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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
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
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,
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.
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
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.
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.
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
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
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.
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
106 PLASMAS AND FL UlDS resonance effect, the phase of the electron's transverse velocity can be synchronized with the radiation electric field. This synchronism is maintained throughout the acceleration length. Problem Areas A number of issues remain to be solved before laser-driven acceler- ation schemes can become a viable alternative to conventional accel- eration mechanisms. Among the most important unsolved problems in this area is that of refocusing of the intense laser beam for multistage acceleration. The laser acceleration schemes mentioned previously are not compatible with single-stage acceleration of particles to tera- electron-volt energy levels. All of these schemes require multistage acceleration even if the ultrahigh field gradients can be achieved. For example, assuming a gradient of 108 V/cm for a laser-driven accelera- tor, lengths of 100 m will be required to reach tera-electron-volt energies. However, owing to the diffraction characteristics of radiation beams, refocusing methods will certainly be necessary to maintain a collimated laser beam over these distances. Because of the high intensity of these beams, conventional focusing procedures do not appear to be possible. Possible solutions to this problem may involve plasma self-focusing of laser light or the use of multilayered dielectric- coated laser waveguides. Recommendations for the Next 10 Years The subject area remains speculative, and as yet no configuration or scheme can be convincingly shown to be capable of achieving tera- electron-volt particle energies. Recently the DOE increased its support of laser-driven accelerator schemes to a level of $750,000 per year. This increase comes at an appropriate time in the evolution of this field, since many conceptual schemes have reached a point where serious detailed and costly studies will be required. It is therefore prudent to at least maintain the present funding level. As mentioned, a number of laser-driven accelerator schemes are under serious consideration and will require several years for evaluation. Upon completion of the initial phase (around 1986 or 1987) an advisory group consisting of laser, accelerator, and plasma physicists should be convened to evaluate comprehensively the progress and likelihood of success of the various acceleration schemes. A decision to change the funding profile for the various schemes could be made at this time based on the outcome of the review.
GENERAL PLASMA PHYSICS 107 The DOE was and probably will be the primary source of funds for laser-driven accelerator research. DOE funding started in 1976 at a $100,000 per year level until 1983, at which time it was increased to $750,000 per year. It is expected that this level will remain fairly constant until around 1986. At that time a major review will take place to decide the future funding profile. COHERENT, FREE-ELECTRON RADIATION SOURCES The possibility of developing lasers and masers in which the active medium is a stream of free electrons has evoked much interest in recent years. The potential advantages are numerous and include continuous frequency tuning through variation of the electron energy, and very high-power operation, since no damage can occur to this lasing medium as can happen in solid, liquid, and gas lasers. The concept of transforming the kinetic energy of free electrons into coherent electromagnetic radiation is by no means new; as early as 1933, P. Kapitza and P.A.M. Dirac predicted the possibility of stimu- lated photon scattering by electrons. Indeed, the klystron, the magnetron, and the traveling-wave tube conceived and developed in the 1940s and 1950s are examples of such free-electron sources capable of generating coherent microwave radiation. In the decameter- and centimeter-wavelength ranges, these devices can be made to emit at power levels as high as tens of megawatts and with good efficiencies exceeding 60 percent. Today these systems, and variations thereof, have become indispensable instruments of modern science, technol- ogy, and communication. The new generation of free-electron radiation sources being actively pursued at many centers aim to extend the electromagnetic spectrum from the microwave to the millimeter, infrared, visible, and ultraviolet regimes with previously unattainable intensities and efficiencies. Po- tential applications are numerous. They include the following: (a) Spectroscopy. This area involves spectral studies in condensed- matter physics and of atoms, molecules, and ions; isotope separation; surface studies in the presence of absorbed molecular species; dynam- ics of charged carriers in semiconductors; fast chemical kinetics; and photochemistry . (b) Accelerators. High-power microwave tubes have traditionally been important in the development of radio-frequency (rf) accelerators. The development of high-power, centimeter-wave sources could be of much value for the high-energy-accelerator community. Conventional
108 PLASMAS AND FLUIDS rf accelerators use microwave klystrons operating in the vicinity of 25 MW of peak power. Recent developments indicate that the novel sources could operate at hundreds of megawatts or even gigawatts. These higher powers translate into fewer power tubes; the use of centimeter waves could lead to higher average accelerating gradients and therefore shorter accelerators. (c) Radar. Most radar applications have been at microwave frequen- cies (centimeter waves and longer), owing primarily to the availability of power tubes and components and to the low atmospheric losses at these wavelengths. Since the new sources can operate in the millime- ter- and submillimeter-wavelength regions, applications to future ra- dars are possible. Relative to conventional microwave radars operating at millimeter wavelengths the new systems would have narrow beam widths, large bandwidths, and small antennas. Narrow beam widths would, for example, be important in low-elevation-angle tracking. Large bandwidths enhance resistance to electronic countermeasures and permit high resolution. Millimeter waves are less affected by fog, clouds, rain, or smoke than are optical or infrared waves. (d) Thermonuclear Fusion. The problems of plasma heating are still impeding the practical development of magnetic fusion power reactors. The development of high-power sources at millimeter wavelengths could solve some of these problems. Furthermore, there is now good evidence that electromagnetic waves can drive current in tokamaks, thus opening the possibility of initiating current flow (ramp-up) in tokamaks or even steady-state tokamak operation. In addition to the above, one can perceive applications in biology and medicine, and as is true for all new advances in technology, the ultimate and most important applications have yet to be identified. The fundamental principle operative in all free-electron radiation sources is electron bunching in the presence of an ambient electromag- netic field. The field can be externally applied, or it may be emitted spontaneously by the accelerating electrons. In a system properly prepared, as for example by judicious phasing of the If field, the electrons initially distributed at random can be made to form clusters. If the dimensions of the clusters are comparable with or smaller than the wavelength of the desired radiation, each cluster radiates in a coherent manner like a giant electron. The newly produced radiation reinforces the original field, which leads to even tighter clusters, and so on. Thus, the principle of bunching is synonymous with the stimulated emission well known in conventional lasers.
