Magnetohydrodynamic wave polarization (${\mathbf{u}}^{\prime }=U\hat{\mathbf{e}}$)

A polarization specifies the direction or trajectory of the oscillating velocity and magnetic field in a magnetohydrodynamic wave. The linear Alfvén wave has velocity perpendicular to the plane of the background magnetic field and wavevector; the magnetosonic waves have velocity in that plane. A real fixed polarization vector gives a linear oscillation. Two orthogonal components of equal amplitude in quadrature give a circular trajectory. For propagation parallel to a uniform field, combining the two degenerate transverse linear polarizations produces circular polarization; at finite amplitude its constant transverse magnetic-field magnitude removes the longitudinal magnetic pressure gradient.