Alfvén wave
In plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave in which ions oscillate in response to a restoring force provided by an effective tension on the magnetic field lines.
Definition
An Alfvén wave in a plasma is a low-frequency (compared to the ion cyclotron frequency) travelling oscillation of the ions and the magnetic field. The ion mass density provides the inertia and the magnetic field line tension provides the restoring force.
The wave propagates in the direction of the magnetic field, although waves exist at oblique incidence and smoothly change into the magnetosonic wave when the propagation is perpendicular to the magnetic field.
The motion of the ions and the perturbation of the magnetic field are in the same direction and transverse to the direction of propagation. The wave is dispersionless.
Alfvén velocity
The low-frequency relative permittivity 
of a magnetized plasma is given by
where 
is the magnetic field strength, 
is the speed of light, 
is the permeability of the vacuum, and 
is the total mass density of the charged plasma particles. Here, 
goes over all plasma species, both electrons and (few types of) ions.
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