GENERAL PLASMA PHYSICS 109 The three most prominent free-electron radiation sources actively studied during the past several years are (a) cyclotron resonance masers (CRM) of which the gyrotron is a typical example; (b) the free-electron laser (FEL); and (c) the relativistic magnetron. Of the three, the gyrotron is by far the most advanced as a practical device and at present offers the most efficient means of generating intense radiation in the centimeter- and millimeter-wavelength ranges. The FEL has great potential of becoming a promising source at submil- limeter wavelengths; and the relativistic magnetron has produced unprecedented power levels (~1-10 GW) at centimeter wavelengths. The CRM consists of a beam of monoenergetic electrons streaming along and gyrating in an external guiding magnetic field. The emission mechanism is essentially stimulated synchrotron (or cyclotron) radia- tion. Electron bunching is in the azimuthal direction and leads to the formation of clusters that rotate about the magnetic field lines. The radiation frequency is approximately equal to the electron-cyclotron frequency. In an FEL a beam of monoenergetic electrons is injected into a spatially periodic magnetic (wiggler) field, which imparts an undulatory motion to the electrons. Here electron bunching is axial, that is, in the direction of electron flow. The wavelength of the radiation is propor- tional to the wiggler periodicity. The constant of proportionality depends on the speed imparted to the electrons at the gun. For electrons whose velocity is much less than the speed of light, the constant of proportionality is approximately unity. However, when a high-voltage accelerator is used to produce electron speeds that approach the speed of light, the constant of proportionality can be very small compared with unity, and extremely short wavelength radiation can be thereby achieved. In the relativistic magnetron a relativistic electron stream passes over a periodic assembly of resonators in which electromagnetic radiation is induced and stored. High powers are achieved by using field-emission cathodes to create extremely high current streams. The radiation wavelength is approximately equal to the spacing between resonators. Some outstanding problems are the following: (a) Accelerators. Novel free-electron radiation sources are charac- terized by high-voltage (100 kV-100 MV), high-current (10 A-10 kA) electron streams of superior quality (low emittance). Thus, achieve- ments in the field of radiation sources will be closely linked with progress in accelerator technology and beam-production capabilities. -
110 PLASMAS AND FLUIDS This is particularly true in the case of free-electron lasers, which require accelerators that are at the limits of present-day capabilities. Advanced designs of electron guns and beam-focusing techniques will have to be studied. (b) rf Power-Handling Capabilities. Extremely high levels of elec- tromagnetic radiation require design and development of new millime- ter- and submillimeter-wave components including detectors, mirrors, mode converters, attenuators, and spectrum analyzers. Even at low power levels, development of millimeter and submillimeter hardware is urgently needed. (c) Mode Control. At short wavelengths, the electromagnetic modes in millimeter-wave resonators or optical cavities are closely spaced in frequency. Thus the systems may oscillate simultaneously in two or more modes, which leads to loss of efficiency and degradation of spectral purity. Novel ways of mode control will require further study. (d) Collective and Nonlinear Phenomena. At high currents self- fields associated with the electron streams become prominent and affect the radiation growth rate and spectrum. Furthermore, at high radiation levels, nonlinear wave-particle interactions limit the device efficiency. Both problems have been addressed, but further theory and computer simulations will be required in the future. (e) Personnel. The most urgent problem facing progress in the area of electromagnetic sources is the catastrophic lack of qualified physi- cists and engineers. The generation of outstanding people trained during World War II and their immediate descendants kept the field alive until the late 1950s, at which time enthusiasm diminished. From then on the training of young people virtually ceased. Since the advent of the novel sources in the late 1970s and the importance of rf heating in thermonuclear fusion research, interest has once again been on the increase. However, a crash training program at universities would be necessary for the United States to keep abreast of the research and development in foreign countries. Funding for research and development in coherent free-electron radiation sources has come primarily from DARPA, ONR, AFOSR, AFSC, and NSF. Between the years 1979 and 1983, the funding level totaled approximately $24 million. The total projected level for the years 1984-1985 is approximately $16 million. The overall funding is adequate, but more is needed for basic, university research in this area.
GENERAL PLASMA PHYSICS 1 1 1 ELECTROMAGNETIC WAVE-PLASMA INTERACTION Scattering and Absorption of Electromagnetic Waves by Plasmas The advent of powerful lasers has led, in the past 10 years, to the discovery and understanding of nonlinear phenomena occurring when matter is subjected to intense electromagnetic radiation. The efficiency of absorption of laser light sensitively affects the feasibility of inertial confinement fusion, in which pellets containing deuterium-tritium fuel are compressed and heated by laser-driven ablation. In early experi- ments, energy absorption was found to be lowered by nonlinear processes in the plasma corona, which quickly forms around the solid core of the pellet. Studies of these phenomena both in small-scale experiments and in those involving the largest existing lasers, coupled with extensive numerical simulations, have confirmed many theoretical predictions and have led to the partial control of the deleterious effects, mainly by the use of shorter-wavelength radiation. Absorption of laser light occurs near the critical layer in the corona, where the plasma frequency up is equal to the light frequency DO- The corresponding plasma density is 102~ cm-3 for 1.06-,um light from Nd-glass lasers and 10~9 cm-3 for 10.6-~m light from CO2 lasers. Three processes can cause absorption: (1) classical collisional absorption, or "inverse bremsstrahlung," (2) resonance absorption, and (3) the parametric decay and oscillating two-stream instabilities. The most benign of these mechanisms is inverse bremsstrahlung, which in- creases with laser frequency (because the critical density, and hence the collisionality, is increased) and also with density scale length (because a discontinuous density jump would act like a mirror). Resonance absorption occurs when light is incident at an angle to the plasma normal so that the electric field vector has a component along the density gradient. Plasma waves are then generated at the expense of electromagnetic energy, and the plasma is heated by the damping of these waves. The copious production of superthermal electrons (and of fast ions accelerated by the charge separation electric field) is a dominant feature of long-wavelength experiments, such as with CO2 lasers, and makes resonance absorption an undesirable mechanism. The most devastating effect of fast electrons is their ability to penetrate into the solid core of the target and preheat it, thus preventing its compression to the density required for fusion breakeven. Parametric instabilities involve the unstable decay of light waves, plasma waves, and frequency-shifted light waves. A large step in the theory of these instabilities was made about 10 years ago. Subse
