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General Plasma Physics SCOPE AND OBJECTIVES OF GENERAL PLASMA PHYSICS Plasma physics is a discipline whose primary concerns are the collective motions of charged particles, electrons and/or ions, sub- jected to the action of external electric and magnetic fields and to the action of their own self-fields. This assembly of particles and fields represents a fluidlike medium called a plasma. Basic plasma physics is a study of this fluid. In particular, it concerns itself with such questions as plasma equilibrium and stability, confinement, wave-propagation, instabilities, turbulence, and chaos. We define general plasma physics to include basic plasma concepts and their applications. In this section we have included (with a few exceptions) applications whose main motivation is not thermonuclear fusion or space plasmas. These are dealt with in other sections. Here we examine a number of different applications such as free-electron radiation sources, x-ray lasers, plasma isotope separation, and collec- tive and laser-driven accelerators. Much of this work is motivated and supported by defense-related problems. Application of basic plasma physics to the development of new technologies requires substantial financial support. In this respect we note that the development of plasma physics is largely incidental to the main objectives, and the amount of support for it is also quite ill-defined. Nevertheless, it is imperative to consider basic plasma 95

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96 PLASMAS AND FF UlDS physics along with the development of new technology because their future prospects are so strongly coupled. The 1960s may be regarded as a time in which the linear theory of plasma fluctuations was put on a firm basis. The 1970s saw the development of nonlinear plasma physics: the behavior of large- amplitude waves, including particle trapping, saturation, wave- breaking, and turbulence; the discovery of new nonlinear phenomena such as Langmuir and ion acoustic solitons; ponderomotive effects of intense electric fields; parametric instabilities, which are growing wave-wave interactions; tearing modes that cause magnetic lines of force to become braided or to form magnetic islands. The development and widespread use of computational techniques has provided the missing link between theory and experiment. The broad-based fundamental studies of the past two decades have solidified the underpinnings of the relatively new science of plasma physics, with the result that the predictive power of plasma theory has been considerably increased, and the occurrence of experimental surprises has become less frequent. For instance, the possibility of driving a dc current in a tokamak with radio-frequency fields was indicated by the theory of wave-particle interactions, and the occur- rence of stimulated Brillouin scattering in high-power laser fusion experiments was anticipated by work on parametric instabilities. What will be the principal directions of progress in the 1980s? Surely the increased power of computers will lead to a deeper understanding of nonlinear phenomena, especially in two and three dimensions. The transition from order to chaos has been an area of activity and progress in nonlinear dynamics, and applications in plasma physics will lead the way in further development of this topic of general physical interest. Important unsolved problems remain to be carried over into the next decade; for instance, the scaling of electron transport in toroidal devices, anomalous heat conduction in laser-produced plasmas, the detailed mechanisms in field-line reconnection, and the formation of charge layers (double layers) in the Earth's magnetic field and in laboratory plasma. A dedicated study of plasma physics can be expected to lead to exciting new avenues and possibilities. For example, dense nonneutral plasmas of relativistic electrons will become available with new types of accelerators where collective effects dominate. Possibly revolution- ary new ion and electron accelerators will contribute to high-energy physics, energy problems, and weapons. New coherent sources of radiation, particularly x-ray lasers, will appear initially for defense problems and then for applications not yet perceived. The growth of

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GENERAL PLASMA PHYSICS 97 plasma physics in its impact on related sciences and on areas of practical application has not diminished since its birth in the 1950s, and it is reasonable to expect that this growth will continue in the next decade and beyond. It is unfortunate that support for basic plasma-physics research has practically vanished in the United States. The number of small laboratories engaged in fundamental investigation of plasma behavior is several times larger in Japan and in Western Europe than in the United States, where only a handful of universities are able to derive support for such studies. Continued evolution of our understanding of plasma and discovery of new applications, in the way solid-state physics has continued to develop, for instance, will require a reason- able level of steady support for research that is not mission oriented. Only National Science Foundation (NSF) support is clearly for this purpose, and a few universities have support the total budget for basic plasma physics is about $2 million. The 1970s saw the growth of large machines for fusion studies and defense problems. It was also marked by the decline of basic plasma physics. It was generally believed that because of the large machines and corresponding budgets that a great deal of support was available for basic plasma physics. In fact, the support has almost disappeared, and the activity has been almost completely eliminated. Progress in plasma physics depends on the foundation provided by basic plasma-physics research; if that foundation is not continually strengthened, ultimately the whole field will suffer. INTENSE BEAMS~ELECTRONS, IONS, AND PHOTONS The development of high-voltage pulsed power systems was initiated in the early 1960s by J. C. Martin at the Atomic Weapons Research Establishment in England. The essential feature of this research was the successful development of techniques for using Marx generator technology to pulse charge a high-speed transmission line in order to produce short-duration 10-100-ns high-power pulses. Since that time the development of pulse power technology has been quite rapid. During the 1960s terawatt (10~2 watts) machines were developed, and during the 1970s, tens-of-terawatt machines were built. They were used to produce electron beams, ion beams, and Z-pinch plasmas. The particle beams are of sufficient intensity that the collective self-fields are of decisive importance, which is why the subject has become a part of plasma physics rather than accelerator or particle physics. Initially, the primary purpose was the simulation of nuclear weapons ejects,

