plasma_frequency¶

plasmapy.formulary.
plasma_frequency
(n: Unit(‘1 / m3’), particle: plasmapy.particles.particle_class.Particle, z_mean=None, to_hz=False)¶ Calculate the particle plasma frequency.
Aliases:
wp_
 Parameters
n (
Quantity
) – Particle number density in units convertible to per cubic meter.particle (
Particle
) – Representation of the particle species (e.g., ‘p’ for protons, ‘D+’ for deuterium, or ‘He4 +1’ for singly ionized helium4). If no charge state information is provided, then the particles are assumed to be singly charged.z_mean (
Quantity
, optional) – The average ionization (arithmetic mean) for a plasma where the a macroscopic description is valid. If this quantity is not given then the atomic charge state (int
) of the ion is used. This is effectively an average plasma frequency for the plasma where multiple charge states are present.
 Returns
omega_p – The particle plasma frequency in radians per second.
 Return type
 Raises
TypeError – If
n_i
is not aQuantity
or particle is not of an appropriate type.UnitConversionError – If
n_i
is not in correct units.ValueError – If
n_i
contains invalid values or particle cannot be used to identify an particle or isotope.
 Warns
UnitsWarning
– If units are not provided, SI units are assumed.
Notes
The particle plasma frequency is
\[ω_{pi} = Z e \sqrt{\frac{n_i}{\epsilon_0 m_i}}\]At present,
astropy.units
does not allow direct conversions from radians/second for angular frequency to 1/second or Hz for frequency. Thedimensionless_angles
equivalency allows for that conversion, but does not account for the factor of \(2π\). The alternatives are to convert to cycle/second or to do the conversion manually, as shown in the examples.Example
>>> from astropy import 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>
 Other Parameters
to_hz (bool) – Set
True
to to convert function output from angular frequency to Hz