1 12 PLASMAS AND FL UIDS quently, these phenomena have been detected and verified experimen- tally, both in basic experiments and in solid-target shots at large laser installations. Parametric instabilities can be classified into critical phenomena occurring at n = nc or NO = op. quarter-critical phenomena occurring at n = ncl4 or HO = 2mp, and underdense phenomena occurring at n < nc/4 or up < mo/2- The first class contains the parametric decay and oscillating two-stream (OTS) instabilities men- tioned earlier. The OTS has been seen only in its nonlinear soliton stage, but the former has been studied meticulously in large-scale microwave experiments. In laser experiments there has been little evidence of the importance of these parametric instabilities to absorp- tion. Phenomena at quarter-critical density include the two-plasmon de- cay and absolute Raman instabilities. The latter is a limiting case of the stimulated Raman scattering (SRS) instability discussed below; the former is a stronger eject involving the generation of two plasma waves, preferentially at 45° to the laser beam. The main features of the two-plasmon decay instability were confirmed in a basic experiment in which the decay waves were detected by Thomson scattering. This instability also produces fast electrons and is often seen in solid-target experiments from its characteristic signature of scattered light at a frequency (3/2~(0o At densities below quarter-critical, the main effects are filamentation and the SBS and stimulated Raman scattering (SRS) instabilities. Filamentation is the tendency for laser light to break into small beams by creating plasma channels with its own ponderomotive force. Though indirect evidence for this is available, there has yet been no systematic study of filamentation. SBS is an insidious instability in which ion acoustic waves are generated in the plasma, and these act as a grating to reflect the incident light. This predicted effect was first found in small-scale experiments at universities and has been under intensive study at these institutions. Since SRS also generates fast electrons to preheat the core of fusion pellets, the suppression of this instability is of great benefit. By contrast to magnetic fusion, where heat transport by electrons is anomalously fast, a major problem in laser fusion is that heat transport is anomalously slow, about an order of magnitude below the rate calculated from classical collisions. Rapid heat transport is needed laterally to smooth out irregularities in energy deposition from the laser beam, and rapid transport in the forward direction is needed to carry
GENERAL PLASMA PHYSICS 113 heat from the critical density layer to the ablation surface, where the heat is converted to kinetic energy of ablating plasma. That the large currents of heated electrons in a laser-irradiated target can produce multimegagauss magnetic fields has been known since the early 1960s. More recently, large magnetic fields in high-power laser experiments have been detected elegantly by Faraday rotation, and detailed probing of the field structure has been done in microwave experiments. Recent computer simulations and CO2 laser experiments clearly demonstrate the spontaneous generation of magnetic fields and their effect on electron orbits and energy deposition. Since there are several different mechanisms for magnetic field production and since the problem is basically three-dimensional, progress on this compli- cated problem must wait for increased computational capabilities in the next decade. On the optimistic side, one can hope that the production of fields in the 100-MG range by lasers will eventually permit studies of matter in which the atomic structure has been altered by a magnetic field. In summary, the theoretical and experimental discovery of paramet- ric instabilities and the agreement that has been achieved between theory and experiment represent a significant advance in the develop- ment of plasma physics in the past decade. Several large problems remain to be solved, notably the general nature of heat transport in the long mean-free-path regime and the nature and effects of self-generated magnetic fields. Progress on these problems in the next decade will solidify our understanding of how intense electromagnetic waves interact with matter. Funding for laser-plasma interaction studies in small university efforts amounts to less than $0.6 million annually. Fortunately, these programs are supplemented by several university groups in Canada and by a sizable portion of the total effort at the three intermediate-to-large laser installations at the University of Rochester, the Naval Research Laboratory, and KMS, Inc., in Ann Arbor, Michigan. Furthermore, part of the program at the large national laboratories, Livermore and Los Alamos, has been devoted to the understanding of the basic mechanisms operative in the corona. A disproportionately small frac- tion (perhaps 1 percent) of the national budget on inertial confinement finds its way to programs in which the training of students takes place, and consequently the demand for personnel with experience in laser and plasma experiments is quite heavy. A doubling or tripling of support in this area is easily justified.
1 14 PLASMAS AND FLUIDS Isotope Separation The separation of isotopes by use of a plasma has been studied since the Manhattan Project of World War II. At that time the decision was made to proceed with both an electromagnetic-based system (the calutron) and a gas-dynamic-based system (the gaseous diffusion plant). Both of those techniques are still in use today for separating isotopes. The gaseous diffusion plants are large power-intensive units that are principally used for processing large quantities of material (i.e., light-water reactor fuels). A less power-intensive approach would result in a significant increment to the total U.S. power capacity. The calutrons are still in use to provide small quantities of isotopes needed for research studies or for medical purposes. The calutron is a large 180°-reflection mass spectrometer operated in a high-current regime where the space-charge forces of the ion beam are large. The calutrons provide a high degree of separation but have a limited throughput or production capability. This limited production does not allow full utilization of possible applications for isotonically pure material. The years since the Manhattan project have been devoted to the study of basic plasma physics, and out of this have come several new approaches to electromagnetic isotope separation. These plasma-based approaches appear to overcome some of the constraints of the cur- rently available approaches. These techniques developed within the last 10 years have been made possible by the years of basic plasma- physics research that laid the foundation. The electromagnetic separa- tion processes are of interest since they are insensitive to specific materials, unlike laser-based processes, which depend on the elec- tronic structure and thus are limited to specific materials. One of these approaches is based on the ion cyclotron resonance in a uniform magnetic field. When a plasma is immersed in a magnetic field the particles undergo an oscillatory motion about the field lines. The frequency of oscillation is a characteristic depending on the charge-to-mass ratio of the ion and the strength of the magnetic field. By applying an electric field of known frequency the particle distribu- tion functions can be modified. If the frequency is high and matches the electron cyclotron frequency, then the electrons are heated. By selectively energizing one of the species the velocity distribution can be modified to allow a physical separation to occur on a collecting structure. A program to study this has been ongoing since 1974 at TRW and has been successful in being applied to a wide class of materials. Devel- opment of this technique for isotope separation is funded by the
