plasmapy.formulary.frequencies.plasma_frequency_lite(n: float, mass: float, Z: float, to_hz: bool = False) float[source]

The lite-function for plasma_frequency. Performs the same plasma frequency calculation as plasma_frequency, but is intended for computational use and, thus, has all data conditioning safeguards removed.

  • n (float) – Particle number density, in units of m-3.

  • mass (float) – Mass of the particle, in units of kg.

  • Z (float) – The average ionization (arithmetic mean) for the particle species in the plasma. For example, a proton would have a value of Z=1.

  • to_hz (bool, default: False.) – Set True to apply the factor of \(1/2π\) and return a value in units of Hz.


wp – The particle plasma frequency in radians per second. Setting keyword to_hz=True will apply the factor of \(1/2π\) and yield a value in Hz.

Return type:



The particle plasma frequency is

\[ω_p = \sqrt{\frac{n |q|}{ε_0 m}}\]

where \(n\) is the number density, \(q\) is the particle charge, and \(m\) is the particle mass.

This form of the plasma frequency has units of rad/s, but when using the to_hz keyword a factor of \(1/2π\) will be applied to give a value in Hz.


>>> from plasmapy.particles import Particle
>>> mass = Particle("p+").mass.value
>>> plasma_frequency_lite(n=1e19, mass=mass, Z=1)
>>> plasma_frequency_lite(n=1e19, mass=mass, Z=1, to_hz=True)