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October 30, 1993
SHOCKWAV.ASC
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By: Roald Z. Sagdeev
Charles F. Kennel
Reprinted without permission from Scientific American, April 1991
Collisionless Shock Waves
Shock waves resonate through the solar system, much like the
reverberating boom from a supersonic jet. In the latter case, the
disturbance is caused by an aerodynamic shock, an abrupt change in
gas properties that propagates faster than the speed of sound. It
had long been recognized that in a neutral gas, such as the earth's
atmosphere, particles must collide if shocks are to form.
Beginning in the 1950s, we and our colleagues theorized that,
contrary to the expectations of many scientists, similar shock waves
could form even in the near vacuum of outer space, where particle
collisions are extremely rare. If so, shocks could play a
significant role in shaping space environments.
"Collisionless" shocks cannot occur naturally on the earth, because
nearly all matter here consists of electrically neutral atoms and
molecules. In space, however, high temperatures and ultra-violet
radiation from hot stars decompose atoms into their constituent
nuclei and electrons, producing a soup of electrically charged
particles known as a plasma. Plasma physicists proposed that the
collective electrical and magnetic properties of plasmas could
produce interactions that take the place of collisions and permit
shocks to form.
In 1964 the theoretical work found its first experimental
confirmation. Norman F. Ness and his colleagues at the Goddard
Space Flight Center, using data collected from the IMP-1 spacecraft,
detected clear signs that a collisionless shock exists where the
solar wind encounters the earth's magnetic field. (Solar wind is
the continuous flow of charged particles outward from the sun.)
More recent research has demonstrated that collisionless shocks
appear in a dazzling array of astronomical settings. For example,
shocks have been found in the solar wind upstream (sunward) of all
the planets and comets that have been visited by spacecraft.
Violent flares on the sun generate shocks that propagate to the far
reaches of the solar system; tremendous galactic outbursts create
disruptions in the intergalactic medium that are trillions of times
Page 1
larger. In addition, many astrophysicists think that shocks from
supernova explosions in our galaxy accelerate cosmic rays, a class
of extraordinarily energetic elementary particles and atomic nuclei
that rain down on the earth from all directions.
The study of plasmas began in the 19th century, when Michael Faraday
investigated electrical discharges through gases. Modern plasma
research dates from 1957 and 1958. During those years, Soviet
Sputnik and American Explorer spacecrafts discovered that space near
the earth is filled with plasma. At the same time, till then secret
research on controlled thermonuclear fusion conducted by the U.S.,
Soviet Union and Europe was revealed at the Atoms for Peace
Conference in Geneva, greatly increasing the freely available
information on plasmas.
Fusion research focuses on producing extremely hot plasmas and
confining them in magnetic "bottles," to create the conditions
necessary for energy-producing nuclear reactions to occur. In 1957,
while searching for a method to heat fusion plasmas, one of us
(Sagdeev) realized that an instantaneous magnetic compression could
propagate through a collisionless plasma, much as a shock moves
through an ordinary fluid.
Magnetic fields that thread through plasmas make them behave
somewhat like such a fluid. A magnetic field exerts a force (the
Lorentz force) on a moving electrically charged particle. The field
can be thought of as a series of magnetic lines through the plasma,
like the field lines around a bar magnet that can be made visible
with iron filings.
The Lorentz force always acts perpendicular both to the direction of
the magnetic field line and to the direction in which a particle is
moving. If the particle moves perpendicular to the field, the force
acts like a rubber band, pulling the particle back and constraining
it to move in small circles about the magnetic field line. The
particle can, however, move freely in the direction of the magnetic
field line. The combination of the free motion along and
constrained, circular rotation across the magnetic field shapes the
particle's trajectory into a helix that winds around a magnetic
field line.
