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OCR for page 95
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
OCR for page 96
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
OCR for page 97
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,
OCR for page 98
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.
OCR for page 99
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
OCR for page 100
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.
OCR for page 101
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.
OCR for page 102
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
OCR for page 103
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
OCR for page 104
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.
OCR for page 105
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
OCR for page 133
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
OCR for page 134
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
OCR for page 135
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
OCR for page 136
136 PLASMAS AND FLUIDS
modus operandi, for it ensures that diagnostics are practical, usable,
and utilized on experiments. It should be complemented and supple-
mented by an increased effort, independent of specific devices, de-
voted to diagnostics that require longer development before being
ready for application to experiments and to diagnostic and computer
developments, which should be generally applicable or standardized.
STRONGLY COUPLED PLASMA PHYSICS
A strongly coupled plasma is a form of dense ionized matter in which
coulombic correlations among the charged particles determine bulk
and dynamic properties. The interaction coupling parameter defined as
the ratio of the average coulomb potential energy between particles to
the average kinetic energy for such a plasma is greater than unity and
for some systems much greater than unity. This degree of coupling is
in marked contrast to the more commonly studied laboratory plasmas,
which are low density and weakly coupled. A strongly coupled plasma
thus is a fluid that resembles a neutral electrically conducting liquid. At
sufficiently high density the coulombic correlations become so strong
that the fluid undergoes a first-order phase transition to a lattice.
Much of the matter in the universe is in the strongly coupled plasma
state since stellar interiors are highly ionized and often at very high
density. Physical systems that may be described as strongly coupled
plasmas include the following:
(i) Inertial-confinement fusion targets compressed by lasers;
(ii) Interiors of large planets;
(iii) Stars in late stages of evolution, e.g., red giants
(iv) Liquid metals;
(v) White dwarf interiors; and
(vi) Neutron star crusts.
History
It was recognized some decades ago that matter at extreme densities
has a significant limiting form in which the electrons because of the
large Fermi energy become nearly uniform in density. In this limit, one
will have a system of heavy (hence classical) ions or nuclei moving in
a background of electrons that provide electrical neutrality and stabil-
ity due to the large electronic pressure. For ionic matter formed from
a single element and a neutralizing background of electrons this limit is
called the one-component classical plasma (OCP). It has been the
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GENERAL PLASMA PHYSICS 137
subject of intense analytic and numerical study since it is the prototype
strongly coupled plasma and is essential for understanding the proper-
ties of the physical systems mentioned above. In the universe the OCP
limit is approached only in white dwarf star interiors, and thus it is
difficult to reach for experiments on the Earth. Conceptually the OCP
limit, however, plays the same role for strongly coupled plasmas that
the hard-sphere fluid plays for the theory of neutral liquids.
Cluster expansion methods used for dense gases and liquid-state
theory proved in the 1960s to be not particularly useful for strongly
coupled plasmas, and numerical simulation methods were developed.
In 1966, the availability of large computers at the Lawrence Livermore
Laboratory made it possible to carry out the first detailed study of the
OCP fluid state and to give some hint of the phase transition. The
Monte Carlo method was used. In this procedure a few hundred
charged particles are moved randomly in a three-dimensional cell in a
manner to give average thermodynamic properties equivalent to the
canonical ensemble of statistical mechanics. The simulation process
gives numerical results for the coulombic interaction energy and the
pair distribution function. The data thus obtained should be regarded as
the results of numerical experiments, which are subject to problems
typical of real experiments. Although the numerical simulation meth-
ods are slow and expensive, the data obtained have been invaluable
and have spurred major theoretical understanding of the properties of
the OCP and related strongly coupled coulombic systems.
