A plasma is an ionized, electrically conducting gas of charged particles. For an ionized gas to qualify as a plasma the density of charged particles must simultaneously satisfy two important criteria: (i) the density should be sufficiently high that the long range Coulomb force be a significant factor in determining the statistical properties of the particles; (ii) it should be low enough that the Coulomb force of a near neighbour particle be much less than the cumulative long range Coulomb force exerted by the many distant particles. The most characteristic aspect of the plasma state is perhaps that the particles exhibit collective behaviour because of the long range nature of the Coulomb force.
Above a temperature of about 
most matter exists in an
ionized state. For this reason the plasma state is frequently called the
fourth state of matter. That is, if one adds heat to a solid
one obtains a liquid, add heat to a liquid and one obtains a gas, add
sufficient heat to a gas and the atoms themselves become ionized
and one obtains a plasma. Such high temperatures are, however,
not necessary, for a plasma to exist. Provided there is a mechanism
for ionizing the gas and the density is sufficiently low for recombination
to be slow, a plasma can exist at relatively low temperatures. This is
frequently the case in laboratory produced plasmas and, indeed, in the
Earth's own ionosphere--an example of a plasma produced by photoionization
of the tenous outer layers of the atmosphere.
By some estimates 
of the observable universe is in the plasma state.
Why then is there so little natural plasma on Earth? The answer is simply
that the temperature here on Earth is too low and the density of matter
is too high. However, as we have mentioned, as we begin to leave the
Earth environment, e.g., in the upper layers of the atmosphere, we meet
plasma. Still further up one would come across our nearest example of
an astrophysical plasma: the solar wind. The solar wind is a
tenuous plasma of ejected solar material that streams toward the earth
and fills much of interstellar space. We are shielded from these
energetic particles by our own Earth's magnetic field, which helps
to divert the flow of the solar wind around us. However, during solar
storms energetic solar particles still reach earth through the magnetic
"funnels" at the poles and we observe these as aurorae. Our high altitude
satellites, on which we are becoming increasingly reliant for day to
day living (e.g., satellite TV and phones; global positioning systems),
are, however, at some risk. For this reason a detailed
knowledge of the sun and the solar wind plasma is required so that
satellites can be rotated prior to the onset of a severe solar storm
to avoid damage to delicate instrumentation. This has lead to the development
of so-called space weather forecasting. Space weather forecasting
combines plasma physics with a detailed knowledge of processes going
on in our Sun, and is a modern application of plasma physics.
The condition that the Coulomb
force of a near neighbour particle be much less than the cumulative long
range Coulomb force exerted by the many distant particles can be
satisfied if there are many particles in a Debye
sphere. A Debye sphere is a sphere of radius one Debye length.
A Debye length is a typical length over which a charged
particle's bare electric field has substantial influence. In terms of the
density and temperature of the plasma components the Debye length 
can be defined by
where 
, 
and 
are, respectively, the number
density, charge and temperature of the particle species 
; 
is
Boltzmann's constant. In many
cases 
and e denoting ions and electrons, respectively.
For distances
exceeding the Debye length, the electric field of an individual charged
particle is effectively shielded out by the surrounding plasma. If 
is the electrostatic potential of a charge at rest in a plasma, then it
can be shown that
where r is the radial distance from the charge. This potential differs
from that of an isolated charge in a vacuum only by the exponential term.
So, the Debye sphere, which is a sphere with radius equal to the Debye length,
centred on the charge, is a charged particle's typical "sphere of influence" on
neighbouring plasma particles. Not surprisingly, the number of plasma particles
that occupy this volume, 
, plays an important role in defining
the Coulomb collisional
properties of the plasma and determines the significance of discrete particle
effects in general. In plasma physics the so-called plasma parameter
is related to this number.
The plasma parameter g is defined by
where n is the average plasma density.
If the number of particles in a Debye sphere is
sufficiently large, hence g is sufficiently small, the average
kinetic energy of a plasma particle, 
, exceeds the average
interparticle potential
energy, 
, and the plasma behaves,
statistically, much like an ideal gas (an ideal gas has zero potential
energy between the particles). To ensure that be large, the
plasma density must be low, since
where we have assumed an isothermal (
) plasma of singly charged
ions and electrons for simplicity.
Because the collision frequency decreases with density n, and also decreases
with increasing temperature T, the condition 
(equivalently
) corresponds to a decreasing collision frequency.
It is interesting that for small values of g the plasma behaves almost like an ideal gas despite the presence of many interacting particles. As has been mentioned, this is so because the Coulomb force between near-neighbour particles is very weak and is much less than the cumulative Coulomb force of the many distant particles.
The fact that plasma particles behave collectively means that plasmas
can support a wide variety of wave motions and oscillations. One such
basic oscillation arises if a group of electrons is slightly displaced
from their equilibrium positions. The displaced electrons feel an
electrostatic force seeking to return them to their equilibrium positions
but upon arrival there they now have a kinetic energy equal to the
potential energy of their initial displacement. The electrons overshoot,
reconvert their kinetic energy to potential energy and a simple
oscillation is set up. The frequency of this fundamental oscillation is
known as the plasma frequency and is defined by
where n is the mean plasma density and 
is the electron mass.