The Lorentz force makes it difficult to disperse the plasma in the
direction perpendicular to the magnetic field. The maximum distance
over which particles can move away from the field, called the Larmor
radius, is inversely proportional to the field strength. In the
weak interplanetary magnetic field, the Larmor radius amounts to
several kilometers for electrons and several hundred kilometers for
more massive ions. These distances may seem large, but they are
tiny compared with the size of the region where the solar wind
encounters the earth's magnetic field.
The shock that forms there, called a bow shock, has the same
parabolic shape as the waves that pile up ahead of a speedboat. It
stretches more than 100,000 kilometers across. When the scale is
larger than the Larmor radius for ions, the collective motion of
plasma particles across the magnetic field actually drags the field
lines along with it. The magnetic field thus becomes "frozen" into
the plasma.
Page 2
In short, a magnetic field endows collisionless plasmas with elastic
properties analogous to those of a dense gas, and so a plasma wave
crossing a magnetic field behaves somewhat like an ordinary sound
wave. The theoretical analysis of collisionless shocks therefore
started by following the ideas developed from earlier research on
aerodynamic shocks.
Suppose, for example, a sudden compression creates a sound wave in
air. As the wave travels, its shape--that is, its profile of
pressure and density--changes. Because the most compressed regions
of the wave move the fastest, the wave grows stronger and its
leading edge becomes sharper. The great German mathematician
Bernhard Riemann showed how this phenomenon, called wave steepening,
creates shock waves.
Ultimately the faster-moving denser air behind catches up with the
slower air ahead. At this point, the sound wave behaves somewhat
like an ocean wave heading toward shore. A water wave steepens,
overturns and then crashes into foam.
A sound wave reaches an analogous but different climax. As the wave
grows so steep that it is about to overturn, individual gas
molecules become important in transporting momentum between
neighboring points in the gas: molecules from the faster, denser
region of the wave rush ahead of the steepening wave front,
colliding with molecules in the slower region ahead of the wave and
exchanging momentum with them. In this way, the slower molecules
are brought up to the speed of the moving wave.
This exchange of momentum is caused by molecular viscosity. In this
process, momentum is passed from the overtaking wave crest and
imparted to the undisturbed region ahead of it, much as in a relay
race a baton is passed from one runner to the next. Molecular
viscosity becomes highly efficient when the thickness of the wave
front shrinks to the average distance that a particle can travel
before it collides with another, a distance known as the collision
mean free path. (The mean free path of a molecule in air is about
one ten-thousandth of a centimeter long.) At this thickness,
steepening and viscosity balance each other, and a steady shock wave
forms. The resulting shock represents an almost steplike change in
gas velocity, density and pressure.
Before physicists knew of a mechanism that could replace molecular
viscosity in plasmas, it made little sense for them to talk of
collisionless shocks. Consequently, the topic lay fairly dormant
for many years. Then, in the late 1950s, one of us (Sagdeev) and,
independently, Arthur R. Kantrowitz and Harry E. Petschek, then at
the Avco-Everett Research Laboratory near Boston, suggested that a
similar sort of momentum relay race could take place in a tenuous
plasma. They theorized that in a plasma, waves rather than
individual particles pass along the baton.
The plasma relay race depends on the fact that the speed of a plasma
wave changes with wavelength, an effect called dispersion. Indeed,
whereas in ordinary gases the speed of a sound wave is practically
independent of wavelength, in collisionless plasma a wave is very
dispersive. That is, its speed may either increase or decrease as
its wavelength shortens, depending on the angle between the
direction of propagation of the wave and orientation of the magnetic
field.
Page 3
According to Fourier's theorem, a fundamental theorem of
mathematics, any wave profile consists of many superimposed waves,
or harmonics, of different wavelengths. (By analogy, white light is
composed of many distinct colors, each of a different wavelength.)
If the wave profile steepens, it excites harmonics of ever shorter
wavelength.
For wave propagation that is not exactly perpendicular to the
magnetic field, dispersion causes shorter-wavelength harmonics to
travel faster than the longer-wavelength ones (negative disperson).
The effects of dispersion become significant when a steepening shock
front becomes about as thin as the Larmor radius for ions.
