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On the generation and radiation of magneto-acoustic waves

The generation, and thence the dissipation, propagation and radiation, of waves in a compressible fluid subjected to a magnetic field is studied as an extension of the ‘acoustic analogy’ (Lighthill 1952) to magneto-acoustics. A formal theory of magneto-acoustic waves introduces (i) a single differential operator describing propagation, (ii) a dynamic and a magnetic tensor modelling generation and (iii) a dissipation tensor to complete the wave equation. The interpretation of these tensors indicates the magnitude of the physical processes of wave generation, by turbulence and inhomogeneities, and of wave dissipation, by viscous and electrical resistance and heat conduction. The total quadrupole components are classified according to the mode of emission. If the magnetic field or compressibility is neglected we obtain, respectively, ‘aerodynamic acoustics’ and a corresponding theory for Alfvén waves. These hydrodynamic and hydromagnetic results contrast with magnetodynamics, when the magnetic field is dominant. The magneto-acoustic far field implies a law of directivity and intensity of radiation. The main results have been collected in three summary tables (see appendix).