General dispersion relation for nonpotential ion harmonic waves propagating in plasmas with arbitrary β

The dispersion relation for nonpotential ion harmonic waves propagating at any angle to the magnetic field in plasmas with arbitrary β is derived for ω/kz≫Vi, where ω/kz is the parallel phase velocity and Vi is the ion thermal speed. It is shown that these slow waves can propagate in plasmas when the electron plasma pressure to magnetic pressure ratio βe, is much less than 1 and only in the wavenumber range k≳ (Πe/c)(ω/Ωecosϑ)1/2, where Πe is the plasma frequency, Ωe is the electron gyrofrequency, c is the velocity of light, and ϑ is the propagation angle. Finally, a comparison between the properties of these slow waves and those of the fast electromagnetic ones, is given.