GENERAL PLASMA PHYSICS 115 Department of Energy. The primary emphasis of this program is the separation of the isotopes of uranium for nuclear-reactor fuels. These developments have been performed in a prototype facility utilizing a 2.2-tesla, 0.5-meter-long, 0.1-meter-diameter superconducting magnet system. The process utilizes an electron cyclotron resonance plasma source with the production of the metal neutrals occurring by sputter- ing. These heavy-ion plasma sources have operated in the range of 1-10 mA per cm2. The separation of isotopes occurs after the selective energization of one of the isotopes via ion cyclotron heating. The ion cyclotron separation process, however, occurs in a uniform magnetic field. This allows detailed comparisons of the experiments with the theoretical calculations. The verification of isotopic selectivity by separation has been shown for several elements. For these elements macroscopic samples have been collected, removed from the device, and analyzed. Samples of potassium, nickel, indium, lead, and uranium have been collected. For the nickel separations, material has been enriched from 67.6 percent nickel-50 to 97 percent nickel-58 in a single pass. Delivery of nickel samples for use in neutron activation diagnostics has been made. In the lead separations significant enrichments were observed for the much smaller relative mass separation. In addition to the collected samples diagnostic measurements over a wide range of materials have shown the broad applicability of this technique. Another promising approach to isotope separation has been pro- posed recently at Yale University. This is a vacuum-plasma-arc centrifuge. The gas-dynamic centrifuge in use for the separation of isotopes improves with rotation speed. The increases in velocity are limited by material constraints. A plasma in a magnetic field offers the possibility of a much higher rotational velocity. A major problem that occurs is the formation of a stable arc discharge along and across the magnetic field. It is the radial space-charge electric field crossed with the axial magnetic field that gives rise to the large rotation velocities. The collisional relaxation of the plasma then gives a radial profile that varies for each isotope. The basic research on the vacuum arc in an ambient magnetic field has allowed the use of the plasma centrifuge as a means for separating species. These applications of the fundamentals of plasma physics have led to an enhanced capability. Previously isotopic uses were restricted to either very small or very large quantities. Both of these techniques offer the potential to separate intermediate quantities of material. The implications of this will evolve as the applications for isotonically selected materials emerge. Particularly in the nuclear environment of
1 16 PLASMAS AND FLUIDS both fission and fusion this capability can be used to reduce the structural radioactivity associated with their implementation. A second area where potential uses of isotonically engineered materials are large is in medical diagnostics. Since the advent of the CAT scanners the diagnostic information available has grown quite fast. Because of this increased diagnostic capability, and the concern over the radiation hazards of these scans, work has been proceeding rapidly with the development of alternatives. Recently dramatic advances in whole- body nuclear-magnetic-resonance (NMR) scans have been achieved. Further advances may be obtained by utilizing samples tagged with isotopes that have a given magnetic moment. Diagnostic measurements of the metabolic processes may be possible. The contributions of these outgrowths of fundamental research will be seen in the years to come. NONLINEAR PHENOMENA IN PLASMAS The past 10 years have seen enormous fundamental advances in the understanding of nonlinear phenomena in plasmas. These advances have contributed greatly not only to plasma physics but also to other fields where the understanding of plasmas is important (particularly space physics and astrophysics) and have also influenced the develop- ment of nonlinear theory in general. In the following subsections we discuss some of these advances. The topics discussed are by no means meant to form a complete enumeration of these advances. Rather, our purpose is to indicate the character and flavor of the research and accomplishments in nonlinear plasma phenomena in the past decade. We therefore limit our detailed discussion to a few illustrative topics. Chaos in Hamiltonian Systems According to the Kolmogorov-Arnol'd-Moser (KAM) theorem, a small perturbation to an integrable Hamiltonian system will leave intact the topology of most of the phase-space orbits. On the other hand, it is known from numerical experiments that sufficiently large perturbations can convert the vast majority of the phase-space orbits to ones that have chaotic and ergodic properties on a large scale. How does the transition from one type of motion to the other occur as the perturba- tion is increased? This question has been of great interest to plasma physicists principally because of two applications: (1) the problem of characterizing the topology of the path followed by a magnetic field line and (2) the problem of discovering how a charged particle moves in inhomogeneous electromagnetic fields. The single most significant
GENERAL PLASMA PHYSICS 117 advance in Hamiltonian ergodic theory in the last decade is related to the above-mentioned question. In particular, it is now fairly well understood how the last phase-space dividing orbit dies. Beyond the destruction of the last confining phase-space orbit, plasma physicists have also been intensely interested in the diffusive properties of orbits for situations with widespread chaos. Successful techniques have recently been formulated by plasma physicists for calculating the resulting diffusion coefficients, in some cases analyti- cally. Generally, these results show a correction to the quasi-linear estimate. Plasma-physics applications of the above basic theoretical developments have been made to the stochastic heating of plasmas by the absorption of externally launched waves, to the ergodic trajectories of wave packets of plasma waves, to the confinement of particles in the presence of collective fluctuations, to the theory of particle transport in rippled magnetic fields, and to the breakup of nested confining mag- netic surfaces in fusion devices (e.g., tokamaks), among others. Soliton and Related Phenomena In a nonlinear wave, the nonlinear effect can often balance the dispersive effect, resulting in very stable nonlinear, nondispersive pulses called solitons. These solitons emerging from collisions with each other remain unchanged except for their phases. Soliton solutions have been found in many nonlinear wave equations of physical interest using the inverse-scattering method, first discovered by plasma theo- rists in 1967 for solving exactly the Korteweg-deVries equation, unifying a wide range of scientific endeavor. The ion acoustic solitons and their collisions were observed experimentally in 1970. Solitons in inhomogeneous plasmas were also studied theoretically and experi mentally. Soliton research has extended to many branches of physics, such as high-energy physics, solid-state physics, and optical communications, as well as to other fields. Early studies were done with simplifying assumptions of one dimension without magnetic field, dissipation, or instabilities. Recently, solitons in two and three dimensions have been investigated. As the magnetized plasma supports many natural oscil- lations with rich dispersive and nonlinear properties, it is an ideal medium for soliton studies. Indeed, solitons of upper hybrid and lower hybrid waves as well as waves at cyclotron frequency and Alfven frequency have been studied theoretically. The recently developed concepts for the studies of chaos very likely would help us to understand the behavior of more-complicated systems containing all
1 18 PLASMAS AND FF UlDS nonlinear, dispersive, unstable, dissipative effects. The chaotic motion of solitons would be one of the interesting future subjects. Strong Langmuir Turbulence Weak turbulent processes, i.e., nonlinear wave-wave scattering and nonlinear Landau damping of (Langmuir) plasma waves, tend to transfer wave energy to long-wavelength modes, leading to condensa- tion on the longest-wavelength mode. However, the long-wavelength mode is unstable to modulational instability because the ponderomo- tive force of the field intensity pushes on the plasma particles to create a cavity (caviton), which in turn traps more waves, leading to the collapse of Langmuir waves into patches of wave packets of the order of 10-Debye lengths. This Langmuir collapse thus provides a natural sink for the wave energy at long wavelength, and a complete descrip- tion of Langmuir turbulence is within reach. Since collapse was first proposed in 1972 there have been intensive theoretical efforts because of its importance in laser-plasma and relativistic beam-plasma interac- tion. Evidence of cavitons was reported in microwave-plasma reso- nance and in beam-plasma experiments. This has since been shown to be an important mechanism also for beam-plasma interaction in space. Parametric Instabilities Parametric decay of a large-amplitude wave into two daughter waves has been extensively studied in plasmas because of its importance to the wave heating of magnetically confined plasmas and laser-plasma coupling in inertial fusion experiments. Indeed, such parametric wave coupling is the basis of the free-electron laser described in a previous section. Many basic experiments were performed in magnetized plas- mas with a wide range of pump frequencies to observe the threshold pump power and resulting anomalous absorption. In the past decade, theoretical progress has been made in the effects of plasma inhomogeneity on the threshold power for the excitation and nonlinear effects of parametric instabilities. Magnetic Reconnection According to the "frozen-in" theorem of ideal magnetohydrodynam- ics (MHD), magnetic flux lines in a plasma behave as if they were tied to the motion of the bulk plasma; in this sense, magnetic topology is preserved under plasma motions. However, plasma resistivity allows a
