Plasma density (source code)

= Plasma density

<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 $Z_i e$,
$$
n_e\simeq\sum_i Z_i n_i.
$$
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, giving
$$
\omega_{pe}^2=\frac{n_e e^2}{\epsilon_0m_e},\qquad
f_{pe}\simeq8.98\times10^3\sqrt{\frac{n_e}{\mathrm{cm}^{-3}}}\,\mathrm{Hz}.
$$
The first formula uses SI units; the numerical version expresses electron density in particles per cubic centimetre.<NRL Plasma Formulary (2019)>[Fundamental Plasma Parameters, printed page 28, electron plasma frequency; SI expression obtained by unit conversion]{ref}

If an identified electron plasma oscillation has frequency $2000\,\mathrm{Hz}$, this model gives
$$
n_e=\left(\frac{2000}{8980}\right)^2\mathrm{cm}^{-3}\simeq0.0496\,\mathrm{cm}^{-3}=4.96\times10^4\,\mathrm m^{-3}.
$$
This 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.