In
, an upper hybrid oscillation is a mode of
oscillation
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
of a magnetized
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 ...
. It consists of a
longitudinal
Longitudinal is a geometric term of location which may refer to:
* Longitude
** Line of longitude, also called a meridian
* Longitudinal engine, an internal combustion engine in which the crankshaft is oriented along the long axis of the vehicl ...
motion of the electrons perpendicular to the
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 ...
with 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 ...
:
,
where (in
cgs units)
:
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 ...
, and
:
is the electron
cyclotron frequency
Cyclotron resonance describes the interaction of external forces with charged particles experiencing a magnetic field, thus already moving on a circular path. It is named after the cyclotron, a cyclic particle accelerator that utilizes an oscillati ...
.
This oscillation is closely related to the
plasma oscillation 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 ...
found in unmagnetized plasmas or parallel to the magnetic field, where the ω
pe term arises from the electrostatic Coulomb restoring force and the 3''k''²''v''
e,th² term arises from the restoring force of electron pressure. In the upper hybrid oscillation there is an additional restoring force due to the
Lorentz force
In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...
. Consider a
plane wave
In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space.
For any position \vec x in space and any time t, th ...
where all perturbed quantities vary as exp(''i''(''kx''-ω''t'')). If the displacement in the direction of propagation is δ
x, then
:''v''
x = -''i''ωδ
:''f''
y = ''nev''
x''B''
z/''c'' = -''i''ω(''neB''
z/''c'')δ
:''v''
y = -''f''
y/''i''ω''nm'' = (''eB''
z/''mc'')δ
:''f''
x = -''nev''
y''B''
z/''c'' = -(''nm'')(''eB''
z/''mc'')²δ
:''a''
x = -ω
ce²δ
Thus the perpendicular magnetic field effectively provides a
harmonic
A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...
restoring force with a frequency ω
ce, explaining the third term in the dispersion relation. The particle orbits (or fluid trajectories) are
ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...
s in the plane perpendicular to the magnetic field, elongated in the direction of propagation.
The frequency of long wavelength oscillations is a "hybrid", or mix, of the electron plasma and electron cyclotron frequencies,
:ω
h² = ω
pe² + ω
ce²,
and is known as the upper hybrid frequency. There are also a lower hybrid frequency and
lower hybrid oscillation
In plasma physics, a lower hybrid oscillation is a longitudinal oscillation of ions and electrons in a magnetized plasma. The direction of propagation must be very nearly perpendicular to the stationary magnetic field, within about radians. Othe ...
s.
For propagation at angles oblique to the magnetic field, two modes exist simultaneously. If the plasma frequency is higher than the cyclotron frequency, then the upper hybrid oscillation transforms continuously into the plasma oscillation. The frequency of the other mode varies between the cyclotron frequency and zero. Otherwise, the frequency of the mode related to the upper hybrid oscillation remains above the cyclotron frequency, and the mode related to the plasma oscillation remains below the plasma frequency. In particular, the frequencies are given by
:
See also
*
Plasma oscillation 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 ...
*
Lower hybrid oscillation
In plasma physics, a lower hybrid oscillation is a longitudinal oscillation of ions and electrons in a magnetized plasma. The direction of propagation must be very nearly perpendicular to the stationary magnetic field, within about radians. Othe ...
*
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 ...
Waves in plasmas
{{plasma-stub
To derive the dispersion relation of ion cyclotron waves in quantum plasma we use quantum plasma parameters such as fermi temperature,pressure and compensating the debroglie wavelength in quantum plasma.