The OCP equation of state was applied to white dwarf star structure
calculations and gave rise to the suggestion that the center of these
stars might be crystallized. The OCP pair distribution data were
Fourier analyzed to give the OCP plasma structure factor, which was
then used in realistic calculations of various transport properties such
as diffusion, electrical conductivity, thermal conductivity, and viscos-
ity. Applications of the OCP results were made to red giant stars and
to calculations of dense plasmas that it was hoped would be produced
in inertial-confinement fusion targets. In 1973, the OCP data from the
Monte Carlo study were used to improve significantly the theory of
thermonuclear reaction rates in stars. In the early 1970s the Monte
Carlo method was extended away from the OCP limit to allow the
neutralizing electrons to be treated as a polarizable fluid that partially
screens each ion. This simulation gave rise to a much better under-
standing of the evolution and structure of Jupiter.
The availability of good numerical experiments for the OCP fluid
spurred efforts to use the integral equations of liquid-state theory to the
OCP and related strongly coupled plasmas. The hyper-netted chain
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138 PLASMAS AND FLUIDS
(HNC) equation was solved to great accuracy in 1974, and the results
were found to be remarkably close to the Monte Carlo results. The
integral equation approach is advantageous because it is about a
thousand times faster than the more exact simulation methods. In fact
for numerous applications it was found that the HNC results were
adequate for practical calculations of the equation of state of ionic
mixtures and for electrical conductivity.
In the late 1970s, it was found experimentally that electrons could be
trapped on the surface of liquid helium and thus confined to motion on
a two-dimensional surface. It was found that the electron density could
be increased so that the resulting two-dimensional plasma could be
produced in weak coupling and then as a strongly coupled plasma,
which finally exhibited a two-dimensional phase transition. This sys-
tem was particularly interesting since it provided a clean method of
studying strong coulombs correlations, albeit in two dimensions.
Two-dimensional Monte Carlo simulations were carried out for both
the fluid and solid phases, and the density for the phase transition was
found to be in good agreement with the experimental observation. As
in the three-dimensional case, the HNC equation was applied to the
two-dimensional electrons and was found to be in good agreement with
the more expensive numerical simulations.
Recent Progress
At the Livermore and Los Alamos Laboratories the Monte Carlo
simulation technique has been very much refined. The availability of
the Cray computers, currently the world's largest, made it possible to
study the OCP fluid and solid phases with simulations involving up to
a thousand particles and tens of millions of configurations to be
averaged. This is a model involving heavy (classical) ions moving in a
nearly uniform density background of electrons. The internal energy
results are good to four- and five-figure accuracy, and the pair
distribution function is known everywhere to better than a fraction of
1 percent. The OCP thermodynamic functions are now known better
than those for any other simple liquid, including even the well-studied
hard-sphere system.
With the very exact Monte Carlo results as a guide the HNC
equation was modified by the inclusion of an approximate bridge graph
function. This is an integral equation approach to the problem that
computes more rapidly (by a factor of 1031. When solved numerically,
the internal energy from this equation agrees with the Monte Carlo
results to within the level of the Monte Carlo noise. This is a
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GENERAL PLASMA PHYSICS 139
remarkable agreement of a theoretical liquid-state calculation with
numerical experiment, which opens the way for a wide variety of
quantitative calculations of thermodynamic properties and transport
properties of dense partially ionized plasmas and liquid metals.
Spectral lines emitted by highly compressed targets in laser fusion
experiments have provided another significant and useful connection
between theory and experiment. At the densities and temperatures
reached in these compression experiments, elements such as argon are
ionized to the point that only one or two electrons are still bound. Thus
it is now possible to study spectral lines from hydrogenic and helium-
like argon. These lines are in the x-ray region and are broadened by the
Stark effect owing to neighboring ions in the plasma. A by-product of
the Monte Carlo simulation of the OCP has been an easy calculation of
the electric microfield distribution needed for the calculation of spec-
tral line shapes. The experimental measurement of several lines of the
Lyman series has given a reasonable test of current line-broadening
theories and the usefulness of the Monte Carlo microfield for predicting
spectral line shapes from highly ionized strongly coupled plasmas.
