Propagation of hydromagnetic waves in a nonuniform magnetic field

The propagation of hydromagnetic waves in an infinite extent of an incompressible, inviscid, and perfectly conducting fluid in a slightly nonuniform magnetic field is investigated. The amplitude and phase fluctuations on the waves due to the inhomogeneity of the magnetic field are obtained using a perturbation method. It is found, from the first approximation, that the wave will not always propagate along the magnetic lines of the force as it does in a uniform field, and it is in general associated with an elliptical fluid motion. The cases of unidirectional and two-dimensional convergent fields are treated in detail.