature gradient mode, resulting in mode spectra in excellent agreement with tokamak experiments. Also, a hybrid magnetohydrodynamic-gyrokinetic code has successfully simulated both fishbone and toroidal Alfvén eigenmodes, although greater computing power is needed to definitively study the latter.

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Plasma Science: From Fundamental Research to Technological Applications Large-Orbit Effects on Plasma Stability The influence of large-orbit particles in a plasma on low-frequency stability was computed by the Vlasov formalism in the form of a modified energy principle. The observed stability of field-reversed configurations has been attributed to this effect. A formal theory of interaction of a dilute species of energetic particles (described by the Vlasov equation) with magnetohydrodynamic Alfvén waves (described by fluid equations) has been developed and applied, with quantitative success, to tokamak plasmas and to the magnetosphere. The complex geometry of tokamaks, which is periodic the short-way-around the doughnut, altered the Alfvén wave propagation and attenuation bands as periodic media generally do. Almost-undamped Alfvén wave modes emerged that could be destabilized by energetic particles with velocities comparable to the Alfvén speed. This development forms the basis on which to expect challenging physics when thermonuclear reactions take place in magnetically confined plasmas. Three-Dimensional Magnetohydrodynamics Three-dimensional resistive magnetohydrodynamic simulations have successfully modeled turbulent generation of toroidal flux in force-free reversed-field pinch experiments. Three-dimensional resistive magnetohydrodynamics further gives a good account of magnetic reconnection in tokamaks and associated magnetic oscillations, including spontaneous formation of singular current sheets. However, a few troubling enigmas remain to be explored. Numerical Simulation of Plasma Processes The numerical study of plasmas has advanced markedly during the past decade, with applications to the ionosphere, the magnetosphere, solar flares, solar pulsations, stellar convection, nonlinear magnetohydrodynamics, gyrokinetics, and so on. (See Plate 8.) The progress has been due to a combination of improvements in algorithms and the advent of cheaper more powerful computers, both supercomputers and workstations, that provide great power, rapid turnaround, and networking at very modest cost. The computational discovery of nonlinear coherences that compensate for linear damping of microinstability modes in tokamaks calls into question the use of quasilinear correlation functions to estimate transport consequences of microinstabilities in tokamaks. Nonlinear Laser-Plasma Interaction Virtually all of the many instabilities driven by intense electromagnetic waves interacting with plasma were identified theoretically and studied in laser-plasma experiments during the past decade. Key nonlinear signatures predicted

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Plasma Science: From Fundamental Research to Technological Applications by numerical simulations and theory, such as the production of very energetic electrons, were confirmed. Various control techniques were also demonstrated, including collisional suppression and laser beam incoherence. Progress in this area had a major impact on research in inertial fusion, leading to the use of shorter-wavelength lasers. Nonlinear Processes in Ionospheric Plasmas The interaction of high-power radio-frequency waves with plasmas, in particular the ionosphere, has stimulated the theoretical development of a coupled ion acoustic-Langmuir wave turbulence model, generically known as the Zakharov equations. Computational studies of this model have identified spontaneous creation of cavitons—small-scale density structures that self-consistently trap Langmuir waves. Recently, fluid representations of collisionless damping have become available that will further increase the sophistication of the Zakharov approach. Barium cloud releases in the ionosphere stimulated development of a new form of two-dimensional turbulence with key differences from two-dimensional hydrodynamic turbulence. Simulations based on these equations exhibited striking similarities to experimental releases. The equations were further applied to naturally occurring striations in the equatorial F-region and again enjoyed quantitative successes, especially with regard to the spectrum of turbulence. The cross-magnetic-field current of the equatorial electrojet drives E × B turbulence in the equatorial region of the ionosphere. The nature of this low-frequency turbulence has been studied by radar backscatter diagnostics and in situ rocket campaigns. The plasma is weakly ionized so that the basic equations are well formulated and robust. The cascade theory of turbulent eddies, in the direct interaction approximation, predicts the nature of the nonlinear interactions and the line-width of the frequency spectrum, and is in accord with observations and numerical computations. Collisional Relaxation of Nonneutral Plasmas The consequences of binary collisions in nonneutral plasmas have been predicted to depend dramatically on magnetic field strength. In particular, when the duration of a collision, based on the distance of closest approach, exceeds the cyclotron period, the magnetic moment becomes an adiabatic invariant and the relaxation of perpendicular velocities becomes exponentially small. Quantitative experimental confirmation of an exponentially small equipartition rate between parallel and perpendicular temperatures has been demonstrated.