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98 PLASMAS AND FLUIDS and research programs were mainly funded by the Department of Defense (Defense Nuclear Agency) and the Department of Energy. During the past 10 years, other applications have developed including light-ion inertial-confinement fusion, compact torus/magnetic-confine- ment fusion, microwave generation, collective accelerators, laser pumping, and x-ray sources. The major accomplishments of the past 10 years (up to 1984) are as follows. Development of Low-Impedance Multiterawatt Machines The new generation of pulse power machines includes PITHON (5 TW) at Physics International Company; Blackjack V (10 TW) at Maxwell Laboratories, Inc.; and the Particle Beam Fusion Accele- rator (PBFA I) at Sandia National Laboratory (SNL) (20 TOO). PBFA II at SNL is currently under construction, with a design power of 100 TW. Intense Ion Beams Intense electron beams (currents up to a few mega-amperes and voltages up to 10 MV) were developed in the 1960s. In the 1970s, a great deal of research was carried out on ion diodes and ion-beam propagation at the Naval Research Laboratories (NRL), SNL, Cornell University, and the University of California, Irvine (UCI). Diodes were developed to be used with existing pulse power machines. Ion beams with ion currents up to about 0.5 MA were obtained with reflex diodes, pinch diodes, and magnetically insulated diodes. In each case both electrons and ions are present in the diode, but the electron motion is inhibited by magnetic or electric fields so that the current is primarily an ion current. For some time both electron and ion beams were considered for inertial confinement fusion; the Electron Beam Fusion Accelerator (EBFA) project was changed to Particle Beam Fusion Accelerator (PBFA) during this period. The survivor was light-ion inertial fusion, and light-ion focused beams achieved a power density of 10~2 W/cm2. Another motivation for ion beams was to make a compact torus configuration with ion rings. Although ion currents as high as 0.7 MA were achieved, this was insufficient for compact torus configurations that require field reversal. It was established that neutralized ion beams could be transported across magnetic field lines, focused, and injected into a tokamak.

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GENERAL PLASMA PHYSICS 99 Development of High-Energy, High-Current Machines Pulse power machines based on Marx generators and pulse lines have been limited to about 10 MV. The Advanced Test Accelerator (ATA) was developed and construction completed at Lawrence Livermore National Laboratories (LLNL) in 1983. It is an induction accelerator capable of accelerating 10 kA of electrons to an energy of 50 MV. The successful development of this machine will provide access to electron-beam parameters that should open up new fields and applications. It should have an impact comparable with that of the Marx-generator/pulse-line systems. It is now being used in beam- propagation studies. Designs for using the beam in a high-power free-electron laser configuration operating at infrared frequencies are under way. Z-Pinch X-Ray Sources An annular plasma is formed by exploding thin foils or multiple wires or by gas flow through a nozzle and subsequent ionization. A large current is produced in the plasma with a pulse power (up to 5 MA) machine that causes the plasma to implode, reaching densities of 102~ electrons/cm3. On impact the kinetic energy of the plasma (hundreds of kilojoules) is thermalized and radiated. The observed radiation in- volves a continuum corresponding to temperatures of 100-1000 eV and K-shell line radiation of typically a few keV according to the plasma composition. The intense soft-x-ray source is of interest for atomic physics of highly stripped ions in plasma and for various applications including lithography, microscopy, and x-ray lasers. Propagation of Charged-Particle Beams in Gas and Plasma During the past 15 years there has been a substantial research effort devoted to propagation of relativistic electron beams and high-current ion beams in gas and plasma. This problem is of interest in connection with directed energy weapons as well as with the need to transport and condition beams efficiently for various other applications, including, in particular, heavy-ion and light-ion inertial fusion. Such beams are subject to a variety of instabilities: two-stream and return-current instabilities have been identified as dominant in certain regimes where the plasma density is relatively low, while the hose instability appears to be dominant in cool weakly ionized gas at densities above a few Torr. These instabilities have been studied both theoretically and

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100 PLASMAS AND FF UlDS experimentally with reasonable agreement reached. In recent years, multiply pulsed electron-beam generators and energies from 5 to 50 MeV have become available. These facilities should open up a variety of far more interesting propagation studies over a wide parameter space; as such they have led to a surge of theoretical development as well. Research interest now centers on such areas as equilibrium and instabilities of beams in self-generated density/conductivity channels, transport processes in the plasma channels (hydra, chemistry, radia- tion, and collisional processes in partially ionized gases), and optimi- zation of beam parameters for efficient transport. Other applications of intense beams to collective accelerators, laser accelerators, and coher- ent-radiation sources have developed sufficiently in the last 10 years that they are discussed in separate sections. Expectations and Recommendations for the Next 10 Years The plasma physics encountered in the study of intense beams is mainly determined by the accelerator capability. In considering the next 10 years we need to consider the availability of existing acceler- ators and new accelerators likely to be developed. The scaling laws of low-impedance Marx-generator/pulse-line ma- chines are now well understood. It is unlikely that machines larger than Blackjack V or PBFA II will ever be built. Major advances beyond the present state will only take place if new technology is developed. The present trend is toward inductive energy storage and the development of a fast opening switch. A plasma erosion opening switch has been developed at NRL that has been tested on the pulse lines Gamble I (1 MV, 500 kA) and Gamble II (3 MV, 1 MA). Energy was transferred from the pulse lines to an inductor. Then the energy was switched to the load. Pulse compression of a factor of 3 and power multiplication of a factor of 2 were observed compared with direct coupling from pulse line to load. At present the erosion switch is used to upgrade the performance of large existing accelerators such as Blackjack V and PBFA I. Such switch developments may lead to new machines with much larger power and energy. Applications of pulse power machines are currently limited because of the deficiencies of the repetition-rate technology. This also depends on the creation of new switches that can survive. Recent advances in magnetic switches have revived interest in this problem, which had been postponed for the past 10 years. The new area of high energy and high current will be limited to LLNL and LANL unless less-expensive machines can be developed.

