Magnetohydrodynamic (MHD) plasma theory deals with a compressible, conducting **fluid** immersed in a magnetic field. The wave modes derived using this theory are called magnetohydrodynamic or MHD waves. In the general case, with the wave propagation in an arbitrary direction with respect to external magnetic field **B**, **three MHD wave modes** are found:

- Pure (or oblique) Alfven wave
- Slow MHD wave
- Fast MHD wave

(There will be a figure here showing how the different wave modes are related.) These relate with the three different oblique shock types in ideal MHD.

All these waves have constant phase velocities for all frequencies, and hence there is no dispersion. At the limits when the angle *a* between the wave propagation vector **k** and magnetic field **B** is either 0 (180) or 90 degrees, the very same wave modes are called as:

- Sound wave
- longitudinal wave
- propagates parellel to
**B** - phase velocity is the adiabatic sound velocity
- no associated
**E**,**j**, or**B** - found also in a compressible,
*non*conducting fluid

- Alfven wave
- transverse wave
- propagates also parellel to
**B** - phase velocity is the Alfven velocity
- associated
**B**found - known also as the shear Alfven wave or the slow Alfven wave, and sometimes as the torsional Alfven wave

- Magnetosonic wave
- longitudinal wave
- propagates perpendicular to
**B** - associated
**B**and**E**found - known also as the compressional Alfven wave or the fast Alfven wave, and sometimes as the magnetoacoustic wave

When the fluid is not perfectly conducting, but has a finite conductivity, or if viscous effects are present, the MHD oscillations will be damped.