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Plasma Science: From Fundamental Research to Technological Applications Free-electron Lasers and High-Power Microwave Sources Significant progress has been made in the fundamental nonlinear theory of high-power, coherent radiation generation in free-electron devices such as gyrotrons and free-electron lasers, particularly in areas related to nonlinear saturation mechanisms and efficiency optimization, mode selection and phase stability, and the effects of stochastic particle orbits. This has led to a new generation of laboratory microwave sources that have applications ranging from heating and noninductive current drive in fusion plasmas to communications and radar. RESEARCH OPPORTUNITIES This section identifies future research opportunities of fundamental importance in theoretical and computational plasma physics, including basic plasma theory and applications to laboratory plasmas, and space and astrophysical plasmas. Additional research opportunities in plasma theory and computations are incorporated in other chapters of this report. Basic Plasma Theory and Applications to Laboratory Plasmas The creative interplay between theoretical and computational studies and laboratory experimentation has been the classic engine that advances scientific understanding. In recent years, computations have begun to serve partially the role of experiments, with "simulation experiments" revealing unanticipated structures and coherences. The panel's vision of research frontiers in plasma physics during the next decade presumes that a program in basic laboratory experimentation will come into being, so that the range of topics investigated will be appreciably broader than those topics tied almost exclusively to fusion physics and defense applications. Of course, this will serve to extend and test current theoretical capabilities and to present qualitatively new challenges. Hence, the synergism among basic plasma theory, laboratory experiments, and space and astro-physical plasma observations promises to play an appreciably stronger role during the next decade. Continuing progress is expected to be made in all of the areas identified earlier in the preceding section, "Recent Advances." In addition, the following topics, surely not comprehensive or mutually exclusive, represent research opportunities of high intellectual challenge in basic plasma theory and applications to laboratory plasmas. Nonlinear Plasma Processes Much of the progress in plasma physics during the past has been made by linear (small-signal) theory, which has provided conceptual and in many cases

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Plasma Science: From Fundamental Research to Technological Applications quantitative understanding. But nonlinear theory is of great intrinsic interest and is essential for the description of most important applications of plasma physics that involve magnetohydrodynamics, kinetic theory, turbulence, the interaction of charged particles with intense electromagnetic fields, and so on. Therefore, increased attention should be given to nonlinear theory aimed at the development of new analytical and numerical tools. Numerical Simulation A most promising area for the future is that of numerical simulation, driven by continuing dramatic advances in computational speed and computer organization, and decreases in the cost of hardware. These ongoing improvements in hardware, coupled with the parallel design of new and more efficient algorithms, should allow the solution of many of the nonlinear problems that currently defy direct analytical solution. Numerical computation offers the best hope of dealing meaningfully with the large problems in complex geometries that characterize so many of the significant applications of plasma physics. One anticipates the development of teams of computational specialists, theorists, experimentalists, and engineers, organized to optimize the solution of particular large technical problems. Training of students for this type of operation should be encouraged in universities. Novel Analytical Techniques The challenge of nonlinear theory suggests the adaptation or innovation of novel analytical techniques. The use of percolation theory for certain transport problems in plasmas appears to be promising. The development of modern statistical analyses, perhaps employing artificial intelligence (symbolic dynamics), may lead to greatly improved data analysis and new physical insights. The transfer from pure mathematics of well-developed areas such as wavelet theory, which are relatively unknown in physics and engineering, offers great promise. Boundary Layers Boundary layers are of great importance in plasmas. These occur in such diverse applications as the sheath region near the first wall of a fusion reactor, the region in a coronal hole where the solar wind is emitted as the system changes from collision-dominated to collision-free, and magnetic reconnection in plasmas of interest in space. They are often distinguished by the need for a full kinetic theory, and they will require a synthesis of analytical boundary layer techniques and advanced numerical methods.