Outlook for the Next 10 Years
Future improvement on present-day understanding of ionic matter
will probably come about by a fully quantum treatment of strongly
coupled plasmas. Considerable progress has already been made on the
quantum many-body problem at zero temperature, and the properties
of the electron gas at T = 0 have been computed. Work is proceeding
rapidly on electron and proton systems, e.g., hydrogen, and it is
expected that a detailed understanding of the formation of metallic
hydrogen at high pressure will result. The next stage of this kind of
investigation will require practical computing procedures for the quan-
tum treatment of electrons and point nuclei at finite temperature, as for
example, using the Feynman path integral method. As with the
classical numerical simulation methods, the quantum plasma simula-
tions will be costly and time-consuming numerical experiments.
Clearly, strongly coupled plasma physics is an important area of
research because of its astrophysical applications and technological
applications. The level of research in this area is increasing rapidly in
several countries around the world, and U.S. leadership is by no means
assured during the 1980s. In the United States much of the important
work in this field is done at national laboratories because of the
availability of large computers and large laser systems. Only a few
American universities have good research efforts where students can
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140 PLASMAS AND FLUIDS
gain experience with established researchers. In spite of the U.S.
advantage in large computers, a French group continues to make
fundamental advances in both computation and basic theory. Several
groups in Japan are attacking problems in strongly coupled plasmas
such as simulations on liquid metals, laser-produced plasmas, and
transport calculations for astrophysical plasmas. With the advent of the
new Japanese supercomputers, it is certain that researchers in posses-
sion of such computers, for example the Japanese groups, will become
leaders in numerical simulation with both classical and quantum
methods. For the United States to continue to make- significant
contributions to strongly coupled plasma phenomena, it would be
advisable to strengthen support for this area of physics in U.S.
. . .
universities.
NONNEUTRAL PLASMAS
A nonneutral plasma is a collection of charges that satisfy the usual
many-body criterion to be a plasma but in which there is not overall
charge neutrality. These systems usually have intense self-electric
fields and may also have intense self-magnetic fields. They are called
plasmas, even though they are not charge neutral, because they exhibit
many of the collective phenomena characteristic of a neutral plasma.
For example, many types of waves that are supported by a neutral
plasma have nearly identical counterparts in nonneutral plasmas. For
example, nonneutral plasmas exhibit the phenomena of Debye shield-
ing, that is, the plasma particles act collectively to cancel (or shield) the
field of an extra charge placed in the plasma.
Nonneutral plasmas in the form of electron beams have been used in
applications such as microwave-generating devices for many years (see
section on Coherent Free-Electron Radiation Sources), but it was only
within the last decade that nonneutral plasma physics was recognized
as a separate subfield. Theoretical foundations of the subject were
provided by many papers written in the 1960s. At the beginning of the
1970s, interest was stimulated by several experimental programs on
toroidal confinement at the AVCO Corporation and on mirror confine-
ment at the University of Maryland. In both cases confinement times of
about 10 ms were reported.
During the 1970s, theoretical studies continued on equilibria and
stability for confinement in various magnetic field configurations and
for relativistic as well as nonrelativistic plasma, the analysis of waves,
and the development of transport theories. The experimental studies at
AVCO and the University of Maryland terminated. Further studies of
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GENERAL PLASMA PHYSICS 141
magnetic confinement were carried out at Maxwell Laboratories, Inc.,
and the University of California, Irvine (UCI). A new experiment on a
hybrid confinement system (Penning trap) was started at University of
California, San Diego (UCSD). In the pure magnetic confinement
experiments magnetic compression always produced a plasma of high
density (n ~10~°-10~ cm-3) and high temperature (104-106 eV). In the
hybrid trap with confinement by electrostatic fields in one direction and
magnetic fields in the other directions, densities are typically of order
107-108 cm-3 and the temperature is less than 1 eV. The pure electron
plasma experiments are very clean and yield experimental data of high
precision compared with conventional plasma experiments where ions
because of their large mass create substantial difficulties for experi-
m~ents and theory. Similar remarks apply to experiments with a small
density of ions compared with the electron density. At present,
experimental programs on the physics of nonneutral plasmas exist at
UCSD, UCI, University of California, Los Angeles, and the University
of North Carolina..
