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The electron plasma frequency is the characteristic angular frequency of small collective electron displacements against an effectively stationary neutralizing ion background. For electron number density $n_e$, its cold, unmagnetized value in SI units isHere $e$ is the magnitude of the electron charge and $m_e$ the electron mass. Angular frequency and cycles per second differ by $2\pi$.^[ref]

A displaced slab gives a simple derivation. Shift a uniform electron population by a small distance $x$ relative to fixed positive ions. The exposed charge produces a restoring electric field $E=n_{e}ex/{ϵ}_0$. Newton's equation for an electron then giveswhich is a harmonic oscillator with the frequency above. This argument describes a collective charge-separation mode, not an individual electron's orbital frequency.

For $n_e=10^6{\mathrm{m}}^{-3}=1{\mathrm{cm}}^{-3}$, $f_{pe}\simeq 8.98\mathrm{kHz}$. Increasing density by a factor of four doubles the frequency. An identified plasma oscillation can therefore diagnose density, while interpreting an arbitrary spectral peak this way would be unjustified.

Finite temperature changes the wave's dispersion relation; magnetic fields, collisions and ion motion introduce additional modes or damping. The same cold model also gives the transverse wave cutoff in a cold unmagnetized plasma, but an observed electromagnetic cutoff and a local electrostatic oscillation are distinct measurements.

Plasma density must specify what is being counted or weighed. For species $s$, its number density $n_s$ counts particles per unit volume. Electron density $n_e$, ion density $n_i$ and total mass density $\rho ={\sum }_s{m}_s{n}_s$ need not be interchangeable. In a quasineutral mixture with ion charges $Z_{i}e$,For singly ionized hydrogen, $n_e\simeq n_i$, while the ions provide nearly all the mass. Adding heavier ions changes the relation between electron density and mass density.

An electron plasma frequency measurement offers a density diagnostic. In the cold, unmagnetized approximation with effectively fixed ions, displacement of electrons creates an electric restoring force, givingThe first formula uses SI units; the numerical version expresses electron density in particles per cubic centimetre.^[ref]

If an identified electron plasma oscillation has frequency $2000\mathrm{Hz}$, this model givesThis is an inference from an identified wave mode, not a particle counter reading. Magnetization, wave propagation, multiple species and instrument effects can change which spectral feature is observed, so interpreting a frequency requires the relevant plasma wave model.