- Plasma oscillation
**Plasma oscillations**, also known as "**Langmuir waves**" (afterIrving Langmuir ), are rapid oscillations of the electron density in conducting media such as plasmas ormetal s. The frequency only depends weakly on the wavelength. Thequasiparticle resulting from the quantization of these oscillations is theplasmon .Langmuir waves were discovered by American physicists

Irving Langmuir andLewi Tonks in the1920s . They are parallel in form to Jeans instability waves, which are caused by gravitational instabilities in a static medium.**Explanation**Consider a neutral plasma, consisting of a gas of positively charged

ion s and negatively chargedelectrons . If one displaces by a tiny amount all of the electrons with respect to the ions, theCoulomb force pulls back, acting as a restoring force.**'Cold' electrons**If the electrons are cold, it is possible to show that the charge density oscillates at the "plasma frequency":$omega\_\{pe\}\; =\; sqrt\{frac\{4\; pi\; n\_e\; e^\{2\{m$ (cgs units) $=\; sqrt\{frac\{n\_e\; e^\{2\{mepsilon\_0$ (SI units) $=\; (56.4,mathrm\{rad/s\})\; imes(n/mathrm\{m^\{-3)^\{1/2\}$,where "$n\_e$ " is the density of electrons, "e" is the electric charge, "m" is the mass of the electron, and $epsilon\_0$ is the

permittivity of free space . Note that the aboveformula is derived under theapproximation that the ion mass is infinite. This is generally a good approximation, as the electrons are so much lighter than ions. (One must modify this expression in the case of electron-positron plasmas, often encountered inastrophysics ). Since thefrequency is independent of thewavelength , theseoscillation s have aninfinite phase velocity and zerogroup velocity .**'Warm' electrons**If warm electrons are considered with an

electron thermal speed $v\_\{e,th\}\; =\; sqrt\{frac\{k\_B\; T\_\{mathrm\{e\}\{m\_e$, the electron pressure acts as a restoring force as well as the electric field and the oscillations propagate with frequency andwavenumber related by:$omega^2\; =\; omega\_\{pe\}^2\; +\; 3\; k^2\; v\_\{mathrm\{e,th^2$,called the Bohm-Grossdispersion relation . If the spatial scale is large compared to theDebye length , theoscillation s are only weakly modified by thepressure term, but at small scales the pressure term dominates and the waves become dispersionless with a speed of $sqrt\{3\}\; cdot\; v\_\{e,th\}$. For such waves, however, the electron thermal speed is comparable to thephase velocity , i.e., :$v\; sim\; v\_\{ph\}\; stackrel\{mathrm\{def\{=\}\; frac\{omega\}\{k\},$so the plasma waves canaccelerate electrons that are moving with speed nearly equal to the phase velocity of the wave. This process often leads to a form of collisionless damping, calledLandau damping . Consequently, the large-"k" portion in thedispersion relation is difficult to observe and seldom of consequence.In a

bounded plasma, fringing electric fields can result in propagation of plasma oscillations, even when the electrons are cold.In a

metal orsemiconductor , the effect of theion s' periodic potential must be taken into account. This is usually done by using the electrons'effective mass in place of "m".**See also***

Upper hybrid oscillation , in particular for a discussion of the modification to the mode at propagation angles oblique to the magnetic field

*Waves in plasmas

* In 2006, plasma physicists at the Universities of Texas and Michigan were able to photograph Langmuir waves, generated by a 30 TW laser pulse, for the first time. [*[*]*http://www.eurekalert.org/pub_releases/2006-10/aps-fwe_1102706.php Fastest waves ever photographed*]**References*** Longair, Malcolm S., "Galaxy Formation", 1998.

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### Look at other dictionaries:

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