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Plasma Science: From Fundamental Research to Technological Applications Kinetic Theory In the past, much theoretical work has been done employing fluid theories in circumstances where they are strictly not valid, because fluid descriptions are more tractable than kinetic ones. Such treatments are commonplace in astrophysics, space plasma physics, and long mean-free-path fusion physics. Advances driven by novel analytical approaches coupled with advances in computation are highly likely. The systematic exploitation of dimensionless small parameters to obtain reduced kinetic descriptions is one promising approach. Stochastic Effects in Evolving Plasmas In plasma physics, the conceptual advances of nonlinear dynamics and stochasticity theory have been applied to abstracted, simplified problems, capable of formulation in terms of Hamiltonian dynamics. Examples include criteria for stochastic magnetic field line "orbits" in tokamak and stellarator devices, nonlinear wave-particle interactions, and particle orbits near magnetic field nulls in the magnetosphere. During the next decade a key challenge for theoreticians will be to incorporate stochasticity self-consistently into evolving plasma systems. Magnetospheric magnetic reconnection serves as a useful example. How will stochastic orbits alter the evolution of magnetic fields and field nulls when the extent of the stochastic regions must be self-consistently determined in terms of the evolving field? Diagnostic and data processing advances that can identify stochasticity in plasma systems must be developed concurrently. Alpha-Particle Effects in Magnetically Confined Plasmas The level of sophistication of theoretical models and instrumentation techniques, and the high quality of plasma conditions achieved in laboratory experiments have progressed to the point that the deuterium-tritium experiments planned on the Tokamak Fusion Test Reactor (TFTR) and the Joint European Torus (JET) are expected to elucidate important physics issues regarding the influence of alpha particles on plasma stability and transport processes. There are two major phenomena associated with the appearance of significant densities of alpha particles in fusion devices. First, coherent plasma oscillations can be excited by resonant interaction with the alpha particles, either at low frequencies, corresponding to the toroidal precession rate, or at high frequencies, corresponding to the direct interaction of alpha particles with shear Alfvén waves. Such collective oscillations are driven unstable by the alpha-particle pressure gradient and result in the rapid expulsion of a significant number of high-energy particles. Several such modes have already been predicted theoretically and identified on existing devices, where they are excited by high-energy particles produced by injected beams or ion cyclotron heating. Second, high-energy particle orbits are

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Plasma Science: From Fundamental Research to Technological Applications modified by the presence of toroidal field ripple, and if sufficiently large, ripple can cause the orbits of trapped particles to become stochastic and to be lost from the plasma in a time that is short compared to the slowing-down time. Concept Improvement As the tokamak confinement approach continues to make significant technical progress toward achieving the conditions required for fusion power production, it is increasingly important to improve the tokamak concept, particularly in the long-pulse and steady-state regimes that can lead to compact designs for economical power production. This will require a significant theoretical and experimental effort in the study of advanced-tokamak regimes that optimize the bootstrap-current fraction produced by the collisional equilibration between trapped and passing particles, improve the efficiency of noninductive current drive, optimize the current profile and plasma shapes, and explore regimes of enhanced confinement and increased plasma beta. To ensure fully equilibrium (i.e., "steady-state") conditions, these plasma regimes must be studied for pulse lengths longer than the characteristic time scales of plasma processes and plasma-wall interactions. This will require steady-state power handling, particle exhaust, and impurity control by divertors at high power fluxes, as well as the development of advanced plasma fueling, current-drive, and control techniques. These are key features of the Tokamak Physics Experiment (TPX) planned for operation around the turn of the century. Nonlinear Interaction of Intense Electromagnetic Waves with Plasmas During the next decade, more quantitative models must be developed that describe the nonlinear interaction and competition of plasma instabilities driven by intense electromagnetic waves. This is a timely challenge for many reasons. In laser-plasma experiments, these instabilities are being characterized in greater detail, using increasingly sophisticated diagnostics. Nonlinear models based on the Zakharov equations are already illustrating the rich competition between different instabilities, and successful comparisons with experiments are being made. Finally, advances in computational physics and computers are allowing improved simulations, including, for example, meaningful three-dimensional simulations of laser-beam filamentation by both ponderomotive and thermal mechanisms. More quantitative models of the nonlinear behavior of laser-plasma instabilities would allow optimized regimes of operation for inertial fusion and improved interpretation of data from ionospheric and space plasmas. Because these instabilities involve the most basic plasma waves, improved understanding of the nonlinear behavior would be a very significant contribution to plasma science, no doubt stimulating new advances and applications.