Plasmas, unlike ordinary gases, support a wide variety of wave modes
because the particles are charged. Such wavelike disturbances can
typically be described by an electric field of the form
, where 
and
are in general complex valued. If the wave is electromagnetic in
nature (and plasmas support a wide variety of electromagnetic wave modes)
then the magnetic field obeys a similar relation also. The (angular)
frequency and the wave vector are functionally related to one
another, at least in linear theories of plasma waves, by a dispersion
relationship 
. A knowledge of the dispersion
characteristics of the propagating waves is certainly necessary for an
understanding of the plasma state.
A plasma, however, is a nonlinear medium and unless the waves are truly of small amplitude, nonlinear effects must be taken into account. Such nonlinear effects conspire to produce wavelike disturbances that are not of the form given above and interesting phenomena such as solitons (solitary waves) and double layers are frequently observed in space plasmas. Solitons and double layers are examples of coherent nonlinear phenomena. More generally, the presence of nonlinear effects leads to plasma turbulence.
Perhaps the simplest of all plasma waves is the Langmuir wave. It is also
known
variously as the space charge wave, electron plasma wave or simply the
plasma wave. The
Langmuir wave is an electrostatic (or longitudinal) wave that propagates
only in a finite temperature plasma, i.e., one in
which there is a finite spread of electron velocities. The
oscillations at the plasma frequency 
(see above) now
propagate as a wave because particles, by virtue of their random thermal
motion, can penetrate into adjacent (displaced) charge layers. Another
consequence of the finite velocity spread is to cause the waves to damp
via a process known as Landau damping (see later).
The ion-acoustic or ion sound wave is another electrostatic wave occuring
in a field free plasma. At long wavelengths (small wavenumbers k) these
waves are approximately dispersionless, propagating with speed,
At shorter wavelengths, i.e., when the wavelength approaches the electron
Debye length, the electron shielding of the ion motion becomes less
efficient and the wave approaches an ion oscillation (analogous to the
electron plasma oscillation above) at the ion plasma frequency
At these wavelengths the wave is, however, strongly Landau damped.
If the plasma is field free in equilibrium, i.e., it does not possess a
mean magnetic field in the absence of the wave, then the only
electromagnetic wave that can propagate in a plasma possesses the
following dispersion relationship
where c is the speed of light in vacuo.
One immediately notices a similarity with the dispersion relation for the
Langmuir wave, but it is to be recalled that the Langmuir wave was purely
electrostatic and possessed no oscillating magnetic field component.
Electromagnetic waves in a field-free plasma propagate only for
frequencies exceeding the plasma
frequency. For frequencies below the wavenumber is
imaginary, since
is negative for 
. Such waves, possessing imaginary
wavenumber, are evanescent. For wave frequencies greatly exceeding the
plasma frequency the plasma perturbs the wave only slightly from its
vacuum form 
.
Whistlers are an example of an electromagnetic wave which may propagate
in a plasma that contains a mean magnetic field, 
, in
equilibrium. The
electric field for the whistler is right hand elliptically polarized (with
respect to
the mean magnetic field) in general, reducing to pure circular
polarization
when the wave propagates parallel to . The dispersion relation,
for parallel propagation, is
where 
is the electron cyclotron frequency,
or gyrofrequency. The electron cyclotron frequency is the frequency of
gyration of an electron in the mean magnetic field.
Whistlers are a common phenomenon in our own magnetosphere. They may be excited, for example, when electromagnetic energy from a lightning strike enters a magnetic field line duct (a process, which is more efficient near the magnetic poles). Such electromagnetic energy can be guided along closed magnetic field lines though the enhanced ionization usually present near such magnetic field ducts. The wave travels along the field line and can be observed at the opposite pole (conjugate point). Because the wave is highly dispersive (see above) different frequencies arrive at the conjugate point at different times and, using a radio receiver, a descending glide tone can be heard for each lightning strike occuring in the opposite hemisphere. Whistlers also occur widely in the plasmasphere, magnetosheath and terrestrial foreshock, for example.
At frequencies below the ion cyclotron frequency 
a dispersionless (at long wavelength) electromagnetic
wave can propagate. This is a magnetohydrodynamic wave called the
Alfvén wave. The phase velocity of the wave satisfies
where 
is the permeability of free space.
Alfvén waves can be excited by the interaction of the solar wind with the Earth's magnetosphere. The magnetic field lines of the magnetosphere act like giant guitar strings that are ``plucked'' via their interaction with the solar wind. Large wavelength standing Alfvén waves can be generated via this method. Alfvén waves are a common feature of most space plasmas.
Landau damping is a physical effect that is related to the details of the
underlying velocity distribution functions of the plasma particles. It
occurs in the absence of short-range binary collisions and hence it is
sometimes called collisionless damping. In a plasma, an initial
disturbance is damped (in the absence of binary Coulomb collisions) as it
propagates away from its point of origin. This can be explained by the
following argument. Those particles that
interact most strongly with a plasma wave are those whose
velocities are closest to the wave phase velocity. These particles
see an approximately stationary electric field. In a stable thermal
distribution,
for any particular wave speed 
, there are always more
particles travelling slightly slower than the wave than those travelling
slightly faster than the wave. If the particles travelling slower than the
wave are accelerated by the wave and take energy from it, and those that
travel faster than the wave give energy to the wave, then there are more
particles taking energy from the wave than those giving energy to it and
the wave damps.
Still under construction...
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