The coupling of shear Alfvén and compressional waves in high‐β magnetospheric plasma

The coupling of the compressional instabilities in a two‐component, hot and cold inhomogeneous plasma to the resonant shear Alfvén mode is studied in a slab geometry with straight field lines. The lowest order effect of the field inhomogeneity is incorporated into the dispersion relation by retaining the ▽ B drift of the particles. It is found that the high‐phase velocity compressional mode with ω/ k ∥ > V ∥ i shows insignificant coupling to the shear Alfvén wave, while the low‐phase velocity branch with ω/ k ∥ < V ∥ i shows significant coupling. It is also shown that the coupling factor is of the form β ∥ i n c / n i k ⊥ ² r B ², so that a more realistic field geometry should be used to model the magnetospheric field in the study of low‐frequency geomagnetic pulsations.