At this point, the shorter-wavelength harmonics race ahead of the
front into the undisturbed plasma upstream. These harmonics carry
along the momentum, like the fast molecules in a sound wave.
The competing actions of steepening and dispersion yield a series of
wave pulses that propagate in the direction of the shock. As a
result, the front acquires the shape of a "wave train." The weakest
(smaller-amplitude) waves announce the arrival of the train, and
successively stronger oscillations build up until the full shock
transition arrives. The length of the train (in other words, the
thickness of the shock front) depends on how rapidly the energy of
the waves dissipates.
For waves propagating exactly perpendicular to the magnetic field,
dispersion causes the harmonic wave speed to decrease at shorter
wavelengths. Short-wavelength harmonics now trail behind the shock
front, and so they cannot affect steepening of the overall wave. In
this case, the shock passes the momentum baton to a series of
compressional pulses called solitons.
Solitons in perpendicular shocks are approximately the thickness of
an electron's Larmor radius, and they are created when the wave
profile steepens to that scale. The steepening front radiates an
ordered sequence of solitons, led by the largest (highest-amplitude)
one and trailed by successively smaller ones that ultimately blend
into the smooth state behind the shock. The length of the soliton
train depends on how fast the soliton energy is dissipated into
heat.
Waves on the surface of shallow water behave very much like
dispersive waves in collisionless plasma. The theory of shallow
water waves was developed in the late 19th century, culminating in
the classic work of Diederik J. Korteweg and G. DeVries that first
described the solitons that occasionally propagate down Dutch
canals. The seemingly recondite analogy between shallow water
solitons and plasma solitons expresses a general physical truth:
solitons can form whenever wave steepening and dispersion compete.
One implication of this fact is that solitons form even in shocks
that do not propagate exactly perpendicular to the magnetic field.
The wave pulses mentioned earlier can also be thought of as
solitons, the difference being that these solitons are rarefactive
(low density) rather than compressive. In this case, short-
wavelength harmonics travel relatively slowly (positive dispersion),
and the greater the amplitude of the rarefactive soliton, the more
slowly it propagates.
Page 4
As a result, the wave train terminates with the strongest soliton.
Surface tension in water creates small waves that have positive
dispersion and rarefactive solitons. The physics of water waves
therefore provides an analogy to both types of dispersion found in
collisionless plasma.
The elegant theory of solitons is an impressive achievement of
modern mathematical physics. In 1967 Martin Kruskal and his
colleagues at Princeton University proved that any wave profile in a
dispersive medium that can support steepening evolves into a
sequence of solitons. By relating soliton theory to the problem of
elementary particle collisions, which has been studied in depth in
quantum physics since the 1920's, they showed that solitons preserve
their identities when they collide, just as particles do.
The understanding of dispersive shocks remains incomplete without a
knowledge of how to dissipate the energy of waves or solitons into
heat. If not for the effect of dissipation, the train of wave
structures making up the shock front would be infinitely long. In
effect, the fundamental question of how collisionless shock waves
transport energy and momentum has reappeared, but in a new guise.
In 1945 the great Soviet physicist Lev D. Landau discovered a
dissipation mechanism that requires no collisions between particles.
Among the randomly moving particles in a plasma, a few happen to
travel at a velocity that matches the velocity of the plasma wave.
These particles are said to be in resonance with the wave. An
intense exchange of energy can take place between a wave and the
particles resonant with it.
In the early 1970s one of us (Sagdeev) and Vitaly Shapiro, also at
the Institute of Space Research in Moscow, showed that Landau's
mechanism damps solitons by accelerating resonant ions.
Consider, for example, a train of compressive solitons propagating
perpendicular to the magnetic field. Each soliton generates an
electric field parallel to its direction of motion. Ions traveling
close to the resonant velocity move slowly compared with the
solitons, and the soliton electric field is able to stop and reverse
the motion of these ions. The soliton loses part of its energy to
the ions resonant with it during the interaction.
