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Concept
Alfvén wave
Summary
In plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of plasma wave in which ions oscillate in response to a restoring force provided by an effective tension on the magnetic field lines.
An Alfvén wave is a low-frequency (compared to the ion gyrofrequency) travelling oscillation of the ions and magnetic field in a plasma. The ion mass density provides the inertia and the magnetic field line tension provides the restoring force. Alfvén waves propagate in the direction of the magnetic field, and the motion of the ions and the perturbation of the magnetic field are transverse to the direction of propagation. However, Alfvén waves existing at oblique incidences will smoothly change into magnetosonic waves when the propagation is perpendicular to the magnetic field.
Alfvén waves are dispersionless.
The low-frequency relative permittivity of a magnetized plasma is given by
where B is the magnetic field strength, is the speed of light, is the permeability of the vacuum, and the mass density is the sum
over all species of charged plasma particles (electrons as well as all types of ions).
Here species has number density
and mass per particle .
The phase velocity of an electromagnetic wave in such a medium is
For the case of an Alfvén wave
where
is the Alfvén wave group velocity.
(The formula for the phase velocity
assumes that the plasma particles are moving at non-relativistic speeds,
the mass-weighted particle velocity is zero in the frame of reference,
and the wave is propagating parallel to the magnetic field vector.)
If , then .
On the other hand, when , . That is, at high field or low density, the group velocity of the Alfvén wave approaches the speed of light, and the Alfvén wave becomes an ordinary electromagnetic wave.
Neglecting the contribution of the electrons to the mass density,
where is the ion number density and is the mean ion mass per particle,
so that
In plasma physics, the Alfvén time is an important timescale for wave phenomena. It is related to the Alfvén velocity by:
where denotes the characteristic scale of the system.
Official source
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