Upper hybrid oscillation


Upper hybrid oscillation

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:omega^2 = omega_{pe}^2 + omega_{ce}^2 + 3 k^2 v_{mathrm{e,th^2,where (in cgs units):omega_{pe} = (4pi n_ee^2/m_e)^{1/2}is the electron plasma frequency, and:omega_{ce} = eB/m_ecis 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 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. Consider a plane wave where all perturbed quantities vary as exp("i"("kx"-ω"t")). If the displacement in the direction of propagation is δx, 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 = -ωce²δThus 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,:ωh² = ωpe² + ωce²,and is known as the upper hybrid frequency. There are also a lower hybrid frequency and lower hybrid oscillations.

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:omega^2 = (1/2)omega_h^2,left( 1 pm sqrt{ 1 - left( frac{cos heta}{omega_h^2/2 omega_comega_p} ight)^2 } ight)

See also

* Plasma oscillation
* Lower hybrid oscillation


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • 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 radic;( m e/ m i) radians.… …   Wikipedia

  • 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. The frequency only depends weakly on the wavelength. The quasiparticle… …   Wikipedia

  • Electrostatic ion cyclotron wave — An electrostatic ion cyclotron wave is a longitudinal oscillation of the ions (and electrons) in a magnetized plasma, propagating nearly (but not exactly) perpendicular to the magnetic field. The angle (in radians) between the direction of… …   Wikipedia

  • Manhattan — New York Island redirects here. For the Pacific island, see Teraina. For other uses, see Manhattan (disambiguation). Manhattan   Borough of New York City   New York County …   Wikipedia

  • United States — a republic in the N Western Hemisphere comprising 48 conterminous states, the District of Columbia, and Alaska in North America, and Hawaii in the N Pacific. 267,954,767; conterminous United States, 3,022,387 sq. mi. (7,827,982 sq. km); with… …   Universalium

  • literature — /lit euhr euh cheuhr, choor , li treuh /, n. 1. writings in which expression and form, in connection with ideas of permanent and universal interest, are characteristic or essential features, as poetry, novels, history, biography, and essays. 2.… …   Universalium

  • Limit superior and limit inferior — In mathematics, the limit inferior (also called infimum limit, liminf, inferior limit, lower limit, or inner limit) and limit superior (also called supremum limit, limsup, superior limit, upper limit, or outer limit) of a sequence can be thought… …   Wikipedia

  • Rocket engine — RS 68 being tested at NASA s Stennis Space Center. The nearly transparent exhaust is due to this engine s exhaust being mostly superheated steam (water vapor from its propellants, hydrogen and oxygen) …   Wikipedia

  • Outline of meteorology — See also: Index of meteorology articles Eye of Hurricane Isabel from the International Space Station, September 15, 2003. Meteorology is the interdisciplinary scientific study of the atmosphere that focuses on weather processes and forecasting.… …   Wikipedia

  • Famine — This article is about scarcity of food. For other uses, see Famine (disambiguation). Child victim of the Holodomor. A famine is a widespread scarcity of food. This phenomenon is usually accompanied or followed by regional malnutrition, starvation …   Wikipedia


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.