GENERAL PLASMA PHYSICS 1 19 magnetic topology change. For example, magnetic fields with opposite directions separated by a current sheet can reconnect by forming magnetic islands. Such relaxation of topological constraints, or recon- nection, is often accompanied by a significant release of magnetic energy. The rate of reconnection is thus an outstanding question of plasma physics and finds application in fusion devices, solar flares, and magnetospheres. Considerable progress has been made in understand- ing this phenomenon in the past 10 years. The reconnection starts with an exponential growth of a small- amplitude perturbation with growth time much shorter than resistive skin time. This exponential growth phase ceases at a relatively small island size to be followed by an algebraic rate proportional to the resistivity. Resistive MAD equations were solved numerically, and results were applied to a cylindrical or a toroidal plasma (as in a tokamak or perhaps a solar hare). The growth of the magnetic island is shown to lead to nonlinear coupling to modes of different helicities resulting in ergodic field-line behavior (as discussed in the previous section) and ensuing anomalous plasma heat loss. In addition to the work on spontaneous reconnection, reviewed above, much notable progress has also resulted from research on forced reconnection, with applications to laboratory plasmas and space plasmas (e.g., knotting of magnetic field lines in turbulent solar convection zones and solar wind-magnetopause interaction). The past decade has seen much progress on tearing modes and reconnection processes in laboratory experiments. Extensive measure- ments were made on the nature of tearing modes and their nonlinear consequences such as minor (internal) and major disruptions in tokamaks. Basic experiments on forced reconnection were also carried out for detailed measurements of the properties of the neutral sheet including the three-dimensional particle-distribution function and fluc- tuations. Turbulent Relaxation to Force-Free States In experiments with the reversed field pinch, it has been observed that the plasma first passes through a highly turbulent phase after which it settles down to a steady and relatively quiescent configuration with the toroidal field reversed on the outside. One of the major advances in plasma turbulence has been the understanding of the turbulent processes leading to the relaxation to the final state and of the nature of that state. This understanding has been achieved through an interplay of theoretical analysis, computer simulations, and laboratory
120 PLASMAS AND FLUIDS experiment. Within the framework of resistive MHD turbulence, the theory postulates that the quiescent, final state is the one with minimum magnetic energy subject to the constraint of magnetic helicity A BdV = K (A and B are the magnetic vector potential and the magnetic field, and the integration is over the entire plasma volume V). The predicted state explains many observations in pinch experiments, and the sustainment of this state over a period much longer than the resistive skin time suggests the importance of dynamo action, a process that is being actively researched. Other Major Achievements in the Past Decade in addition to the above-discussed achievements of nonlinear plasma physics, we note the following equally important additional advances. Double layers (plasma layer structures across which the electrostatic potential experiences a jump) are now fairly well understood theoret- ically and in laboratory experiments and have, in addition, been observed to be of great importance in space plasmas. Collisionless shock waves (shocks in which dissipation of energy in large scales occurs by transfer to small-scale collective modes and by collisionless kinetic particle effects rather than by particle-particle collisions) are now much better understood; this knowledge has found application in space physics and astrophysics. New approaches to the problem of determining the observed anom- alously large particle and thermal transport in magnetically confined plasmas have been formulated using renormalized turbulence theory (e.g., the "direct interaction approximations. Strange attractors have been shown to occur in certain nonlinear plasma situations. Lie algebraic techniques have been developed to a high degree of sophistication for a variety of situations in nonlinear plasma theory. Finally, our computational tools for examining nonlinear plasma phenomena have greatly expanded as a result of the development of innovative new numerical algorithms and concepts. PLASMA THEORY DEVELOPMENTS RELATED TO MAGNETIC CONFINEMENT More than half of the federal funding of plasma-physics theory over the past decade has been in connection with the magnetic-confinement approach to controlled thermonuclear fusion. Thus, many recent plasma-theory developments have been in this context. A summary of
GENERAL PLASMA PHYSICS 121 how these developments have aided fusion research was presented earlier in this chapter. Here, we briefly review some examples of the more basic aspects of plasma theory developed in the magnetic- confinement fusion program. Magnetic-Flux Geometries and Coordinate Systems While some magnetic-plasma-confinement schemes have an ignor- able coordinate (e.g., the toroidal angle in tokamaks) the magnetic structures in most (e.g., tandem mirrors and stellarators) are fully three-dimensional. Considerable progress has been made over the past decade in developing large computer codes to calculate relevant magnetic fields with and without plasma. Further, magnetic-fiux coor- dinates are developed from these results and, since the motion of single particles within magnetically confined plasmas is quite complex and determined by the direction of the magnetic field and its gradients, they are utilized for almost all of magnetic fusion theory. Finally, criteria have been developed for when magnetic-flux surfaces cannot be defined because the magnetic field lines become stochastic (at least in some region), typically because of the overlapping of magnetic islands that are due to resonant magnetic perturbations of incommensurate helicity or pitch. Single-Particle Orbits In the small gyroradius expansion appropriate for most magnetically confined plasmas, the particles gyrate (in cyclotron motion), bounce (in motion along the magnetic field), and drift (in a direction perpendicular to both the magnetic field and its gradient) on successively longer time scales. Previously, these various motions have been derived by suc- cessively expanding and averaging Newton's law with a Lorentz force. Recently, a powerful (but noncanonical) Hamiltonian formulation of these orbits has been developed and utilized to calculate higher-order (in the small gyroradius expansion) corrections to the orbits. Also, the degree to which the magnetic moment is adiabatically conserved has been explored through both Hamiltonian transformations such as those indicated above and by mapping techniques. For slightly nonadiabatic motions, and also for the transition to stochastic magnetic fields, some techniques have been developed to characterize the motion in phase space in this transition to diffusive behavior in the totally stochastic . . . quasi- Near regime.
