Hall current and Alfven wave

In ideal inhomogeneous magnetohydrodynamics (MHD), the Alfven wave (the dominant low frequency mode of a magnetized plasma) displays a continuous spectrum associated with singular eigenfunctions. It is shown that the coupling of the Hall term with the sound wave induces higher (fourth) order derivative in the Alfven mode equation, and by resolving the singularity replaces the MHD continuum by a discrete spectrum. The mode structure resulting from the Hall resolution of the singularity is compared with the standard electron-inertia approach