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GENERAL PLASMA PHYSICS 101 (The cost of ATA is about $50 million or about $1/volt). High-current betatrons can be modified by adding a toroidal magnetic field to control the space charge. This type of accelerator is being developed at NRL and UCI, and such an accelerator for research purposes should be much less expensive than ATA. The acquisition of experimental information and the resultant progress in plasma physics proceeds a great deal more slowly than one might expect considering the number of laboratory machines and physicists. As long as new machines are being built, much of the staff are occupied with the task. After the machine is completed the management of the machine takes more staff, but usually the labora- tory gets involved in yet a larger machine before completion of the smaller machine. Budget limitations often force the shutdown of a relatively new machine to make the resources available for the larger machine. Budget allocations for machines typically take precedence over anything else. For example, in 1982, SNL received a budget allocation of about $20 million to build PBFA II and a reduction in operating budget. This is typical of most laboratories except for universities and NRL, which have not built any large machines in recent years. As a result, most of the research has been done at universities and at NRL. Large machines do not advance our knowl- edge until many years after they are built after the machine is no longer interesting in itself, it may be used to study intense beams if it has survived the budget axe. For example, Blackjack V has been in operation since 1978 but has never been available for making beams of electrons or ions. Of course, the large machines are not built to learn plasma physics, which is perceived to be at most incidental to the main purpose. In the long run, the basic understanding of plasmas is usually important to the main purpose. If a means could be found to make large machines available for research after the original purpose has been served, it would be a great stimulation. COLLECTIVE ACCELERATORS Collective accelerators make use of the electric and magnetic fields of charged particles in the region of the space where particles are to be accelerated or focused, or both. In principle, very large accelerating and focusing fields are possible, and the fundamental goal is to make use of these large fields to build high-performance accelerators very economically. During the past 10 years research has been carried out on five different types of ideas.

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102 PLASMAS AND FLUIDS Space-Charge Accelerators Intense relativistic electron beams are used to make a moving potential well to pull ions along with the beam. Accelerating fields typically of 1 My/cm have been observed over a distance of about 10 cm. The number of ions accelerated is about 10~2, and this requires about 10~6 electrons. In one form of this accelerator called the Luce diode, proton energy as high as 45 MeV was observed. The central problem is control of the motion of the moving potential well. Many ideas were studied, and most of them were shown to be valid in principle but not precise enough to accelerate ions to high energy. The only continuing effort is on the Ionization Front Accelerator at SNL. In this scheme the electron beam propagates through a gas that is not significantly ionized by the beam. Ionization of the gas is accomplished in a controlled way by means of a laser and a series of light pipes; this controls propagation of the electron beam and the motion of the potential well for ions. Wave Accelerators Waves supported by a relativistic electron beam are used to trap and accelerate ions as in a conventional linear accelerator. The waves must have variable phase velocity and should be "negative energy waves" so that ion acceleration that takes energy from the wave will cause the wave to grow rather than damp. A space-charge wave (Cornell University) and an electrostatic electron cyclotron wave (Austin Research Associates) have been studied for this purpose. The space- charge-wave effort continues at Cornell University. There is another related effort at NRL in which an electron beam is chopped into a sequence of rings that pass through a series of short solenoids. The resultant accelerating field resembles that of a wave with controlled phase velocity. It is a wave accelerator, but the wave is not bound by the plasma dispersion relation. This is a continuing effort. Electron-Ring Accelerators The electron-ring accelerator (ERA) was proposed by Soviet phys- icist V.I. Veksler in 1956. An electron ring is formed in a magnetic mirror, and ions are trapped in it. Acceleration takes place by means of an electric field or changing magnetic field along the ring axis. This is the most extensively investigated collective accelerator. There have been projects at Dubna in the Soviet Union, Lawrence Berkeley

