Improved basis set for low frequency plasma waves

[1] It is shown that the low frequency plasma wave equation can be obtained much more directly than by the previously used method of solving for the determinant of a matrix involving the three components of the electric field vector. The more direct method uses a two-dimensional current density vector space that is precisely equivalent to the previously used three-dimensional electric field vector space. Unlike the electric field, the current density is restricted by the quasi-neutrality condition to a two-dimensional vector space. Comparison with previously obtained dispersion relations is provided and a method is presented for obtaining exact analytic solutions for the three roots of the cubic dispersion relation. The commonly used kinetic Alfvén dispersion relation is shown to be valid only for near-perpendicular propagation in a low beta plasma. It is shown that at a cross-over point where the perpendicular wave phase velocity equals the ion acoustic velocity, the coupling between Alfvén and fast modes vanishes and the Alfvén mode reverts to its cold form even in situations where the Alfvén velocity is smaller than the electron thermal velocity. A method is prescribed by which measurement of wave electric current density completely eliminates the space-time ambiguity previously believed to be an unavoidable shortcoming of single-spacecraft frequency measurements.