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Plasma Science: From Fundamental Research to Technological Applications Current-Carrying Plasmas with Flow One research opportunity in laboratory plasma physics, which is synergistic with space and astrophysical plasmas (see next section, ''Space Plasmas"), is the investigation of current-carrying plasmas with flow. In these plasmas, global and/or turbulent flows are essential to the physics. By contrast, magnetic fusion plasmas are effectively stationary. Flowing plasmas present a new challenge to the experimentalist to design facilities in which the desired phenomena occur and to develop scaling arguments that laboratory plasmas are representative of the physics of space and astrophysical systems. To the theorist and applied mathematician, flowing plasmas are no less of a challenge because of the presence of several varieties of discontinuities, which must be understood as isolated, often collisionless processes and then incorporated self-consistently into the overall model just as hydrodynamicists incorporate shocks into supersonic flows. Discontinuities abound in plasmas. Even flows with velocities well below the Alfvén speed lead to singular current sheets in tokamaks and in the solar corona. And one need look no further than the solar photospheric magnetic field, which is concentrated into small regions of high intensity, to recognize that any theoretical understanding of dynamo generation of magnetic fields must accommodate an extraordinary degree of spatial intermittency. There has yet to be a successful laboratory demonstration of a hydromagnetic dynamo. With adequate support, visualization diagnostics can be implemented that promise to yield insights into magnetohydrodynamic flows comparable to those observed in hydrodynamic experiments. Engineering Design Tools The next decade should also see the development from the results of well-founded theories of simpler but robust tools for engineering design in the several areas of application of plasma physics, such as magnetic and inertial fusion, microwave devices, high-efficiency lamps, plasma processing, and particle accelerators. Space Plasmas In 1978, the National Research Council report Space Plasma Physics: The Study of Solar System Plasmas, prepared by a Space Science Board study committee headed by Stirling A. Colgate, strongly endorsed space plasma physics as "intrinsically an important branch of physics."2 The Colgate report is widely considered to be the impetus for the present programmatic emphasis in the field. 2   National Research Council, Space Science Board, The Study of Solar System Plasmas, National Academy Press, Washington, D.C., 1978.