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GENERAL PLASMA PHYSICS 103 Laboratory, University of Maryland, and Garching in the Federal Republic of Germany. Only the Dubna group is still working on electron-ring accelerators. They reported significant progress in 1978- acceleration of 5 x 10~ nitrogen ions to 4 MeV/nucleon with an electron ring that contained 10~3 20-MeV electrons. Collective Focusing Accelerators Here, collective fields are used only for focusing, and acceleration is conventional. One form at SNL is called Pulselac. It consists of a series of ion diodes. Electrons are injected to provide charge neutralization and transverse focusing, and transverse magnetic fields prevent elec- tron acceleration. Another form is a cyclic accelerator that is studied at UCI. Electrons are confined in a bumpy torus, and the electrostatic fields focus a smaller number of ions that are accelerated as in a betatron. 3000 A of C+ ions have been accelerated to 600 keV in Pulselac. Electron confinement in the cyclic accelerator has been documented. Both projects are still active. The experimental results in almost all of the collective accelerator experiments have demonstrated that the principles are sound. How- ever, the number of ions accelerated and the final energy have not been impressive; in general both have been less than expected initially. The experiments still active, the Ionization Front Accelerator (SNL), space-charge wave accelerators (Cornell, NRL), and collective focus- ing accelerators (SNL, UCI) will probably give similar results. The question is, "What will happen after the initial research is completed assuming that it is successful?" The next phase in which more interesting particle parameters are reached will surely be much more expensive. The only collective accelerator to date to proceed to the next phase is the ERA in Dubna, where a heavy-ion ERA to reach 20 MeV/nucleon was authorized in 1981. During the past 10 years the level of support was $2 million to $3 million/year in the United States. A level of support of about $5 million/year for research was recom- mended in a 1981 DOE study. It is also important that about $10 million be available to convert a successful research effort into a useful accelerator. LASER-DRIVEN ACCELERATORS The availability of high-power laser beams ~-1014 W) brings about the possibility of using these high fields to accelerate particles to energies in the tera-electron-volt range and beyond. Using conven

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104 PLASMAS AND FLUIDS tional acceleration methods it is difficult to envision particle energies going above a tera-electron volt without an enormous investment in money and real estate. For example, if we assume for conventional accelerator schemes electric field gradients as high as 100 MeV/m, acceleration lengths of about 10 km would be needed to reach tera-electron-volt energies. Such accelerators are in principle feasible however, the cost may be prohibitive. The possibility of utilizing the extremely high electric fields associ- ated with laser beams to accelerate charged particles has been under investigation for over two decades. Electric fields associated with intense laser beams can be as high as 109 V/cm. Direct use of these fields for continuous particle acceleration is of course not possible owing to the transverse polarization and rapid oscillation of the fields. A number of laser-driven acceleration schemes have been suggested that either utilize a small fraction of the laser field for acceleration or use the laser beam or beams to excite a plasma wave, which in turn traps and accelerates charged particles. Owing to the speculative nature of the various laser-driven acceler- ation schemes the subject has suffered from a lack of funding. Recently, because of the progress made in understanding the physics and limitations associated with the various schemes, the funding profile appears to be more favorable, at least for the next few years. The following list gives a brief qualitative description of the various acceleration mechanisms (not necessarily in order of priority) that are considered potentially attractive. Beat-Wave Accelerator This is a collective acceleration scheme that utilizes the enormous self fields of an excited plasma wave. The plasma wave is excited by the parametric coupling of two laser beams having a frequency difference equal to the characteristic plasma frequency. Since the phase velocity of the high-amplitude plasma wave is slightly less than the velocity of light, electrons can be trapped and accelerated by the plasma wave. A potentially attractive variation of the beat-wave accelerator is the Surfatron. In the Surfatron a transverse magnetic field is externally applied, permitting the accelerated particles to E x B drift in a~direction transverse to the laser propagation direction. In this configuration the electrons can remain in phase with the plasma wave, allowing unlimited electron acceleration to take place. Recent experi- ments at UCLA have demonstrated the principle of wave formation using two high-power lasers.

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GENERAL PLASMA PHYSICS 105 Inverse Free-Electron-Laser Accelerator In this scheme a particle beam together with an intense laser pulse is propagated through a spatially periodic magnetic field known as a wiggler field. The wiggler period and laser wavelength are such that the transverse particle velocity due to the wiggler field is in phase with the transverse electric field of the laser radiation. By appropriately con- touring both the wiggler amplitude and period the injected particles can be continually accelerated. The inverse of this process has been used to generate radiation and is the well-known free-electron-laser mech- anism. (See section below on Coherent, Free-Electron Radiation Sources.) Grating Accelerator When electromagnetic radiation propagates along a diffraction grat- ing a slow electromagnetic surface wave is excited along the grating's surface. This scheme utilizes the slow electromagnetic wave with phase velocity less than the speed of light to trap and accelerate a beam of injected electrons. High-Gradient Structures r This scheme is basically a scaled-down version of a conventional slow-wave accelerator structure. Radiation power sources in the centimeter wavelength range appear appropriate for this approach. The potential advantage of this scheme is that owing to the short wave- length employed, relatively low radiation energy per unit length is needed to fill the small structure, and breakdown field limits appear to be higher. Inverse Cerenkov Accelerator This approach takes advantage of the fact that the index of refraction of a neutral gas is slightly greater than unity. The laser radiation within the gas has a phase velocity~less than the speed of light, making it possible to trap and accelerate an injected beam of particles. Cyclotron Resonant Accelerator Here an electron beam is injected along a uniform magnetic field together with a parallel propagating laser beam. Because of a self

