The role of O+ and He+ on the propagation of Kinetic Alfv\'en Waves in the Earth's inner magnetosphere

Interactions between plasma particles and electromagnetic waves play a crucial role in the dynamics and regulation of the state of space environments. From plasma physics theory, the characteristics of the waves and their interactions with the plasma strongly depend on the composition of the plasma, among other factors. In the case of the Earth's magnetosphere, the plasma is usually composed by electrons, protons, O+, and He+ ions, all with their particular properties and characteristics. Here, using plasma parameters relevant for the inner magnetosphere we study the dispersion properties of Kinetic Alfv\'en Waves (KAW) in a plasma composed by electrons, protons, He+ ions, and O+ ions. We show that heavy ions induce significant changes to the dispersion properties of KAW, such as polarization, compressibility, and electric-to-magnetic amplitude ratio, and therefore the propagation of Kinetic Alfv\'en Waves is highly determined by the relative abundance of He+ and O+ in the plasma. These results when discussed in the context of observations in the Earth's magnetosphere, suggest that for many types of studies based on theory and numerical simulations, the inclusion of heavy ions should be customary for realistic modeling of plasma phenomena in the inner magnetosphere or other space environments in which heavy ions can contribute with a substantial portion of the plasma such as planetary magnetospheres and comet plasma tails.