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Plasma Science: From Fundamental Research to Technological Applications Specifically, it identified six areas of research as important to develop the basic understanding of space plasmas and, therefore, of fundamental intellectual value to plasma physics. The areas are magnetic reconnection, turbulence, the behavior of large-scale flows, particle acceleration, plasma confinement and transport, and collisionless shocks. Substantial progress has been made in each area over the intervening 14 years. Examples are cited here and in Chapter 6, which is devoted specifically to space plasma physics. All of these areas offer significant research opportunities in theoretical and computational plasma physics during the next decade. Future research opportunities in space plasma theory are summarized below. Magnetic Reconnection Magnetic reconnection is a process by which stored magnetic energy can be converted explosively into plasma kinetic energy. It is invoked ubiquitously as a mechanism in space and astrophysical problems—in solar and stellar flares, which occur commonly in stressed bipolar magnetic regions; in flux transfer events, which intermittently erode the outer layer of Earth's day-side magnetic field and add the flux to a stressed antisunward magnetotail; and in the magnetospheric substorm, where the calamitous relaxation of the magnetotail is accompanied by pronounced auroral brightenings, enhanced electrical currents in the ionosphere, and the antisunward escape of a large blob of accelerated plasma. Observation of the reconnection process itself is fragmentary, and evidence is circumstantial. The mechanism occurs readily in models based on the magnetohydrodynamic (MHD) equations but is due to resistivity, externally postulated or spuriously generated by numerical discretization. Space plasmas are collisionless to a high degree, and reconnection is significant only when the resistivity due to classical two-body interactions is enhanced by anomalous collective processes. Candidate mechanisms such as the lower-hybrid-drift instability have been suggested. Further research needs to be carried out to investigate the microphysics and integrate the results into an MHD description of large-scale behavior. In turn, quantitative MHD predictions must benefit from the enhanced numerical capabilities of new computer architectures and algorithms that maximize their effectiveness. Turbulence Space plasmas are characterized by turbulence on all scale lengths. Hydrodynamic turbulence occurs in the convection zone of the Sun and, through coupling to rotation, may play an important role in the dynamo mechanism and global oscillation modes. Models that explore these processes on an elementary scale are being developed but are limited by numerical considerations. Magnetohydrodynamic turbulence is generated in the solar wind by the intersection of

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Plasma Science: From Fundamental Research to Technological Applications plasma streams emanating from different longitudes on the rotating Sun. This turbulence plays an important role in heating the solar wind. Indeed, the solar wind has become a fundamental medium for investigating MHD turbulence—its generation, evolution, and dissipation—with advanced statistical concepts. An unusual microscale turbulence occurs when newly created plasma experiences the solar wind blowing across it, as is the case when cometary molecules are ionized. This turbulence is important in transferring momentum from the solar wind and can produce a deflection of the solar wind flow if the so-called mass loading is significant. Microturbulence plays many roles in magnetospheric plasma physics. Its importance in the magnetic reconnection process has already been mentioned. Another example, especially well studied from the standpoint of observations, modeling, and theory, is equatorial spread-F, a fluid-like turbulence in which flux tubes interchange in the low-latitude regions of Earth's collisional ionosphere. Large-Scale Flows The outward flow of the solar wind is one of the permanent features of space plasmas. Its speed varies by factors of two or three temporally and exhibits marked spatial variations, but the phenomenon is seen in every possible observation. Much less documented and understood is the coupling of such flow to planetary magnetospheres. Low-altitude observations at Earth indicate that the magnetospheric plasma is impelled into convection by coupling to the solar wind. The processes for this coupling are poorly understood: a steady magnetic reconnection may be the agent, or the magnetopause, the outer magnetospheric boundary, may experience Kelvin-Helmholtz instability so that the flow penetrates viscously. However, there is unanimity that the controlling processes take place in spatially localized boundary layers, with dimensions of the order of a few ion Larmor radii. The sense of the flow is antisunward at high latitudes and sunward at low latitudes, so that a circulation pattern is established. Because of the high electrical conductivity along magnetic flux tubes, it is expected that the entire magnetospheric plasma must participate in this convection. However, years of effort to measure steady magnetospheric convection far from Earth's surface largely have been inconclusive. The most recent data analysis suggests that the process may proceed in a bursty fashion. If so large, constraints would seemingly exist on the underlying physics: that it be initiated locally and hence probably involve microprocesses, and yet that it be transmitted globally on a rapid time scale. Particle Acceleration Because of their strong manifestations, energetic charged particles are central to astrophysics, and effort has focused there on acceleration processes that

