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Concept
Plasma oscillation
Summary
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 in the dielectric function of a free electron gas. The frequency depends only weakly on the wavelength of the oscillation. The quasiparticle resulting from the quantization of these oscillations is the plasmon.
Langmuir waves were discovered by American physicists Irving Langmuir and Lewi Tonks in the 1920s. They are parallel in form to Jeans instability waves, which are caused by gravitational instabilities in a static medium.
Consider an electrically neutral plasma in equilibrium, consisting of a gas of positively charged ions and negatively charged electrons. If one displaces by a tiny amount an electron or a group of electrons with respect to the ions, the Coulomb force pulls the electrons back, acting as a restoring force.
If the thermal motion of the electrons is ignored, it is possible to show that the charge density oscillates at the plasma frequency
(SI units),
(cgs units),
where is the number density of electrons, is the electric charge, is the effective mass of the electron, and is the permittivity of free space. 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.
Proof using Maxwell equations. Assuming charge density oscillations the continuity equation:
the Gauss law
and the conductivity
taking the divergence on both sides and substituting the above relations:
which is always true only if
But this is also the dielectric constant (see Drude Model)
and the condition of transparency (i.e. from a certain plasma frequency and above), the same condition here apply to make possible also the propagation of density waves in the charge density.
This expression must be modified in the case of electron-positron plasmas, often encountered in astrophysics.
Official source
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