The process does not end here, because the magnetic Lorentz force
curves the path of the reflected ion so that it returns again and
again to the same soliton. Each encounter adds to the energy of the
particle. The Lorentz force, which grows stronger as the particle
velocity increases, eventually throws the ion over the top of the
first soliton. The acceleration continues as the ion encounters the
remaining solitons in the wave train.
The resonant ions gain energy much as surfers gain speed by riding
ocean waves. This analogy inspired John M. Dowson of the University
of California at Los Angeles to design a new kind of charged
particle accelerator, which he dubbed the SURFATRON.
The heating of ions by solitons can form a shock if the number of
ions in resonance is great enough. Such is the case if the ions are
hot. If not, the solitons find another way to dissipate energy:
they themselves generate microscopic plasma waves that heat the
plasma.
Page 5
Plasma electrons flow over ions, thereby creating the electric
current responsible for the characteristic soliton magnetic field
profile. If the ions are cold, the electrons can easily move at
supersonic velocities relative to the ions, in which case the
electrons amplify extremely small scale electric field oscillations
called ion acoustic waves. These waves, which do not affect the
magnetic field, grow in an avalanche-like fashion.
The plasma particles collide not with one another but with these ion
acoustic waves. After the waves develop, the plasma enters a
microturbulent state.
In 1968 Robert W. Fredericks and his colleagues at TRW in Los
Angeles were the first to detect ion acoustic waves in shocks. They
made this discovery using instruments on the OGO-5 spacecraft that
were designed specifically to study plasma waves in space. Since
then, plasmawave detectors have been included on most space mission
concerned with solar system plasmas, notably the International Sun-
Earth Explorers (ISEE 1, 2 and 3) in earth orbit and the Voyager 1
and 2 missions to the outer planets. The late Fred Scarf of TRW and
his collaborators often played back the microturbulent-wave electric
fields recorded by the ISEE and Voyager spacecraft through an
ordinary loudspeaker. To most listeners, shocks would sound
cacophonous; to our ears, however, they were a symphony of space.
Although easy to record, microturbulence has proved difficult to
understand completely. Theorists turned to numerical computations
to help elucidate the behavior of a strongly microturbulent plasma.
By solving millions of equations of motion for the particles,
computer simulation shows how ion acoustic waves grow and heat the
plasma. Today's supercomputers are just beginning to give
scientists comprehensive understanding of many different kinds of
microturbulence.
Even without knowing the detailed nature of microturbulent plasma,
physicists can deduce its general behavior. Electrons in the plasma
transfer their momentum to ion acoustic waves, which in turn
transfer it to ions. This process retards the motion of the
electrons in the plasma and so creates resistance to the electric
current. In some shocks, ion acoustic-wave resistance grows
sufficiently intense to suppress the generation of solitons. When
this happens, no wave train forms, and the shock is called
resistive.
Although both simple dispersive and resistive shocks have been found
in space, most shocks observed there have entirely different
characteristics from those discussed so far. Most shocks are
sufficiently powerful that neither dispersion nor resistance can
prevent steepening from causing the waves to overturn. Overturning
then leads to a host of new shock phenomena.
A consideration of shallow water waves, once more, helps to
illustrate the process of overturning. When a shallow ocean wave
grows sufficiently high, the tip of its wave crest swings forward
through an arc and ultimately collapses under gravity. The water
stream from behind the crest collides with that ahead, giving rise
to the foam on whitecaps. Thus, a large wave crashing toward shore
repeatedly overturns, or "breaks."
Page 6
A plasma wave also develops overlapping velocity streams as it
overturns. The fastest stream, which comes from the wave crest,
invades the plasma ahead of the shock front. The Lorentz force
turns the ions in this stream back into the shock. These reflected
ions ultimately mix with those behind the front. If the shock is
weak, its structure will remain steady. If the shock is strong, ion
reflection will temporarily overwhelm steepening; however, the shock
soon steepens again, and the cycle repeats.