122 PLASMAS AND FLUIDS Coulomb Collisional Processes Coulomb collisions provide the irreducible minimum transport in magnetically confined plasmas. The Coulomb collision operator is a second-order differential operator in velocity space of the Fokker- Planck type. Elaborate two-dimensional (the gyrophase angle is aver- aged out) computer codes have been developed over the past decade to solve for the distribution function in the presence of collisions and various velocity space loss regions. Also, the collisional scattering rates into loss cones, over potential barriers, and into pumped regions of velocity space, have been calculated analytically. When there are not substantial loss regions in velocity space, as for example in most toroidally confined plasmas, the distribution function becomes nearly Maxwellian and the spatial gradients of density and temperature provide the forces that are related through an Onsager matrix of transport coefficients to the particle and heat fluxes in the plasma. To calculate the transport coefficients in magnetized toroidal plasmas, account is taken of the gyromotion (classical transport) and bounce and drift motions (neoclassical transport) of the nearly collisionless plas mas. Macroscopic Equilibria In plasma physics a system is said to be in macroscopic equilibrium when the forces on the plasma are in balance. Usually such force balance equilibria are calculated in an ideal magnetohydrodynamics (MHD) model. Two-dimensional magnetized plasma equilibria can often be calculated analytically, but fully three-dimensional high-pres- sure equilibria usually are calculated numerically or utilizing expansion parameters, usually weak toroidicity or long-thin cylinder approxima- tions. In addition, recently some primarily numerical models have been developed for anisotropic-pressure (perpendicular pressure different from that parallel to magnetic field) MHD equilibria, such as those occurring in tandem-mirror systems. Macroscopic Instabilitie~Ideal Magnetohydrodynamics When a plasma is placed on a ``magnetic hill,', it often develops a collective instability of the Rayleigh-Taylor type that allows it to fall off the hill at a very rapid (hydromagnetic or sound speed) rate. Magnet- ically confined plasmas are usually stabilized against such rapid losses by putting them in magnetic wells of an absolute or average (over the
GENERAL PLASMA PHYSICS 123 length of a field line) type. For the most common average magnetic wells an additional complication called a ballooning instability can arise. Here, for sufficiently high plasma pressures the plasma can collectively balloon in local magnetic-hill regions and can, at least theoretically, thereby escape the plasma-confinement region. Finally, in toroidal magnetic-confinement devices the plasma can kink into helical distortions of the original equilibria and again avoid confine- ment. Extensive and elaborate computer codes have been developed for investigating these possible macroinstabilities of confined plasmas. Macroscopic Instabilitie~Resistive Magnetohydrodynamics In toroidal magnetic-confinement systems, magnetic field lines can close back on themselves after an integer number of transits around the torus, thereby forming a rational surface. The finite (i.e., nonzero) resistivity of real, slightly collisional tokamak plasmas of current interest often allows collective plasma instabilities of a kink-tearing type to form near the low-order (i.e., ratios of small integers) rational surfaces. Such collective instabilities cause magnetic islands to occur at the rational surface and to grow in width linearly with time. Since these collective modes play such a central role in the macroscopically observable behavior of tokamak discharges, a number of precise nonlinear computer codes have been developed to model them, and the code predictions have been compared in great detail with experimental observations. In general they correlate very well and are among the best examples of nonlinear plasma phenomena that are well diagnosed and understood. Microscopic (Kinetic) Instabilities and Turbulent Transport When the macroscopic collective plasma instabilities have been eliminated or their ejects limited through careful tailoring of the magnetic-confinement system, there still remain more microscopic collective instabilities that can relax the sources of free energy (such as loss-cones and pressure gradients) in the plasma more rapidly than Coulomb collisional processes. The microscopic instabilities usually are derived from fully kinetic rather than fluid theories. In open-ended magnetic-confinement devices (e.g., magnetic mirrors) the empty loss cone in velocity space has been found to drive a wide variety of microinstabilities. These modes generally have frequencies near the ion-cyclotron frequency, so that the modes can tap the loss-cone source of free energy by destroying the constancy of the ion magnetic
124 PLASMAS AND FF UlDS moment. Correlation of numerical calculations of the quasi-linear (lowest-order nonlinear) effects of loss-cone modes with experimental results have generally confirmed the veracity of the theoretical models for these types of microinstabilities and the greatly increased loss rates they cause. In toroidal plasmas the density and temperature gradients provide the source of free energy for drift-wave-type microinstabilities in which the wave frequency is of the order of the Doppler-shifted frequency owing to the diamagnetic flows in the plasma. The expan- sion-free energy is tapped via additional effects that are due to finite ion gyroradii, including toroidal trapping of particles, toroidal drifts, and finite collisionality relative to the bounce motion. There has been extensive development of linear drift-wave instability theory toward making it applicable to plasmas confined in present tokamak experi- ments. Also, a number of nonlinear models (such as weak turbulence, strong turbulence, mode coupling, and the direct interaction approxi- mation) of drift-wave turbulence and its effect on plasma transport have been developed. While some of these models seem to be on the right track, in that they can clarify a number of generic features of anomalous transport, there is not yet any fully satisfactory theoretical model of the anomalous radial electron heat transport process in tokamaks. Summary Over the last decade, theoretical and computational tools for under- standing plasma confinement and heating in magnetic systems have developed tremendously, to the level where they can now, at least in many areas (Coulomb collisional effects, equilibrium, ideal and resis- tive MUD global modes) closely model the experimental observations with most of the important physical phenomena included. However, turbulent phenomena within the plasma, and the transport they induce, remain the major unresolved issues. ATOMIC PHYSICS IN (AND FOR) PLASMAS The importance of atomic processes in plasmas has grown with the advances in general plasma research. Several of these advances, in turn, became possible, e.g., through the development of intense neutral beams for plasma heating, i.e., via applications of atomic-physics methods. Much of the early progress in laboratory plasma physics evolved from gaseous electronics research in which a multitude of atomic and molecular reactions were investigated; likewise, major
GENERAL PLASMA PHYSICS 125 advances in fusion research and radiation-source development have strong roots in the study of atomic collisions and spectroscopy. Atomic physicists continue to be motivated in their research by these various challenging applications and by the great need for better atomic data in astrophysical research. There is also a symbiotic relationship between basic atomic-physics research and plasma physics because high- temperature plasma devices facilitate the study of highly ionized atoms. Examples of research areas that developed substantially in the early 1970s are analysis of atomic spectra from highly stripped metallic impurity elements, measurements of electron-ion collisional rate coef- ficients for ionization and recombination and corresponding calcula- tions, detailed line radiation loss calculations for candidate materials as limiters in tokamaks, calculations of Stark broadened x-ray lines for inertial fusion density diagnostics, and investigations of schemes for laboratory x-ray lasers. Considerable progress was made in calcula- tions of emission and absorption spectra of dense high-temperature plasmas, both for diagnostics and for energetics. Recent Progress Self-consistent calculations of plasma hydrodynamics and atomic radiation have become possible and are of great value in laser fusion research and in developing intense radiation sources. Improved diag- nostics of magnetic fusion plasmas were obtained by the use of newly measured magnetic dipole transitions in highly ionized iron group elements. Charge exchange from hydrogen into highly excited states of impurity ions has opened new possibilities for spatially resolved spectroscopic measurements in tokamaks. Results from plasma and crossed-beam experiments along with numerous calculations begin to provide a quantitative knowledge of dielectronic recombination. (This process tends to balance electron-ion collisional ionization of impuri- ties in most high-temperature plasmas.) Crossed-beam measurements have become available to check the calculations of excitation cross sections for complex ions of low charge states, while plasma measure- ments of excitation rate coefficients were made for ions up to Few+. Various high-power plasma devices for the generation of intense x-ray radiation were made operational and have become test beds for the study of high-density effects on atomic radiation. Computer simu- lations and laboratory experiments on x-ray laser schemes have advanced to considerable complexity. Much experimental evidence for population inversion was obtained, and there were some reports of net