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Plasma Science: From Fundamental Research to Technological Applications elevate their energy selectively from a thermal bath. Space plasmas are an accessible microcosm for examining some acceleration processes. Indeed, the observational origins of space plasma physics trace to cosmic-ray physics. Acceleration processes can be either systematic or random. An example of the former is the function of electric double layers that form at low altitudes along terrestrial magnetic field lines as a result of collective processes. Double layers have been created in laboratory devices and replicated in numerical simulations, but owing to their spatial extent, like so many phenomena they are difficult to identify unambiguously from space data. Much more widely invoked, because it is a process capable of raising particles to very high energies, is stochastic acceleration by random and repeated encounters with electromagnetic fluctuations. Outstanding success has been achieved in analyzing this mechanism in connection with shock-induced fluctuations. The treatment has been kinetic and self-consistent in the sense that the accelerated particles contribute to the energizing wave spectrum. An important next step is to assess the relative importance of such accelerated particles to the shock structure itself. Plasma Confinement and Transport Plasma confinement and transport are widely inclusive concepts. At the time of the Colgate study,3 the primary reference was to the longevity of energetic, magnetically trapped particles, such as those populating the Earth's Van Allen belts. Like the solar wind, these are enduring features of the Earth's space environment, and analogous structures have been discovered in the environs of all the magnetized planets. The slow loss of Van Allen particles to Earth's atmosphere due to Coulomb collisions at very low altitudes and wave-particle scattering at higher altitudes is well understood. Of a much more speculative nature is the process that replenishes the belts so that they maintain their long-term existence. The issue is especially important at Jupiter, where MeV electrons are continuously losing energy due to synchrotron radiation. Present conjecture is that global-scale, low-frequency electromagnetic fluctuations, perhaps induced by solar wind buffeting of the magnetosphere or time-dependent atmospheric dynamo processes, allow particles to randomly traverse magnetic field lines to close-in distances, gaining energy in the process. Because of the global nature of the physics, it is difficult to verify this process observationally. What has been done is to create diffusion models using representative fluctuation spectra and to compare output particle distributions with observations—and this has been carried out with reasonable success. However, confinement and transport issues during the next decade will undoubtedly be far more expansive. To what extent are the outer reaches of the Earth's magnetosphere and the Sun's atmo- 3   See footnote 2, p. 167.

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Plasma Science: From Fundamental Research to Technological Applications sphere equilibrium structures? If the current direction of thinking is correct and gross plasma behavior is regulated by processes at a number of thin boundary layers, such as stream-interaction regions in the solar wind and Earth's plasma sheet boundary layer, what processes are responsible for maintaining the existence of such narrow structures? Collisionless Shocks The study of collisionless shocks is arguably the area in which the most significant advances have been achieved during the past decade and where the impact of space on basic plasma physics has been most profound. Success has been achieved as the result of a coordinated approach to the problem, using sets of complementary observations analyzed in the context of contemporary numerical models that integrate relevant microscopic theory. The Earth's bow shock is observable on every spacecraft orbit that reaches the solar wind. The International Sun-Earth Explorer (ISEE) mission is a cooperative venture between NASA and the European Space Agency (ESA). ISEE, with its coordinated pair of maneuverable spacecraft having ideally suited apogees, featured bow-shock physics as a prime scientific objective and has contributed immeasurably to this understanding. Bow shocks have been observed in association with every planet and comet. They are necessary hydromagnetic structures allowing the supersonic, super-Alfvénic solar wind to slow down and divert around an obstacle in its flow. Collisionless shocks are also common coronal and solar wind phenomena. There is rich variety to shocks, and this diversity is still incompletely investigated and understood. A prime determinant is the direction of the magnetic field in the incoming flow with respect to the normal to the discontinuity surface. If the angle is large, the shock is a perpendicular shock and generally laminar and quiescent. If the angle is small, the shock is a parallel one and exhibits a great deal of pulsation, structural disintegration, and reforming. Owing to the geometry, different azimuthal sectors of the same planetary bow shock can be quasiperpendicular, while other sectors are quasiparallel. In both instances there is a wealth of fine-scale plasma structure, both internal and external to the discontinuity. Chaotic Effects During the past decade, realization of the importance of chaos has emerged in all branches of science. This is true of space plasma physics. The focus of attention has been on chaotic particle trajectories, especially those occurring in the equatorial region of the magnetotail where the magnetic field is significantly weakened owing to distention. It is known that a mixture of chaotic and regular orbits exists, but the relative magnitude of their numbers is an open question. First results indicate that injection at the proper locations and ensuing chaos can