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GENERAL PLASMA PHYSICS 133 which may limit or destroy the plasma or evolve into some nonlinear turbulent state. These are presumably among the processes that determine the effectiveness of energy confinement in a particular configuration. Such fluctuations and instabilities have been detected in many ways. In the easiest cases, they can be seen as oscillations in the magnetic field outside the plasma or they are coupled to an electro- magnetic wave, which can propagate through the plasma and be detected outside. A serendipitous indication of internal plasma oscil- lations was provided by simple x-ray detectors on tokamaks in 1974. The detectors are sensitive principally to temperature variations, and their application to tokamaks, coupled with analysis methods akin to those for the tomographs that have revolutionized medical x-ray diagnosis, have produced images of highly complex modes within the plasma that evolve on times of milliseconds. Scattering from Collective Fluctuations A systematic and versatile method of observing density variations within the plasma is to scatter an electromagnetic wave from the fluctuations. Using a laser source, sufficient scattered signal can be obtained. In principle, the frequency, wavelength, and intensity of fluctuations in a chosen region of plasma can all be obtained by this method. Unfortunately, the several constraints for the application of the method have required the use of submillimeter microwaves (far infrared) for many plasmas of interest. Exploitation has waited the development of suitable laser sources and detector technology within the last few years. Its potential is just beginning to be realized. Data Acquisition and Instrumentation A crucial technological development that underlies all of these diagnostics has been the commercial development of advanced com- puterized data-acquisition and -processing systems over the last dec- ade. Although one could imagine implementing any one of these diagnostics, albeit with difficulty, without computers, computerized systems are essential for combining diagnostics to give a complete characterization of the plasma in any major device. The volume of data and the sophistication of analysis required to obtain intelligible results from the raw data both require computers. The consequences for experimental operation and physical understanding have been im- mense. Immediate processing provides a characterization of the plasma that makes possible far more intelligent and productive opera

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134 PLASMAS AND FLUIDS tion of the whole experiment. It also permits each diagnostic to be optimized quickly, and makes even subtle malfunctions quickly appar- ent. Compared with experiments a decade ago, more data, by several orders of magnitude, are collected per day of experimental operation. Furthermore, a larger fraction is analyzed to yield useful results. Although this section concerns the developments in plasma diagnostics for magnetic fusion, we should mention that a comparable fraction of the inertial fusion effort is also devoted to diagnostics. In inertial fusion, x-ray microscopy and x-ray and particle spectrometers are the principal techniques, and these have been developed to a high degree of sophistication. Advances in picosecond streak cameras have been inspired by the need for extreme time resolution. Perhaps the most impressive accom- plishment, however, was the use of microscopic zone plates to focus the alpha-particle products of a laser-induced implosion, showing that true DT fusion indeed took place. Desiderata As impressive as our gains in diagnostic capability and consequent understanding have been, they often serve to underscore those areas where improvement is needed. Several important plasma parameters still elude measurement, and novel, innovative methods for their measurement remain to be devised. At the top of this list are local current density and magnetic field within a plasma, for which measure- ments of both average and fluctuating quantities are sorely needed. A technique to measure the electron velocity distribution function would be extremely useful, as would a more generally applicable method for measuring plasma potential and electric field, the heavy-ion-beam probe being impractical for many plasmas. In addition to completely new diagnostics, new methods or exten- sions of present methods to give improved spatial and temporal resolution are needed for all plasma parameters. The ideal diagnostic would measure a given parameter, e.g., electron temperature, at each point and time throughout an experiment. Instead, we are able to determine only a limited set of such data. The striving to this ideal is not purely academic; every time we have made an improvement in measuring capability, we have discovered new phenomena and deep- ened our understanding. Areas that are almost certain to be fruitful in this regard include better measurements of the fluctuations of turbu- lence in plasmas and more accurate, fine-grain measurements of the spatial variations of density and temperature, for it is the gradients in

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GENERAL PLASMA PHYSICS 135 the quantities that presumably determine the efficiency of energy confinement. To advance our knowledge of plasmas and make effective use of major fusion experiments to establish a firm scientific basis for fusion power, we recommend three policies: Greater effort be devoted to the development of specific novel and improved diagnostic methods. Most often diagnostics are developed for a specific experiment and only to the minimal extent required. Novel diagnostics can be difficult to support if they lack immediate application to a specific experiment. One example, but by no means the only one, of techniques with great and diverse diagnostic promise are those stemming from the development of improved far-infrared tech- nology. Higher priority be given diagnostics during the planning and construction of experimental facilities. Historically, diagnostics have not always been planned with a device or have been deferred during construction to make costs appear to be within budget. As a result, machines often begin with limited capability and are delayed in reaching their full potential. The essential role of diagnostics and their development must be fully appreciated. Additional effort be devoted to computerized data systems to cope with the rapidly expanding capabilities required. CAMAC has been accepted as a de facto standard in all major laboratories, but much more development and standardization for both hardware and software is required to provide the capabilities required for the future without duplication and great waste of resources. Extant and foreseeable diagnostics will make it possible to produce greatly increased amounts of useful data from experiments in the coming decade. More systematic approaches will be required to manage this information. The actual expenditures for diagnostics over the past decade cannot be realistically isolated. The only budget specifically allocated to diagnostic development is a small program within the Division of Applied Plasma Physics in the Office of Fusion Energy (DOE). This is currently funded at a level of $5 million per year and has totaled little more than $30 million over the past 10 years. It represents only a small fraction of the effort devoted to diagnostics. Most diagnostics are funded quite properly as part of the construction and operation of the experiment to which they are attached; no separate budget figures can be extracted. The development, fabrication, operation, and incremen- tal improvements in a typical diagnostic are inextricably associated with the total experimental operation. This has been a very desirable