126 PLASMAS AND FLUIDS gain in laboratory work at high plasma densities for photon energies up to 200 eV. Outstanding Research Problems Theoretical and experimental research leading to a self-consistent treatment of collisional and radiative interactions in dense plasmas containing highly but not completely stripped ions is required to provide sound foundations for several important applications in radia- tion-plasma dynamics. Effects caused by ion-ion collisions, including highly excited ions, on the overall dielectronic recombination need further study to supplement experimental work. The physics of elec- tron collisional ionization must be more fully understood in order to develop reliable calculational tools. The importance of resonances in electron-ion scattering on rate coefficients is still to be assessed. Cross-section measurements for excitation, ionization, and dielec- tronic recombination should be extended to more highly ionized atoms. Quantitative spectroscopy on well-diagnosed plasmas must be per- formed to test the validity of the corresponding atomic data base and reaction kinetics in real plasmas. Specifically for x-ray laser research on line pumping schemes, precision measurements of line coincidences and determinations of line shifts and widths at high-density plasma conditions are essential. Experiments designed to test reaction kinetics and to determine pump line intensities are needed as well. Correspond- ing investigations should be undertaken for other pumping schemes. The most promising laboratory x-ray laser scheme should then be selected and be pursued vigorously to demonstrate significant gain. For the magnetic fusion program, sources will have to be developed to produce neutral beams of energies '500 keV. Also, there is a great need for magnetic-field diagnostics, which could perhaps be met, for example, by laser spectroscopy of Zeeman effects in probe-beam atoms or ions. Recommendations Having concluded that understanding of radiation and other atomic processes in high-density, high-temperature plasmas is an interesting scientific as well as important technological goal, the main recommen- dations are as follows: · Establish a center for radiation physics to provide a national focus
GENERAL PLASMA PHYSICS 127 for research on modifications in atomic properties introduced by the presence of plasma. · Set up a national computer data base for atomic properties. Such a truly comprehensive effort would require close cooperation among several federal agencies and ingenuity transcending that usually found in data library construction. · Provide a dedicated facility for x-ray laser research to accelerate substantially laboratory research in this exciting area. Most likely this facility would be centered around a high-power laser, but other high-power plasma devices should be considered as well. · Encourage the full utilization of national experimental or theoret- ical users facilities (Texas Tokamak TEXT, University of Rochester Laser Facility, Magnetic Fusion Energy Computer Center) to optimize the research obtainable from limited resources. · Improve communications and encourage collaborations between plasma and atomic physicists. Training Basic atomic physics is actively pursued at many universities, typically by groups consisting of a single professor, a postdoctoral fellow, and one or two doctoral candidates, and at several national laboratories. Most often students emerge as highly specialized young scientists with little sense of the ramifications of their subjects on the broader applications, e.g., in defense or energy research. Postdoctoral research experience at one of the laboratories, centers, or national facilities would help considerably in providing the cross-fertilization required for productive research in the various applications. Closer collaboration among scientists in various disciplines is desirable, e.g., physics and astronomy departments could offer jointly atomic-physics and spectroscopy courses and could coordinate corresponding re- search. Course offerings should be re-examined to provide instruction in appropriate areas, e.g., in atomic structure theory, which has almost disappeared from the academic scene but may be important enough to be reintroduced into the curriculum. Closer collaboration between national laboratories and universities would heighten the awareness for such opportunities. It is estimated that about 200 scientists in the United States are engaged in atomic physics closely related to plasma research. This is of the order of 10 percent of the entire atomic-physics community in the United States. To provide for the anticipated growth in plasma-related atomic-physics research, small increases in the fraction of new Ph.D.s
128 PLASMAS AND FLUIDS going into high-density, high-temperature plasma research would be sufficient, provided that postdoctoral training is improved. Funding Levels The total federal funding level for atomic physics in and for plasmas, adjusted for inflation, has been approximately constant in the past 10 years and is at present estimated at $20 million nationally. Of this amount, well over half is available in national laboratories and at most 20 percent each in universities and industrial laboratories. Recommended Funding Levels In view of the critical importance and strong leverage of atomic physics in plasma research, a significant increase over present funding levels is recommended. Such increases should permit the establish- ment of the recommended new centers and facilities and a gradual increase in currently funded research and funding of promising new departures. PLASMA DIAGNOSTICS Measurement provides the basis for physical knowledge, and the techniques for measuring the properties of plasmas, generally referred to as plasma diagnostics, have played a critical role in advancing our knowledge of plasma physics and achieving the conditions required for fusion. The problems of measuring the properties of a plasma, for example density and temperature, are great, literally astronomical. The reason is that the extreme temperatures constrain one to observe from the outside, well removed from the hot gas itself. The techniques include those of classical astronomy: that is, passively observing the radiation from the plasma, both electromagnetic, over the full range of frequencies from radio to x-ray, and particle diagnostics. In addition, one can direct beams of electromagnetic or even particle beams into the plasma and examine the response, which is the method of several powerful diagnostic techniques. Nevertheless, the task of determining with strictly noninvasive techniques the many significant plasma parameters that are varying in complex spatial and temporal patterns remains a formidable challenge. To characterize the state of the plasma and evaluate progress toward the temperatures, densities, and energy confinement times required for fusion, many observations are required. Measurements of the temper
GENERAL PLASMA PHYSICS 129 attires of electrons and ions, of the densities of various ions other than hydrogen, of the currents and electric and magnetic fields within the plasma, and of the drift or rotation velocities are all needed. Since a hot plasma at a temperature of millions of degrees is necessarily far from thermal equilibrium with its surroundings, pro- cesses to heat the plasma are essential, and transport processes, processes that seek to cool the plasma to the temperature of the surroundings, will certainly occur. Understanding these processes is vital, and they are often found to involve instabilities' fluctuations, and turbulence. This requires techniques for measuring the variations in parameters, density, temperature, and fields, over the broad range of spatial and temporal scales that characterize these several processes. This constitutes a demand for an immense breadth and depth of diagnostic techniques. The problems and techniques are common to most magnetically confined plasmas. Diagnostics are always optimized for the parameters of each experiment, certain types of measurement are more important for some confinement geometries than others, and a few techniques are unique to particular types of devices. However, most basic measuring techniques are broadly applicable, and it suffices for this perspective to treat measurements on such devices as tokamaks, mirrors, and pinches together. We have made remarkable progress in this task within the past two decades. At the start of this period, our techniques were truly rudimentary. Metal probes were a major diagnostic, restricted to cold, low-density, or short-lived plasmas. For hotter, higher-density plas- mas, one could measure the density by interferometry but otherwise could not characterize the interior of a hot plasma in detail. As recently as a decade ago, hot plasmas could only be grossly described. Diagnostics were restricted to providing a few numbers, such as peak or average density and temperature, and perhaps a total energy confinement time to quantify the effectiveness of magnetic containment. There was little spatial or temporal detail or basis for inferring the processes that determined the densities and temperatures observed. Great improvements have been made over the past decade in each of these respects. Techniques with greater accuracy and better resolution have been developed for each quantity and combined in a panoply of diagnostics to give a comprehensive, composite picture of a plasma. There have been few singular events to dramatize our progress, but rather a continuing series of developments and improve- ments that only in retrospect can be recognized for the truly momen- tous advances that they constitute.
