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Shock waves resonate through the solar system

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Collisionless Shock Waves in interstellar matter,

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 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 strethes 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.

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.

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 from 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 disperson), and the greater the
amplitude of the rarefactive soliton, the more slowly it propagates.
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 collicions 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.
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 avalanchelike 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.”

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.

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
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 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 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.