In
, an electromagnetic electron wave is a
wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
in a
plasma
Plasma or plasm may refer to:
Science
* Plasma (physics), one of the four fundamental states of matter
* Plasma (mineral), a green translucent silica mineral
* Quark–gluon plasma, a state of matter in quantum chromodynamics
Biology
* Blood pla ...
which has a
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
component and in which primarily the
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
s oscillate.
In an unmagnetized plasma, an electromagnetic electron wave is simply a
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
wave modified by the plasma. In a magnetized plasma, there are two modes perpendicular to the field, the O and X modes, and two modes parallel to the field, the R and L waves.
Waves in an unmagnetized plasma
Langmuir Wave
The
Langmuir wave
Langmuir may refer to:
* Langmuir (crater), an impact crater on the Moon's far side
* ''Langmuir'' (journal), an academic journal on colloids, surfaces and interfaces, published by the American Chemical Society
* Langmuir (unit), a unit of expos ...
is a purely longitudinal wave, that is, the wave vector is in the same direction as the E-field. It is an electrostatic wave, thus it doesn't have an oscillating magnetic field.
A plasma consists of charged particles which react to electric fields, in contrast with dielectric matter. When electrons in a uniform, homogeneous plasma are perturbed from their equilibrium position, a charge separation occurs creating an electric field which acts as restoring force on the electrons. Since electrons have inertia the system behaves as a harmonic oscillator, where the electrons oscillate at a frequency ω
pe, called electron
plasma frequency Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability i ...
. These oscillations do not propagate -- the group velocity is 0.
When the thermal motion of the electrons is taken into account a shift in frequency from the electron plasma frequency ω
pe occurs. Now the electron pressure gradient acts as the restoring force, creating a propagating wave analogous to a sound wave in non-ionized gases. Combining these two restoring forces (from the electric field and electron pressure gradient)
a type of wave, named
Langmuir wave
Langmuir may refer to:
* Langmuir (crater), an impact crater on the Moon's far side
* ''Langmuir'' (journal), an academic journal on colloids, surfaces and interfaces, published by the American Chemical Society
* Langmuir (unit), a unit of expos ...
, is excited. The dispersion relation is:
The first term on the right hand side of the dispersion relation is the electron plasma oscillation related to the electric field force and the second term is related to the thermal motion of the electrons, where C
e is the electron thermal speed and k is the
wave vector
In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), ...
.
Electromagnetic wave
In an unmagnetized plasma, waves above the plasma frequency propagate through the plasma according to the dispersion relation:
In an unmagnetized plasma for the high frequency or low electron density limit, i.e. for
or
where ω
pe is the
plasma frequency Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability i ...
, the wave speed is the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in vacuum. As the electron density increases, the
phase velocity
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...
increases and the
group velocity
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope'' of the wave—propagates through space.
For example, if a stone is thrown into the middl ...
decreases until the
cut-off frequency
In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced ( attenuated or reflected) rather than ...
where the light frequency is equal to ω
pe. This density is known as the critical density for the
angular frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
ω of that wave and is given by
:
(
SI units
The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
)
If the critical density is exceeded, the plasma is called over-dense.
In a magnetized plasma, except for the O wave, the cut-off relationships are more complex.
O wave
The O wave is the "ordinary" wave in the sense that its
dispersion relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the d ...
is the same as that in an unmagnetized plasma, that is,
. It is
plane polarized with
E
1 , , B
0. It has a cut-off at the
plasma frequency Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability i ...
.
X wave
The X wave is the "extraordinary" wave because it has a more complicated dispersion relation:
[D. Gary Swanson, Plasma Waves , Academic Press, 1989. ]
Where
.
It is partly transverse (with E
1⊥B
0)
and partly longitudinal; the E-field is of the form
Where
refer to the Stix notation.
As the density is increased, the phase velocity rises from ''c'' until the cut-off at
is reached. As the density is further increased, the wave is evanescent until the resonance at the upper hybrid frequency
. Then it can propagate again until the second cut-off at
. The cut-off frequencies are given by
:
where
is the
electron cyclotron resonance
Electron cyclotron resonance (ECR) is a phenomenon observed in plasma physics, condensed matter physics, and accelerator physics. It happens when the frequency of incident radiation coincides with the natural frequency of rotation of electrons in ...
frequency, and
is the electron
plasma frequency Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability i ...
.
The resonant frequencies for the X-wave are:
where
and
.
R wave and L wave
The R wave and the L wave are right-hand and left-hand circularly polarized, respectively. The R wave has a cut-off at ω
R (hence the designation of this frequency) and a resonance at ω
c. The L wave has a cut-off at ω
L and no resonance. R waves at frequencies below ω
c/2 are also known as whistler modes.
Dispersion relations
The
dispersion relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the d ...
can be written as an expression for the frequency (squared), but it is also common to write it as an expression for the
index of refraction
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
''ck''/ω (squared).
See also
*
Appleton-Hartree equation
*
List of plasma (physics) articles
This is a list of plasma physics topics.
A
* Ablation
* Abradable coating
* Abraham–Lorentz force
* Absorption band
* Accretion disk
* Active galactic nucleus
* Adiabatic invariant
* ADITYA (tokamak)
* Aeronomy
* Afterglow plasma
* Airg ...
References
{{DEFAULTSORT:Electromagnetic Electron Wave
Waves in plasmas