130 PLASMAS AND FLUIDS Laser Scattering Foremost among diagnostic developments over the past 20 years has been the establishment of Thomson scattering as a universal standard for determining electron temperature. Made possible by the develop- ment of high-power lasers, this physically simple scattering from individual electrons in the plasma has provided straightforward and indisputable measurements of one of the most important plasma properties. Historically, it furnished the first proof that tokamaks of modest size confined hot (several million degrees) plasma, thus starting the succession of larger devices, which have now virtually reached fusion temperatures. Thomson scattering is the benchmark for tem- perature measurements in all devices. Over the last decade, the tech- nique has been developed from a difficult measurement at a single point in space and time to an almost routine measurement of temper- ature simultaneously at many points, often giving an entire spatial profile. Microwave Interferometry Measurements of density have also improved steadily with the development of shorter-wavelength microwave and far-infrared interferometers. These have extended the measurements to higher density and finer spatial resolution. Spectroscopy Spectroscopy has always been an important plasma diagnostic technique, common to laboratory as well as astronomical plasmas, especially solar physics. The techniques had long been well established for cooler plasmas (much less than one million degrees), but the last decade has seen a great development in capability for spectroscopic measurements in hot plasma. Two sorts of information are generally sought spectroscopically. The first is impurity concentration the density of ions aside from hydrogen-and the second is the inferences that can be drawn from the Doppler effect on-line shape the temper- ature and velocity of the ion. Among the major developments in the past decade have been the discovery and cataloging of comparatively strong forbidden magnetic dipole lines in the spectra of highly ionized impurities. These lines are useful because they fall in the visible range of wavelengths, permitting all the established apparatuses and tech- niques to be applied to the high ionization states found in hot plasmas.
GENERAL PLASMA PHYSICS 131 (The more usual allowed transitions, the counterparts of those ob- served in cooler plasmas, fall in the vacuum-ultraviolet to x-ray range in hot plasmas where instruments are more complex and have less resolution.) By using these forbidden lines, Doppler measurements of ion temperatures approaching 100 million degrees have been possible, as well as measurements of plasma drift and rotation. Significant developments in instrumentation have also been made, especially at ultraviolet and x-ray wavelengths. Imaging spectrometers with multiwavelength detectors combine space, time, and wavelength infor- mation. The spatial distribution of an impurity ion, an ion temperature, or a drift velocity can be obtained from a single observation. Charge Exchange Besides measuring ion temperature by Doppler broadening, the traditional method of charge exchange has been refined and improved over the past decade. The principle is simple. Although the hydrogen in a hot plasma is nearly all ionized, a trace of neutral gas measured in parts per million remains. A neutral may exchange its electron with a hot ion, and the resulting energetic neutral, no longer confined by the magnetic field, may escape the plasma. Analysis of the energy of these neutrals indicates the temperature of the confined, hot ions. The instrumentation for these measurements has been improved greatly to detect emerging neutrals at all energies simultaneously, giving imme- diately the entire ion energy spectrum. This has complemented the major effort to heat plasmas by injecting energetic neutral beams. The charge-exchange diagnostics have documented our thorough under- standing of beam penetration and transfer of energy from the beam to the plasma. In reciprocal fashion, injected neutral beams have proven to be a valuable diagnostic in their own right, a capability that is only now being developed fully. Attenuation of the beam as it passes through the plasma gives valuable information, the augmentation of the charge-exchange signal by the injected neutrals gives ion temperatures with superior spatial resolution, and the neutrals drive charge- exchange reactions with impurity ions in the plasma, which have opened new possibilities for spectroscopic diagnostics with unique spatial resolution. Neutrons and Alpha Particles Another major diagnostic development of the last decade has been occasioned by the fusion reaction itself. As temperatures have ap
132 PLASMAS AND FLUIDS preached those required for fusion power, deuterium discharges have begun to produce detectable fusion. The energy spectrum of the emerging alpha particles in mirror machines has been most informa- tive, and the production of neutrons is used generally to infer ion temperatures. Developing capability to measure the energy spectra of the neutrons is providing more-certain measurements. Blackbody and Plasma-Well Interactions Reflecting the steady increase in sophistication of diagnostics have been developments like the demonstration that many plasmas behave as blackbodies at the electron cyclotron frequency, making a simple measurement of electron temperature possible. Techniques from sur- face physics have been adapted to study the interaction of plasma with the walls of the vacuum vessel and the introduction of impurities into the plasma. Broadband measurements of the total radiation from the plasma have been combined with various other diagnostics to allow detailed analyses of energy flows within a plasma. In the best cases, diagnostics are now sufficiently complete to imply values for transport rates, the thermal conductivities of ions and electrons in a particular experiment. Heavy-Ion Diagnostics One of the most obvious characteristic parameters of an electrically conducting medium like a plasma is the electric potential or electric field within the medium, but this has been notoriously difficult to determine for hot plasmas. One technique, the use of an energetic heavy ion beam, has been developed within the past 5 years and demonstrated on mirror machines and some other devices. Much more is expected from this diagnostic in the next decade. Time-Resolved Plasma Activity All of these diagnostics describe the equilibrium state of the plasma, including such parameters as the densities and temperatures of the components, with spatial resolution but on a time scale that is characteristic of the equilibrium. They do not reveal variations on a rapid time or spatial scale, yet we know such variations are phenomena of major importance in plasmas. Experimentally, fluctuations of some sort are seen in nearly every type of plasma. Theoretically, every plasma configuration seems subject to some sort of linear instability,
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
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
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
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
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
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
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
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
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
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
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.