plasmapy.formulary.frequencies.upper_hybrid_frequency(B: Quantity, n_e: Quantity, *, to_hz=False) Quantity[source]

Return the upper hybrid frequency.

Aliases: wuh_

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

  • n_e (Quantity) – The electron number density.


omega_uh – The upper hybrid frequency in radians per second.

Return type:



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


The upper hybrid frequency is given through the relation

\[ω_{uh}^2 = ω_{ce}^2 + ω_{pe}^2\]

where \(ω_{ce}\) is the electron gyrofrequency and \(ω_{pe}\) is the electron plasma frequency.

The upper hybrid frequency is a resonance for electromagnetic waves in magnetized plasmas, namely for the X-mode. These are waves with their wave electric field being perpendicular to the background magnetic field. In the cold plasma model, i.e. without any finite temperature effects, the resonance acts merely as a resonance such that power can be deposited there. If finite temperature effects are considered, mode conversion can occur at the upper hybrid resonance, coupling to the electrostatic electron Bernstein wave.


>>> import astropy.units as u
>>> upper_hybrid_frequency(0.2 * u.T, n_e=5e19 * u.m**-3)
<Quantity 4.00459...e+11 rad / s>
>>> upper_hybrid_frequency(0.2 * u.T, n_e=5e19 * u.m**-3, to_hz=True)
<Quantity 6.37350...e+10 Hz>

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