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136 PLASMAS AND FLUIDS modus operandi, for it ensures that diagnostics are practical, usable, and utilized on experiments. It should be complemented and supple- mented by an increased effort, independent of specific devices, de- voted to diagnostics that require longer development before being ready for application to experiments and to diagnostic and computer developments, which should be generally applicable or standardized. STRONGLY COUPLED PLASMA PHYSICS A strongly coupled plasma is a form of dense ionized matter in which coulombic correlations among the charged particles determine bulk and dynamic properties. The interaction coupling parameter defined as the ratio of the average coulomb potential energy between particles to the average kinetic energy for such a plasma is greater than unity and for some systems much greater than unity. This degree of coupling is in marked contrast to the more commonly studied laboratory plasmas, which are low density and weakly coupled. A strongly coupled plasma thus is a fluid that resembles a neutral electrically conducting liquid. At sufficiently high density the coulombic correlations become so strong that the fluid undergoes a first-order phase transition to a lattice. Much of the matter in the universe is in the strongly coupled plasma state since stellar interiors are highly ionized and often at very high density. Physical systems that may be described as strongly coupled plasmas include the following: (i) Inertial-confinement fusion targets compressed by lasers; (ii) Interiors of large planets; (iii) Stars in late stages of evolution, e.g., red giants (iv) Liquid metals; (v) White dwarf interiors; and (vi) Neutron star crusts. History It was recognized some decades ago that matter at extreme densities has a significant limiting form in which the electrons because of the large Fermi energy become nearly uniform in density. In this limit, one will have a system of heavy (hence classical) ions or nuclei moving in a background of electrons that provide electrical neutrality and stabil- ity due to the large electronic pressure. For ionic matter formed from a single element and a neutralizing background of electrons this limit is called the one-component classical plasma (OCP). It has been the

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GENERAL PLASMA PHYSICS 137 subject of intense analytic and numerical study since it is the prototype strongly coupled plasma and is essential for understanding the proper- ties of the physical systems mentioned above. In the universe the OCP limit is approached only in white dwarf star interiors, and thus it is difficult to reach for experiments on the Earth. Conceptually the OCP limit, however, plays the same role for strongly coupled plasmas that the hard-sphere fluid plays for the theory of neutral liquids. Cluster expansion methods used for dense gases and liquid-state theory proved in the 1960s to be not particularly useful for strongly coupled plasmas, and numerical simulation methods were developed. In 1966, the availability of large computers at the Lawrence Livermore Laboratory made it possible to carry out the first detailed study of the OCP fluid state and to give some hint of the phase transition. The Monte Carlo method was used. In this procedure a few hundred charged particles are moved randomly in a three-dimensional cell in a manner to give average thermodynamic properties equivalent to the canonical ensemble of statistical mechanics. The simulation process gives numerical results for the coulombic interaction energy and the pair distribution function. The data thus obtained should be regarded as the results of numerical experiments, which are subject to problems typical of real experiments. Although the numerical simulation meth- ods are slow and expensive, the data obtained have been invaluable and have spurred major theoretical understanding of the properties of the OCP and related strongly coupled coulombic systems. The OCP equation of state was applied to white dwarf star structure calculations and gave rise to the suggestion that the center of these stars might be crystallized. The OCP pair distribution data were Fourier analyzed to give the OCP plasma structure factor, which was then used in realistic calculations of various transport properties such as diffusion, electrical conductivity, thermal conductivity, and viscos- ity. Applications of the OCP results were made to red giant stars and to calculations of dense plasmas that it was hoped would be produced in inertial-confinement fusion targets. In 1973, the OCP data from the Monte Carlo study were used to improve significantly the theory of thermonuclear reaction rates in stars. In the early 1970s the Monte Carlo method was extended away from the OCP limit to allow the neutralizing electrons to be treated as a polarizable fluid that partially screens each ion. This simulation gave rise to a much better under- standing of the evolution and structure of Jupiter. The availability of good numerical experiments for the OCP fluid spurred efforts to use the integral equations of liquid-state theory to the OCP and related strongly coupled plasmas. The hyper-netted chain