Recent numerical simulations by Kevin B. Quest and his colleagues at
Los Alamos National Laboratory confirm the idea that very strong
shock waves consist of a repeated cycle of steepening, overturning
and ion reflection.
The interactions between reflected and flowing ions can also lead to
microturbulence. The Voyager spacecraft detected ion acoustic
waves, this time generated by ions reflected by Jupiter's bow shock
[see top illustration on page 110]. Near the earth, reflected ions
generate waves in the solar wind at the geometric mean of the
frequencies of rotation of the ions and electrons about the earth's
magnetic field; this mean is called the lower hybrid-resonance
frequency.
In 1985 the Soviet-Czech Intershock spacecraft made the first
definitive measurements of lower hybrid turbulence in the earth's
bow shock. Around both planets, the ion acoustic waves take energy
from ions and give it to electrons. Some heated electrons escape
forward into the solar-wind flow, others back into the shock zone.
So far we have concentrated on those shocks propagating more or less
at right angles to the magnetic field, those physicists call
quasiperpendicular. Plasma turbulence is even more important when
the shock propagates almost parallel to the magnetic field. The
field no longer holds back the fast particles that rush ahead of a
quasiparallel shock. These particles are a major source of
turbulent instability.
The ability of the magnetic field to channel particle motion along
field lines creates a situation analogous to a fire hose left
spraying water on the ground. Bends in the hose become increasingly
curved by the centrifugal force of the flowing water; eventually the
hose wriggles uncontrollably on the ground.
The magnetic field channeling the overlapping plasma streams ahead
of a quasiparallel shock experiences a similar instability, often
called the fire-hose instability. The centrifugal force that bends
the magnetic field lines is proportional to the density of energy in
plasma motion along the magnetic field. Instability occurs when
this energy density exceeds that of the magnetic field. Many
physicists conceived of the fire-hose instability independently, but
the version invented in 1961 by Eugene N. Parker of the University
of Chicago was tailored specifically to quasiparallel shocks.
The plasma fire-hose instability leads to a random flexing of the
magnetic field lines. This kind of magnetic turbulence can be
regarded as a chaotic ensemble of "torsional" waves, that is, ones
that twist the magnetic field lines. They are known as Alfven
waves, after Hannes Alfven of the Royal Institute of Technology in
Stockholm, who first described them.
Page 7
Alfven waves, like ion acoustic waves, can exchange energy and
momentum with ions in resonance with them. As far as the ions are
concerned, the interaction with Alfven waves mimics the effect of
collisions. Thus, Alfven waves limit how far ions escaping the
shock can penetrate upstream and determine the thickness of the
quasiparallel shock.
Theory predicts that collisions between ions and Alfven waves should
be nearly elastic, that is, they should involve only slight changes
in energy despite a large change in momentum (for example, when a
rubber ball bounces off a hard wall, its momentum reverses, but its
energy remains essentially the same). As a result, the Alfven
turbulence inside the shock front should disintegrate relatively
slowly. This notion led us to conclude in 1967 that quasiparallel
shocks could be much thicker than quasiperpendicular ones.
The very first measurements of the earth's bow shock by the IMP-1
spacecraft in 1964 hinted at the substantial differences between
parallel and perpendicular shocks. The data returned by IMP-1 were
somewhat puzzling at first because sometimes the shock appeared thin
and other times it appeared thick. Three years later we suggested
that shock structure could depend on the orientation of the
interplanetary magnetic field.
In 1971 Eugene W. Greenstadt of TRW and his colleagues assembled the
first evidence that the thickness of the earth's bow shock does
indeed vary with the direction of the solar-wind magnetic field.
Since this field constantly changes direction, the regions where the
bow shock is locally quasiperpendicular and where it is
quasiparallel are always moving, even if the shock itself remains
fairly stationary. Wherever the shock is quasiperpendicular, it is
thin; where it is quasiparallel, it is thick [see illustration on
page 107].
