A magnetosonic wave, also called a magnetoacoustic wave, is a linear
magnetohydrodynamic
Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, ...
(MHD) wave that is driven by
thermal pressure
In thermodynamics, thermal pressure (also known as the thermal pressure coefficient) is a measure of the relative pressure change of a fluid or a solid as a response to a temperature change at constant volume. The concept is related to the Pressur ...
,
magnetic pressure
In physics, magnetic pressure is an energy density associated with a magnetic field. In SI units, the energy density P_B of a magnetic field with strength B can be expressed as
:P_B = \frac
where \mu_0 is the vacuum permeability.
Any magnetic fiel ...
, and
magnetic tension. There are two types of magnetosonic waves, the ''fast'' magnetosonic wave and the ''slow'' magnetosonic wave. Both fast and slow magnetosonic waves are present in the
solar corona
A corona ( coronas or coronae) is the outermost layer of a star's atmosphere. It consists of plasma.
The Sun's corona lies above the chromosphere and extends millions of kilometres into outer space. It is most easily seen during a total solar ...
providing an observational foundation for the technique for coronal plasma diagnostics,
coronal seismology
Coronal seismology is a technique of studying the plasma of the Sun's corona with the use of magnetohydrodynamic (MHD) waves and oscillations. Magnetohydrodynamics studies the dynamics of electrically conducting fluids - in this case the fluid ...
.
Homogeneous plasma
In an ideal homogeneous plasma of infinite extent, and in the absence of gravity, the fast and slow magnetosonic waves form, together with the Alfvén wave, the three basic linear
MHD waves. Under the assumption of normal modes, namely that the linear perturbations of the physical quantities are of the form
:
(with the constant amplitude), a
dispersion relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the d ...
of the magnetosonic waves can be derived from the system of ideal MHD equations:
:
where is the Alfvén speed, is the sound speed, is the magnitude of the wave vector and is the component of the wave vector along the background magnetic field (which is straight and constant, because the plasma is assumed homogeneous).
This equation can be solved for the frequency , yielding the frequencies of the fast and slow magnetosonic waves:
:
It can be shown that (with the Alfvén frequency), hence the name of "slow" and "fast" magnetosonic waves.
Limiting cases
Absent magnetic field
In the absence of a magnetic field, the whole
MHD model reduces to the
hydrodynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...
(HD) model. In this case , and hence and . The slow wave thus disappears from the system, while the fast wave is just a sound wave, propagating isotropically.
Incompressible plasma
In case the plasma is
incompressible
In fluid mechanics or more generally continuum mechanics, incompressible flow ( isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An eq ...
, the sound speed (this follows from the energy equation) and it can then be shown that and . The slow wave thus propagates with the Alfvén speed (although it remains different from an Alfvén wave in its nature), while the fast wave disappears from the system.
Cold plasma
Under the assumption that the background temperature , it follows from the
ideal gas law
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...
that the thermal pressure and thus that . In this case, and . Hence there are no slow waves in the system, and the fast waves propagate isotropically with the Alfvén speed.
Inhomogeneous plasma
In the case of an inhomogeneous plasma (that is, a plasma where at least one of the background quantities is not constant) the MHD waves lose their defining nature and get mixed properties.
[{{Cite journal, last1=Goossens, first1=Marcel L., last2=Arregui, first2=Inigo, last3=Van Doorsselaere, first3=Tom, date=2019-04-11, title=Mixed Properties of MHD Waves in Non-uniform Plasmas, journal=Frontiers in Astronomy and Space Sciences, volume=6, pages=20, doi=10.3389/fspas.2019.00020, bibcode=2019FrASS...6...20G, issn=2296-987X, doi-access=free] In some setups, such as the axisymmetric waves in a straight cylinder with a circular basis (one of the simplest models for a
coronal loop
In solar physics, a coronal loop is a well-defined arch-like structure in the Sun's atmosphere made up of relatively dense plasma confined and isolated from the surrounding medium by magnetic flux tubes. Coronal loops begin and end at two footp ...
), the three MHD waves can still be clearly distinguished. But in general, the pure Alfvén and fast and slow magnetosonic waves don't exist, and the waves in the plasma are coupled to each other in intricate ways.
See also
*
Waves in plasmas In plasma physics, waves in plasmas are an interconnected set of particles and fields which propagate in a periodically repeating fashion. A plasma is a quasineutral, electrically conductive fluid. In the simplest case, it is composed of electron ...
*
Alfvén wave
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.
Definition
An Alfvén wave is ...
*
Ion acoustic wave In plasma physics, an ion acoustic wave is one type of longitudinal oscillation of the ions and electrons in a plasma, much like acoustic waves traveling in neutral gas. However, because the waves propagate through positively charged ions, ion aco ...
*
Coronal seismology
Coronal seismology is a technique of studying the plasma of the Sun's corona with the use of magnetohydrodynamic (MHD) waves and oscillations. Magnetohydrodynamics studies the dynamics of electrically conducting fluids - in this case the fluid ...
*
Magnetogravity wave
References
Waves in plasmas