critical_density

plasmapy.formulary.densities.critical_density(omega: Quantity) → Quantity

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

\[n_{c}=\frac{m_{e}\varepsilon_0\omega^{2}}{e^{2}}\]

where \(m_{e}\) is the mass of an electron, \(\varepsilon_0\) is the permittivity of free space, \(\omega\) 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>