Although the solar wind, as a collisionless plasma, is properly described by the kinetic Maxwell-Vlasov description, it can be argued that much of our understanding of the solar wind is based on a fluid description of magnetohydrodynamics that derives from interpretation of observational data together with numerical modeling. In recent years, there has been significant interest in better understanding the importance of kinetic effects, i.e., the differences between kinetic and fluid descriptions. Here we concentrate on the physical properties of oblique kinetic Alfvén waves (KAWs) that appear to be a key ingredient in the solar wind turbulence cascade. We use three different fluid models with various degrees of complexity and calculate the polarization and magnetic compressibility of KAWs (propagation angle θ = 88°), which we compare to solutions derived from linear kinetic theory. We explore a wide range of possible proton plasma β = [0.1, 10.0] and a wide range of length scales krL = [0.001, 10.0], where rL denotes the proton gyroscale. It is shown that the “classical” isotropic two-fluid model is very compressible in comparison with kinetic theory and that the largest discrepancy occurs at scales larger than the proton gyroscale. We also show that the two-fluid model contains a large error in the polarization of electric field, even at scales krL ≪ 1. Furthermore, to understand these discrepancies between the two-fluid model and the kinetic theory, we employ two versions of the Landau fluid model that incorporate linear low-frequency kinetic effects such as Landau damping and finite Larmor radius (FLR) corrections into the fluid description. We show that allowing for anisotropic pressure fluctuations and Landau damping is crucial for correct modeling of magnetic compressibility and that FLR corrections (i.e., nongyrotropic contributions) are required to correctly capture the polarization. We also show that, in addition to Landau damping, FLR corrections are necessary to accurately describe the damping rate of KAWs. We conclude that kinetic effects are important even at scales which are significantly larger than the proton gyroscale krL ≪ 1.

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