In the early 1970s spacecraft began to detect small fluxes of
energetic particles, ion acoustic waves and Alfven waves far
upstream of where the earth's bow shock was understood to be. The
ISEE program, which started in 1977, established that all the
upstream activity is actually part of the extended quasiparallel
shock. The shock is so thick that it dwarfs the earth, and
therefore earth-orbiting satellites cannot really measure its size.
Another, larger class of shocks does lend itself to investigation by
spacecraft, however. Flares in the solar corona occasionally launch
gigantic shock waves that propagate through the interplanetary
medium to the far reaches of the solar system. These can be
observed as they sweep by instrumented spacecraft.
One of us (Kennel), along with colleagues in the ISEE project, found
that the region of Alfven and ion acoustic turbulence upstream of
quasi-parallel interplanetary shocks can be more than a million
kilometers thick.
Alfven waves play a particularly prominent role in the shocks that
form ahead of comets as they pass through the solar wind in the
inner solar system. Cometary nuclei are far too small to cause any
detectable physical disturbance in the flow of the solar wind (the
nucleus of Halley's comet, for instance, measures only about 15
kilometers across), and the nuclei possess a negligible magnetic
Page 8
field. Because of these properties, comets cannot generate shocks
in the way that planets do. Nevertheless, scientists have found
that when comets approach the sun, they create large collisionless
shocks.
Sunlight evaporates atoms and molecules from the surface of a
comet's nucleus. Most of the liberated gas is ionized by solar
ultraviolet light and forms a plasma cloud similar to the earth's
ionosphere. The solar wind never penetrates the cometary
ionosphere, and it is not the ionosphere that forms the shock wave.
The key players in producing cometary shocks are the few neutral
atoms and molecules that manage to escape the comet's ionosphere.
These, too, are ultimately ionized, but farther out, where they have
entered the solar wind.
The newly ionized particles respond to the electric and magnetic
fields of the solar wind by joining the flow. They increase the
mass density of the solar wind, which, according to the law of
conservation of momentum, decreases the wind speed. Because
cometary ions are much heavier than the protons of the solar wind, a
number of cometary ions can slow the wind appreciably.
More than 20 years ago Ludwig Biermann of the Max Planck Institute
for Astophysics in Munich suggested that such a decelerating solar-
wind flow should produce a shock similar to a planetary bow shock.
During its 1986 encounter with Comet Halley, the Soviet spacecraft
Vega-1 heard the plasma wave cacophony that signaled the existence
of a shock wave about one million kilometers from the nucleus, the
distance predicted by Biermann's theory.
The Soviety Vega, Japanese Suisei and the European Giotto spacecraft
encountered both quasiperpendicular and quasiparallel shocks at
Comet Halley. The quasiparallel shocks were similar to those at the
planets. Heavy ions upstream of the quasiperpendicular cometary
shocks generated intense Alfven-wave turbulence, however, something
that does not happen around the planets.
Shocks that generate Alfven waves can also accelerate a small group
of particles to high energies. The "collisions" of particles with
Alfven waves return escaping particles back to the shock front.
Each time they recross the shock, the particles increase their
energy. This acceleration mechanism is based on one proposed by
Enrico Fermi in 1954.
In 1986 one of us (Kennel) and his ISEE collaborators found that a
theory of Fermi acceleration developed for interplanetary shocks by
Martin A. Lee of the University of New Hampshire successfully passed
the test of observations. Yet the Fermi process develops so slowly
that the protons accelerated by quasiparallel interplanetary shocks
only reach energies of a few hundred thousand electron volts in the
one day it takes the shock to travel from the sun to the earth. In
comparison, cosmic rays--energetic subatomic particles and atomic
nuclei from deep space--have energies up to 100 trillion electron
volts.
Exploding stars--supernovas--create very strong shocks that speed
into the interstellar plasma at tens of thousands of kilometers per
second. We cannot put a space probe ahead of a supernova shock, so
we cannot say for sure whether the shock generates Alfven waves and
Page 9
accelerates interstellar ions. We can, however, apply to supernova
shocks the theory of particle acceleration that is being tested
today using solar system shocks.
