plasmapy.formulary.parameters.lower_hybrid_frequency(B: Unit(‘T’), n_i: Unit(‘1 / m3’), ion: plasmapy.particles.particle_class.Particle, to_hz=False)

Return the lower hybrid frequency.

Aliases: wlh_

  • B (Quantity) – The magnetic field magnitude in units convertible to tesla.

  • n_i (Quantity) – Ion number density.

  • ion (Particle) – Representation of the ion 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 ions are assumed to be singly charged.


omega_lh – The lower hybrid frequency in radians per second.

Return type


  • TypeError – If either of B or n_i is not a Quantity, or ion is of an inappropriate type.

  • UnitConversionError – If either of B or n_i is in incorrect units.

  • ValueError – If either of B or n_i contains invalid values or are of incompatible dimensions, or ion cannot be used to identify an ion or isotope.


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


The lower hybrid frequency is given through the relation

\[\frac{1}{ω_{lh}^2} = \frac{1}{ω_{ci}^2 + ω_{pi}^2} + \frac{1}{ω_{ci}ω_{ce}}\]

where \(ω_{ci}\) is the ion gyrofrequency, \(ω_{ce}\) is the electron gyrofrequency, and \(ω_{pi}\) is the ion plasma frequency.


>>> from astropy import units as u
>>> lower_hybrid_frequency(0.2*u.T, n_i=5e19*u.m**-3, ion='D+')
<Quantity 5.78372...e+08 rad / s>
>>> lower_hybrid_frequency(0.2*u.T, n_i=5e19*u.m**-3, ion='D+', to_hz = True)
<Quantity 92050879.3... Hz>
Other Parameters

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