critical_density

plasmapy.formulary.densities.critical_density( omega: Annotated[Quantity, Unit('rad / s')], ) → Annotated[Quantity, Unit('1 / m3')][source]

Calculate the plasma critical density for a radiation of a given frequency.

Parameters:: omega (Quantity) – The radiation frequency in units of angular frequency.
Returns:: n_c – The plasma critical density.
Return type:: Quantity

Notes

The critical density for a given frequency of radiation is defined as the value at which the electron plasma frequency equals the frequency of the radiation.

The critical density is given by the formula

\[n_c=\frac{m_e ε_0 θ^{2}}{e^2}\]

where \(m_{e}\) is the mass of an electron, \(ε_0\) is the permittivity of free space, \(θ\) is the radiation frequency, and \(e\) is the elementary charge.

Examples

>>> import astropy.units as u
>>> critical_density(5e15 * u.rad / u.s)
<Quantity 7.85519457e+27 1 / m3>