Since supernova shocks last about a million years before dying out,
particles have time to reach extremely high energies via the Fermi
process. Working independently, Germogen F. Krymskii of the
Institute of Space Physics Research and Aeronomy in Yakutsk,
U.S.S.R., Roger D. Blandford of the California Institute of
Technology and Ian W. Axford of the Max Planck Institute for
Aeronomy in Katlenburg-Lindau, together with their colleagues,
showed in 1977 that the distribution in energy of the particles
accelerated by collision-less shocks is virtually identical to that
of cosmic rays.
The origin of cosmic rays has long been a puzzle. Many
astophysicists now believe that they are created when supernova
shocks accelerate particles, although it is still not understood how
the particles reach the highest energies observed.
Collisionless shocks probably exist even around remote galaxies.
Dynamic processes in the centers of some active galaxies (possibly
involving a massive black hole) create supersonic jets hundreds of
thousands of light-years long. Shocks are likely to occur when the
jets interact with the plasma surrounding the galaxy. Radio
emissions from the jets indicate that electrons are accelerated to
extremely high energies. Albert A. Galeev, director of the Soviet
Institute of Space Research, suggests that a theory he and his
colleagues developed to explain how lower hybrid waves accelerate
electrons in the earth's bow shock may also clarify how electrons
are accelerated in galactic jets.
Contemporary collisionless shock research encompasses phenomena that
vary tremendously in scale and origin. The concepts that we and
others developed 20 years ago have turned out to be a reasonable
basis for understanding collisionless shocks. Spacecraft have found
individual examples of most of the shock types predicted by theory.
Still to come are refined measurements and numerical calculations
that simulate in detail the impressive variety of shocks found in
nature.
In most cases, the fairly simple mechanisms we have described here
are intertwined in fascinating ways. Yet even now collisionless
shock theory has enabled physicists to speculate with some
confidence on the physical processes underlying some of the grandest
and most violent phenomena in the universe.
ROALD Z. SAGDEEV and CHARLES F. KENNEL have been friends and
colleagues since they met at the International Centre for
Theoretical Physics in Trieste in 1965. Sagdeev heads the theory
division of the Soviet Institute of Space Research and is professor
of physics at Moscow Physico-TEchnical Institute. Last year he
joined the physics department of the University of Maryland at
College Park. In addition to his astronomical and physical
research, Sagdeev has been active in the areas of arms control,
science policy and global environment protection. Kennel is
professor of physics at the University of California, Los Angeles,
as well as consultant to TRW Systems Group, where he participates in
space plasma experiments. He is also a distinguished visiting
Page 10
scientist at the Geophysical Institute of the University of Alaska,
Fairbanks, and a collector of native Alaskan art.
FURTHER READING
SHOCK WAVES IN COLLISIONLESS PLASMAS. D. A. Tidman and N. A. Krall.
Wiley-Interscience, 1971.
UPSTREAM WAVES AND PARTICLES. Journal of Geophysical Research, Vol.
86, No. A6, pages 4319-4529; June 1, 1981.
HANDBOOK OF PLASMA PHYSICS. Edited by M. N. Rosenbluth and R. Z.
Sagdeev. North-Holland Publishing Company, 1983.
COLLISIONLESS SHOCKS IN THE HELIOSPHERE: REVIEW OF CURRENT RESEARCH.
Edited by Bruce T. Tsurutani and Robert G. Stone. American
Geo-physical Union, 1985.
NONLINEAR PHYSICS: FROM THE PENDULUM TO TURBULENCE AND CHAOS. R. Z.
Sagdeev, D. A. Usikov and G. M. Zaslavsky. Translated from
the Russian by Igor R. Sagdeev. Harwood Academic Publishers,
1988.
(Refer to 4THSTATE and POWERING on KeelyNet)
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