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We present a detailed guide to advanced collisionless fluid models that incorporate kinetic effects into the fluid framework, and that are much closer to the collisionless kinetic description than traditional magnetohydrodynamics. Such fluid models are directly applicable to modelling the turbulent evolution of a vast array of astrophysical plasmas, such as the solar corona and the solar wind, the interstellar medium, as well as accretion disks and galaxy clusters. The text can be viewed as a detailed guide to Landau fluid models and it is divided into two parts. Part 1 is dedicated to fluid models that are obtained bymore »
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In Part 2 of our guide to collisionless fluid models, we concentrate on Landau fluid closures. These closures were pioneered by Hammett and Perkins and allow for the rigorous incorporation of collisionless Landau damping into a fluid framework. It is Landau damping that sharply separates traditional fluid models and collisionless kinetic theory, and is the main reason why the usual fluid models do not converge to the kinetic description, even in the long-wavelength low-frequency limit. We start with a brief introduction to kinetic theory, where we discuss in detail the plasma dispersion function $Z(\unicode[STIX]{x1D701})$ , and the associated plasma responsemore »
