Upper hybrid oscillation
Encyclopedia
An upper hybrid oscillation is a mode of oscillation
of a magnetized plasma
. It consists of a longitudinal
motion of the electrons perpendicular to the magnetic field with the dispersion relation
,
where (in cgs units
)
is the electron plasma frequency, and
is the electron cyclotron frequency.
This oscillation is closely related to the plasma oscillation
found in unmagnetized plasmas or parallel to the magnetic field, where the ωpe term arises from the electrostatic restoring force and the 3k²ve,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
. Consider a plane wave where all perturbed quantities vary as exp(i(kx-ωt)). If the displacement in the direction of propagation is δx, then
Thus the perpendicular magnetic field effectively provides a harmonic
restoring force with a frequency ωce, explaining the third term in the dispersion relation. The particle orbits (or fluid trajectories) are ellipses 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,
and is known as the upper hybrid frequency. There are also a lower hybrid frequency and lower hybrid oscillation
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
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...
of a magnetized 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...
. It consists of a longitudinal
Longitudinal wave
Longitudinal waves, as known as "l-waves", are waves that have the same direction of vibration as their direction of travel, which means that the movement of the medium is in the same direction as or the opposite direction to the motion of the wave. Mechanical longitudinal waves have been also...
motion of the electrons perpendicular to the magnetic field with the dispersion relation
,where (in cgs units
Centimetre gram second system of units
The centimetre–gram–second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...
)
is the electron plasma frequency, and
is the electron cyclotron frequency.
This oscillation is closely related to the plasma oscillation
Plasma oscillation
Plasma oscillations, also known as "Langmuir waves" , are rapid oscillations of the electron density in conducting media such as plasmas or metals. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency only depends weakly on the...
found in unmagnetized plasmas or parallel to the magnetic field, where the ωpe term arises from the electrostatic restoring force and the 3k²ve,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
Lorentz force
In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...
. Consider a plane wave where all perturbed quantities vary as exp(i(kx-ωt)). If the displacement in the direction of propagation is δx, then
- vx = -iωδ
- fy = nevxBz/c = -iω(neBz/c)δ
- vy = -fy/iωnm = (eBz/mc)δ
- fx = -nevyBz/c = -(nm)(eBz/mc)²δ
- ax = -ωce²δ
Thus the perpendicular magnetic field effectively provides a harmonic
Harmonic oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, where k is a positive constant....
restoring force with a frequency ωce, explaining the third term in the dispersion relation. The particle orbits (or fluid trajectories) are ellipses 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,
- ωh² = ωpe² + ωce²,
and is known as the upper hybrid frequency. There are also a lower hybrid frequency and lower hybrid oscillation
Lower hybrid oscillation
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...
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 oscillationPlasma oscillationPlasma oscillations, also known as "Langmuir waves" , are rapid oscillations of the electron density in conducting media such as plasmas or metals. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency only depends weakly on the...
- Lower hybrid oscillationLower hybrid oscillationA 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...