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138 PLASMAS AND FLUIDS (HNC) equation was solved to great accuracy in 1974, and the results were found to be remarkably close to the Monte Carlo results. The integral equation approach is advantageous because it is about a thousand times faster than the more exact simulation methods. In fact for numerous applications it was found that the HNC results were adequate for practical calculations of the equation of state of ionic mixtures and for electrical conductivity. In the late 1970s, it was found experimentally that electrons could be trapped on the surface of liquid helium and thus confined to motion on a two-dimensional surface. It was found that the electron density could be increased so that the resulting two-dimensional plasma could be produced in weak coupling and then as a strongly coupled plasma, which finally exhibited a two-dimensional phase transition. This sys- tem was particularly interesting since it provided a clean method of studying strong coulombs correlations, albeit in two dimensions. Two-dimensional Monte Carlo simulations were carried out for both the fluid and solid phases, and the density for the phase transition was found to be in good agreement with the experimental observation. As in the three-dimensional case, the HNC equation was applied to the two-dimensional electrons and was found to be in good agreement with the more expensive numerical simulations. Recent Progress At the Livermore and Los Alamos Laboratories the Monte Carlo simulation technique has been very much refined. The availability of the Cray computers, currently the world's largest, made it possible to study the OCP fluid and solid phases with simulations involving up to a thousand particles and tens of millions of configurations to be averaged. This is a model involving heavy (classical) ions moving in a nearly uniform density background of electrons. The internal energy results are good to four- and five-figure accuracy, and the pair distribution function is known everywhere to better than a fraction of 1 percent. The OCP thermodynamic functions are now known better than those for any other simple liquid, including even the well-studied hard-sphere system. With the very exact Monte Carlo results as a guide the HNC equation was modified by the inclusion of an approximate bridge graph function. This is an integral equation approach to the problem that computes more rapidly (by a factor of 1031. When solved numerically, the internal energy from this equation agrees with the Monte Carlo results to within the level of the Monte Carlo noise. This is a

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GENERAL PLASMA PHYSICS 139 remarkable agreement of a theoretical liquid-state calculation with numerical experiment, which opens the way for a wide variety of quantitative calculations of thermodynamic properties and transport properties of dense partially ionized plasmas and liquid metals. Spectral lines emitted by highly compressed targets in laser fusion experiments have provided another significant and useful connection between theory and experiment. At the densities and temperatures reached in these compression experiments, elements such as argon are ionized to the point that only one or two electrons are still bound. Thus it is now possible to study spectral lines from hydrogenic and helium- like argon. These lines are in the x-ray region and are broadened by the Stark effect owing to neighboring ions in the plasma. A by-product of the Monte Carlo simulation of the OCP has been an easy calculation of the electric microfield distribution needed for the calculation of spec- tral line shapes. The experimental measurement of several lines of the Lyman series has given a reasonable test of current line-broadening theories and the usefulness of the Monte Carlo microfield for predicting spectral line shapes from highly ionized strongly coupled plasmas. Outlook for the Next 10 Years Future improvement on present-day understanding of ionic matter will probably come about by a fully quantum treatment of strongly coupled plasmas. Considerable progress has already been made on the quantum many-body problem at zero temperature, and the properties of the electron gas at T = 0 have been computed. Work is proceeding rapidly on electron and proton systems, e.g., hydrogen, and it is expected that a detailed understanding of the formation of metallic hydrogen at high pressure will result. The next stage of this kind of investigation will require practical computing procedures for the quan- tum treatment of electrons and point nuclei at finite temperature, as for example, using the Feynman path integral method. As with the classical numerical simulation methods, the quantum plasma simula- tions will be costly and time-consuming numerical experiments. Clearly, strongly coupled plasma physics is an important area of research because of its astrophysical applications and technological applications. The level of research in this area is increasing rapidly in several countries around the world, and U.S. leadership is by no means assured during the 1980s. In the United States much of the important work in this field is done at national laboratories because of the availability of large computers and large laser systems. Only a few American universities have good research efforts where students can

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140 PLASMAS AND FLUIDS gain experience with established researchers. In spite of the U.S. advantage in large computers, a French group continues to make fundamental advances in both computation and basic theory. Several groups in Japan are attacking problems in strongly coupled plasmas such as simulations on liquid metals, laser-produced plasmas, and transport calculations for astrophysical plasmas. With the advent of the new Japanese supercomputers, it is certain that researchers in posses- sion of such computers, for example the Japanese groups, will become leaders in numerical simulation with both classical and quantum methods. For the United States to continue to make- significant contributions to strongly coupled plasma phenomena, it would be advisable to strengthen support for this area of physics in U.S. . . . universities. NONNEUTRAL PLASMAS A nonneutral plasma is a collection of charges that satisfy the usual many-body criterion to be a plasma but in which there is not overall charge neutrality. These systems usually have intense self-electric fields and may also have intense self-magnetic fields. They are called plasmas, even though they are not charge neutral, because they exhibit many of the collective phenomena characteristic of a neutral plasma. For example, many types of waves that are supported by a neutral plasma have nearly identical counterparts in nonneutral plasmas. For example, nonneutral plasmas exhibit the phenomena of Debye shield- ing, that is, the plasma particles act collectively to cancel (or shield) the field of an extra charge placed in the plasma. Nonneutral plasmas in the form of electron beams have been used in applications such as microwave-generating devices for many years (see section on Coherent Free-Electron Radiation Sources), but it was only within the last decade that nonneutral plasma physics was recognized as a separate subfield. Theoretical foundations of the subject were provided by many papers written in the 1960s. At the beginning of the 1970s, interest was stimulated by several experimental programs on toroidal confinement at the AVCO Corporation and on mirror confine- ment at the University of Maryland. In both cases confinement times of about 10 ms were reported. During the 1970s, theoretical studies continued on equilibria and stability for confinement in various magnetic field configurations and for relativistic as well as nonrelativistic plasma, the analysis of waves, and the development of transport theories. The experimental studies at AVCO and the University of Maryland terminated. Further studies of

