One of the most striking properties of Kinetic Alfvén Waves (KAW) is that, unlike the also Alfvénic Electromagnetic Ion Cyclotron (EMIC) waves, these waves are right-hand polarized in the plasma frame. In particular, this signature property is key for the identification of KAW from in situ measurements of plasma waves. From the theoretical point of view, both the dispersion relation and the polarization of KAW has been mostly studied in proton-electron plasmas. However, most astrophysical and space plasmas are multi-species, and therefore in these systems the dispersion properties of the KAW may not depend only on the macroscopic parameters of proton and electron distributions, but also on the parameters of heavier ions. Here, using Vlasov linear theory we study the dispersion properties of Alfvénic modes in multi-species plasmas composed by electrons, protons, and O + ions, with macroscopic plasma parameters relevant to the inner magnetosphere. In consistency with recent observations, our numerical results show that the presence of O + ions allows the existence of KAW in a wider wave-number range and at smaller wave-normal angles compared to the electron-proton case, but at the same time isotropic O + ions tend to reduce (or even inhibiting) the growth rates of unstable KAW triggered by anisotropic protons. These results suggest that magnetospheric ions may play an important role on the energy transfer from large macroscopic scales to sub-ionic and electronic scales, especially during intense geomagnetic storms in which O + ions can dominate the plasma composition in the inner magnetosphere.

Kappa distributions (or $$\kappa $$ κ -like distributions) represent a robust framework to characterize and understand complex phenomena with high degrees of freedom, as turbulent systems, using non-extensive statistical mechanics. Here we consider a coupled map lattice Langevin based model to analyze the relation of a turbulent flow, with its spatial scale dynamic, and $$\kappa $$ κ -like distributions. We generate the steady-state velocity distribution of the fluid at each scale, and show that the generated distributions are well fitted by $$\kappa $$ κ -like distributions. We observe a robust relation between the $$\kappa $$ κ parameter, the scale, and the Reynolds number of the system, Re. In particular, our results show that there is a closed scaling relation between the level of turbulence and the $$\kappa $$ κ parameter; namely $$\kappa \sim \text {Re}\,k^{-5/3}$$ κ ∼ Re k - 5 / 3 . We expect these results to be useful to characterize turbulence in different contexts, and our numerical predictions to be tested by observations and experimental setups.

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 of electrons, protons, O+ ions, 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 Alfvén waves (KAWs) in a plasma composed of electrons, protons, He+ ions, and O+ ions. We show that heavy ions induce significant changes to the dispersion properties of KAWs, such as polarization, compressibility, and the electric-to-magnetic amplitude ratio, and therefore the propagation of KAWs 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 the realistic modeling of plasma phenomena in the inner magnetosphere or other space environments in which heavy ions can contribute a substantial portion of the plasma, such as planetary magnetospheres and comet plasma tails.

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In this article, on the basis of the Langevin equation applied to velocity fluctuations, we numerically model the partial variance of increments, which is a useful tool to measure time and spatial correlations in space plasmas. We consider a coupled map lattice model to relate the spatial scale of fluctuations, k, to some macro parameters of the systems, such as the Reynolds number, R λ , the κ parameter of Kappa distributions, and a skewness parameter, δ. To do so, we compute the velocity probability density function (pdf) for each spatial scale and different values of Reynolds number in the simulations. We fit the pdf with a Skew–Kappa distribution, and we obtain a numerical relationship between the level of turbulence of the plasma and the skewness of obtained distributions, namely, 〈 δ 〉 ∼ R λ − 1 / 2 . We expect the results exposed in this paper to be useful as a tool to characterize the turbulence in the context of space plasma and other environments.