# lower_hybrid_frequency

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_

Parameters
• 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.

Returns

omega_lh – The lower hybrid frequency in radians per second.

Return type

Quantity

Raises
• 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.

Warns

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

Notes

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.

The lower hybrid frequency consitutes 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. For the lower hybrid frequency, ion and electron dynamics both play a role. As the name suggests, it has a lower frequency compared to the upper hybrid frequency. It can play an important role for heating and current drive in fusion plasmas.

Examples

>>> 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>

Parameters

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