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GENERAL PLASMA PHYSICS 141 magnetic confinement were carried out at Maxwell Laboratories, Inc., and the University of California, Irvine (UCI). A new experiment on a hybrid confinement system (Penning trap) was started at University of California, San Diego (UCSD). In the pure magnetic confinement experiments magnetic compression always produced a plasma of high density (n ~10~-10~ cm-3) and high temperature (104-106 eV). In the hybrid trap with confinement by electrostatic fields in one direction and magnetic fields in the other directions, densities are typically of order 107-108 cm-3 and the temperature is less than 1 eV. The pure electron plasma experiments are very clean and yield experimental data of high precision compared with conventional plasma experiments where ions because of their large mass create substantial difficulties for experi- m~ents and theory. Similar remarks apply to experiments with a small density of ions compared with the electron density. At present, experimental programs on the physics of nonneutral plasmas exist at UCSD, UCI, University of California, Los Angeles, and the University of North Carolina.. Although nonneutral plasmas have many properties in common with neutral plasmas, there are some interesting differences. For example, a nonneutral plasma consisting of only electrons (or only ions) can be confined forever, at least in principle, and this is definitely not the case for a neutral plasma. In confinement geometries for which the confining electric and magnetic fields have cylindrical symmetry, general stabil- ity and confinement theorems prove that a pure electron plasma (or a pure ion plasma) simply cannot escape. Of course, actual confinement systems cannot have perfect cylindrical symmetry; small construction and field errors or end effects break the cylindrical symmetry and produce a slow loss of the plasma. Nevertheless, pure electron plasmas have been confined for periods as long as a day, which is many orders of magnitude longer than the few second confinement times character- istic of neutral plasmas. (See Chapter 4.) Another difference concerns the possibility of cooling a pure electron plasma to very low temperatures, that is, to a degree or so above absolute zero. For a pure electron plasma, the electrons cannot recombine with ions to form atoms (as electrons would in a neutral plasma) since there are no ions in the confinement regions. Theory predicts that as the temperature of a pure electron plasma is reduced, the electrons will enter the liquid state and then the crystal state, that is, one will obtain a pure electron liquid and a pure electron crystal. An experimental program is under way at UCSD to realize these new states of matter in the laboratory, and there is preliminary evidence that the liquid state may have been obtained. Similar experiments are

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142 PLASMAS AND FL UlDS being carried out with a pure ion plasma at the National Bureau of Standards Laboratory in Boulder, Colorado. This general area of research should be quite exciting in the next few years. Note that this area of research overlaps and complements studies discussed in the section on Strongly Coupled Plasma Physics. Many applications of nonneutral plasmas have developed in the 1970s to a large extent the applications are much older and the importance of the nonneutral plasma was recognized more recently. For example, it was recognized that in a simple mirror the confine- ment in the axial direction is electrostatic; this led to the invention of the tandem mirror and the further refinement of thermal barriers to reduce thermal conduction along the field lines. In the large pulse power machines, the importance of magnetic insulation was recognized. In a magnetically insulated transmission line, the electric fields are so large that copious field emission of electrons takes place; however, with suitable magnetic fields the electrons are confined and do not short out the line. Magnetic insula- tion (confinement) plays a central role in power flow and ultimately limits the concentration of power. It also plays a key role in the design of ion diodes because the electron flow must be inhibited. The operation of relativistic magnetrons also depends critically on the principles of magnetic insulation. In the development of high-current accelerators, the toroidal con- finement of a pure electron plasma is of central importance and is being studied at NRL and UCI in programs to develop a modified Betatron. The electrostatic field of a confined column of electrons can be used to focus strongly a beam of ions. This is called a Gabor lens and was invented in 1947. Recent experiments at the University of Oregon have focused an millielectron-volt beam of ions to about 10 m with such a lens. This principle is central in efforts to develop compact ion accelerators called collective focusing accelerators; a linear accelerator is being studied at SNL (PULSELAC) and a cyclic acceleration experiment is under way at UCI (CFIA). (See section on Collective Focusing Accelerators.) A radial electric field together with an axial magnetic field can produce rotation of a plasma column that is much more rapid than a mechanical centrifuge can achieve. The radial electric field is associ- ated with a nonneutral plasma. The plasma-arc centrifuge for isotopic separation is being studied at Yale University. In summary, the last decade saw the field of nonneutral plasma physics established and a substantial base of knowledge developed. Techniques were borrowed from neutral plasma physics, and rapid

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GENERAL PLASMA PHYSICS 143 progress was made in understanding many of the similarities between nonneutral and neutral plasmas. Also, important differences were identified, and it was realized that some of these offer unique oppor- tunity for interesting physics research and for useful application. The occurrence of nonneutral plasma was recognized in many important applications. We expect that plasma physics will be broadened and enriched by the study and application in the next decade of nonneutral plasmas.