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Plasma Science: From Fundamental Research to Technological Applications lead to the formation of charged-particle beams, which are commonly observed. Particles on chaotic orbits also contribute significantly to the self-consistent current density responsible for the magnetic distention. If chaotic orbits are important, they must also certainly impact collective kinetic phenomena. Study of this subject is still in its infancy. It is quite plausible that similar physics takes place in the other boundary layers mentioned earlier in this section. Summary To summarize, space plasma physics has reached a mature phase. Space plasma physics has passed through the exploratory phase and is beginning an era of understanding. Future efforts will focus on the details of specific structures and processes. Theory and modeling at all levels have become a routine element of missions. As the morphology of and scientific basis for structures and processes become clearer, it is important that a basic understanding of the underlying plasma physics be pursued directly by relevant laboratory simulations, to test quantitatively and in detail the predictions of new theories as they become available. CONCLUSIONS AND RECOMMENDATIONS Plasma physics is the study of collective processes in many-body charged particle systems. The state of such a system departs considerably from the strictly thermodynamic equilibrium state. The understanding of collective processes is the central goal of theoretical plasma physics. There have been significant advances in theoretical and computational plasma physics during the past decade. Priority should be assigned to the research opportunities of high intellectual challenge identified earlier in this chapter. In the remainder of this section, the panel presents a succinct summary of principal findings and recommendations. Fusion, space exploration, and defense applications have been the engines of high national priority that have powered fundamental advances in plasma theory and computational plasma physics. In turn, the improved understanding of basic plasma processes has led to the seminal development of important new concepts and applications. The panel recommends that a vigorous program in plasma theory and modeling efforts in fusion and space exploration should be continued. This is essential for continued progress in the interpretation of experiments and the development of new concepts in these important national programs. Support for individual university investigators to explore fundamental plasma theory and innovative concepts is at precariously low levels. This situation threatens the continued development and nurturing of the very intellectual foundations of modern plasma theory.

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Plasma Science: From Fundamental Research to Technological Applications The panel recommends that the program of individual-investigator research in basic plasma theory should be reinvigorated to explore the broad range of intellectually challenging problems in stochastic effects, novel analytical techniques, nonlinear processes, and other areas, which are essential to the continued vitality of plasma theory as a scientific discipline. Plasma theory is sufficiently advanced that a predictive capability exists for describing the properties of many static plasma configurations and simple wave-particle interactions. However, flowing, turbulent, and highly nonlinear saturation processes are at the forefront of analytical and computational capabilities. The panel recommends that the design of experiments jointly by theoreticians and experimentalists to elucidate the conceptual foundations of nonlinear plasma physics should be encouraged. The panel recommends that plasma theory should be encouraged that seeks to establish a commonality of physical processes and applied mathematical techniques across a wide range of realizations, from pellet compression in inertial fusion to plasma processes on astrophysical scales. Advances in nonlinear plasma science in the past have relied heavily on the insights gained from numerical simulation. The panel envisions that future advances in theoretical plasma physics will have even greater reliance on numerical techniques and on the increased computational capability and visualization techniques available in present-day and future computer systems. A particular challenge is posed by discontinuities such as shocks, current sheets, and double layers. The panel recommends that emphasis should be placed on ongoing programs in grand-challenge computations. Emphasis also should be placed on plasma computations investigating processes common to a wide range of scales. The following of the panel's general recommendations (see Executive Summary) are made to improve the national effort in theoretical and computational plasma science: To reinvigorate basic plasma science in the most efficient and cost-effective way, emphasis should be placed on university-scale research programs. To ensure the continued availability of the basic knowledge that is needed for the development of applications, the National Science Foundation should provide increased support for basic plasma science. Individual-investigator and small-group research, including theory and modeling as well as experiments, needs special help, and small amounts of funding could be life-saving. Funding for these activities should come from existing programs that depend on plasma science. A reassessment of the relative allocation of funds between larger, focused research programs and individual-investigator and small-group activities should be undertaken.