# plasma_frequency

plasmapy.formulary.frequencies.plasma_frequency(n: Unit('1 / m3'), particle: , *, mass_numb: = None, Z: = None, to_hz=False)[source]

Calculate the particle plasma frequency.

Aliases: wp_

Lite Version: plasma_frequency_lite

Parameters:
• n (Quantity) – Particle number density in units convertible to m-3.

• particle (particle-like) – Representation of the particle species (e.g., "p" for protons, "D+" for deuterium, or "He-4 1+" for singly ionized helium-4). If no charge state information is provided, then the particles are assumed to be singly charged.

• Z (real number, optional) – The charge number of an ion or neutral atom, if not provided in particle.

• mass_numb (integer, optional) – The mass number of an isotope, if not provided in particle.

Returns:

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:

Quantity

Raises:
Warns:

UnitsWarning – If units are not provided, SI units are assumed.

Notes

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 using the to_hz keyword argument will apply the factor of $$1/2π$$ to give the frequency in Hz.

Examples

>>> import astropy.units as u
>>> plasma_frequency(1e19 * u.m**-3, particle='p')
<Quantity 4.16329...e+09 rad / s>
>>> plasma_frequency(1e19 * u.m**-3, particle='p', to_hz=True)
<Quantity 6.62608...e+08 Hz>
>>> plasma_frequency(1e19 * u.m**-3, particle='D+')
<Quantity 2.94462...e+09 rad / s>
>>> plasma_frequency(1e19 * u.m**-3, 'e-')
<Quantity 1.78398...e+11 rad / s>
>>> plasma_frequency(1e19 * u.m**-3, 'e-', to_hz=True)
<Quantity 2.83930...e+10 Hz>


For user convenience plasma_frequency_lite is bound to this function and can be used as follows.

>>> from plasmapy.particles import Particle
>>> mass = Particle("p+").mass.value
>>> plasma_frequency.lite(n=1e19, mass=mass, Z=1)
416329...
>>> plasma_frequency.lite(n=1e19, mass=mass, Z=1, to_hz=True)
662608...

Parameters:

to_hz (bool) – Set True to convert function output from angular frequency to Hz