Electromagnetic electron wave
Encyclopedia
An electromagnetic electron wave is a wave
in a plasma
which has a magnetic field
component and in which primarily the electron
s oscillate.
In an unmagnetized plasma, an electromagnetic electron wave is simply a light
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.
or 
, the wave speed is the speed of light
in vacuum. As the density increases, the phase velocity increases and the group velocity decreases until the cut-off frequency where the light frequency is equal to the plasma frequency. This density is known as the critical density for the angular frequency
ω of that wave and is given by
.
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.
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 ck/ω (squared).
Waves in plasmas
Waves in plasmas are an interconnected set of particles and fields which propagates in a periodically repeating fashion. A plasma is a quasineutral, electrically conductive fluid. In the simplest case, it is composed of electrons and a single species of positive ions, but it may also contain...
in a plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
which has a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
component and in which primarily the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s oscillate.
In an unmagnetized plasma, an electromagnetic electron wave is simply a light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
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.
Cut-off frequency and critical density
In an unmagnetized plasma in the high frequency or low density limit, i.e. for or , the wave speed is the speed of lightSpeed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
in vacuum. As the density increases, the phase velocity increases and the group velocity decreases until the cut-off frequency where the light frequency is equal to the plasma frequency. This density is known as the critical density for the angular frequency
Angular frequency
In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...
ω of that wave and is given by
.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 is the same as that in an unmagnetized plasma. It is plane polarized with E1||B0. It has a cut-off at the plasma frequency.X wave
The X wave is the "extraordinary" wave because it has a more complicated dispersion relation. It is partly transverse (with E1||B0) and partly longitudinal. As the density is increased, the phase velocity rises from c until the cut-off at ωR is reached. As the density is further increased, the wave is evanescent until the resonance at the upper hybrid frequency ωh. Then it can propagate again until the second cut-off at ωL. The cut-off frequencies are given byR 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 ωR (hence the designation of this frequency) and a resonance at ωc. The L wave has a cut-off at ωL and no resonance. R waves at frequencies below ωc/2 are also known as whistler modes.Dispersion relations
The dispersion relationDispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....
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 ck/ω (squared).
| conditions | dispersion relation | name |
|---|---|---|
 |
 |
light wave |
 |
O wave | |
 |
 |
X wave |
| (right circ. pol.) |  |
R wave (whistler mode) |
| (left circ. pol.) |  |
L wave |