Exact hybrid-kinetic equilibria for magnetized plasmas with shearing flows

Context. Magnetized plasmas characterized by shearing flows are present in many natural contexts, such as the Earth's magnetopause and the solar wind. The collisionless nature of involved plasmas requires a kinetic description. When the width of the shear layer is of the order of ion scales, the Hybrid Vlasov-Maxwell approach can be adopted. Aims. The aim of the paper is to derive explicit forms for stationary configurations of magnetized plasmas with planar shearing flows,within the Hybrid Vlasov-Maxwell description. Two configurations are considered: the first with a uniform magnetic field obliquely directed with respect to the bulk velocity; and the second with a uniform-magnitude variable-direction magnetic field. Methods. Stationary ion distribution functions are obtained by combining single-particle constant of motions, which are derived studying particle dynamics. Preliminary information about the form of the distribution functions are analytically derived considering a local approximation for the background electromagnetic field. Then, a numerical method is set up to obtain a solution for general profiles. Results. The explicit distribution functions that are found allow to obtain profiles of density, bulk velocity, temperature and heat flux. Anisotropy and agyrotropy in the distribution function are also evaluated. Stationarity of the solution during numerical simulations is checked in the uniform oblique magnetic field case. