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In physics, plasma oscillations, often referred to as "Langmuir waves" or "plasma waves," are periodic oscillations of charge density in conducting media such as plasmas or metals. The particle resulting from the quantization of these oscillations is the plasmon.
Consider a neutral plasma, consisting of a gas of positively charged ions and negatively charged electrons. If one displaces by a tiny amount all of the electrons with respect to the ions, the Coulomb force pulls back, acting as a restoring force. It is possible to show that the charge density oscillates at the plasma frequency
- <math>
\omega_{pe} = \sqrt{\frac{4 \pi n e^{2}}{m}}
<math>,
where n is the density of electrons, e is the electric charge, and m is the mass of the electron. Note that the above formula is derived under the approximation 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 in astrophysics).
If the characteristic wavenumber k of a plasma oscillation is comparable to the product of the electron thermal speed v and the plasma frequency, then the plasma wave may propagate in the medium. These waves will obey a dispersion relation
- <math>
\omega^2 - \omega_{pe}^2 = 3 k^2 v^2,
<math>
called the Bohm-Gross dispersion relation. If the electron thermal speed is comparable to the phase velocity, i.e.,
- <math>
v \sim v_{ph} \equiv \frac{\omega}{k},
<math>
then the plasma waves can accelerate 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, called Landau damping.
In a metal or semiconductor, the effect of the ions' periodic potential must be taken into account. This is usually done by using the electrons' effective mass in place of m.
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