Although nonneutral plasmas have many properties in common with
neutral plasmas, there are some interesting differences. For example, a
nonneutral plasma consisting of only electrons (or only ions) can be
confined forever, at least in principle, and this is definitely not the case
for a neutral plasma. In confinement geometries for which the confining
electric and magnetic fields have cylindrical symmetry, general stabil-
ity and confinement theorems prove that a pure electron plasma (or a
pure ion plasma) simply cannot escape. Of course, actual confinement
systems cannot have perfect cylindrical symmetry; small construction
and field errors or end effects break the cylindrical symmetry and
produce a slow loss of the plasma. Nevertheless, pure electron plasmas
have been confined for periods as long as a day, which is many orders
of magnitude longer than the few second confinement times character-
istic of neutral plasmas. (See Chapter 4.)
Another difference concerns the possibility of cooling a pure electron
plasma to very low temperatures, that is, to a degree or so above
absolute zero. For a pure electron plasma, the electrons cannot
recombine with ions to form atoms (as electrons would in a neutral
plasma) since there are no ions in the confinement regions. Theory
predicts that as the temperature of a pure electron plasma is reduced,
the electrons will enter the liquid state and then the crystal state, that
is, one will obtain a pure electron liquid and a pure electron crystal. An
experimental program is under way at UCSD to realize these new
states of matter in the laboratory, and there is preliminary evidence
that the liquid state may have been obtained. Similar experiments are
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142 PLASMAS AND FL UlDS
being carried out with a pure ion plasma at the National Bureau of
Standards Laboratory in Boulder, Colorado. This general area of
research should be quite exciting in the next few years. Note that this
area of research overlaps and complements studies discussed in the
section on Strongly Coupled Plasma Physics.
Many applications of nonneutral plasmas have developed in the
1970s to a large extent the applications are much older and the
importance of the nonneutral plasma was recognized more recently.
For example, it was recognized that in a simple mirror the confine-
ment in the axial direction is electrostatic; this led to the invention of
the tandem mirror and the further refinement of thermal barriers to
reduce thermal conduction along the field lines.
In the large pulse power machines, the importance of magnetic
insulation was recognized. In a magnetically insulated transmission
line, the electric fields are so large that copious field emission of
electrons takes place; however, with suitable magnetic fields the
electrons are confined and do not short out the line. Magnetic insula-
tion (confinement) plays a central role in power flow and ultimately
limits the concentration of power. It also plays a key role in the design
of ion diodes because the electron flow must be inhibited. The
operation of relativistic magnetrons also depends critically on the
principles of magnetic insulation.
In the development of high-current accelerators, the toroidal con-
finement of a pure electron plasma is of central importance and is being
studied at NRL and UCI in programs to develop a modified Betatron.
The electrostatic field of a confined column of electrons can be used
to focus strongly a beam of ions. This is called a Gabor lens and was
invented in 1947. Recent experiments at the University of Oregon have
focused an millielectron-volt beam of ions to about 10 m with such a
lens. This principle is central in efforts to develop compact ion
accelerators called collective focusing accelerators; a linear accelerator
is being studied at SNL (PULSELAC) and a cyclic acceleration
experiment is under way at UCI (CFIA). (See section on Collective
Focusing Accelerators.)
A radial electric field together with an axial magnetic field can
produce rotation of a plasma column that is much more rapid than a
mechanical centrifuge can achieve. The radial electric field is associ-
ated with a nonneutral plasma. The plasma-arc centrifuge for isotopic
separation is being studied at Yale University.
In summary, the last decade saw the field of nonneutral plasma
physics established and a substantial base of knowledge developed.
Techniques were borrowed from neutral plasma physics, and rapid
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GENERAL PLASMA PHYSICS 143
progress was made in understanding many of the similarities between
nonneutral and neutral plasmas. Also, important differences were
identified, and it was realized that some of these offer unique oppor-
tunity for interesting physics research and for useful application. The
occurrence of nonneutral plasma was recognized in many important
applications. We expect that plasma physics will be broadened and
enriched by the study and application in the next decade of nonneutral
plasmas.
Representative terms from entire chapter:
magnetic field
