# Magnetosonic wave

A magnetosonic wave (also magnetoacoustic wave) is a longitudinal wave[1] of ions (and electrons) in a magnetized plasma propagating perpendicular to the stationary magnetic field. The wave is dispersionless with a phase velocity ω/k given by

${\displaystyle {\frac {\omega ^{2}}{k^{2}}}=c^{2}\,{\frac {v_{s}^{2}+v_{A}^{2}}{c^{2}+v_{A}^{2}}}}$,

where vs is the speed of the ion acoustic wave, vA is the speed of the Alfvén wave, and c is the speed of light in vacuum.

In the limit of low magnetic field (vA→0), the wave turns into an ordinary ion acoustic wave. In the limit of low temperature (vs→0), the wave becomes a modified Alfvén wave. Because the phase velocity of the magnetosonic mode is almost always larger than vA, the magnetosonic wave is often called the "fast" hydromagnetic wave.

Both fast and slow magnetoacoustic waves have been recently discovered in the solar corona,[2] which created an observational foundation for the novel technique for the coronal plasma diagnostics, coronal seismology.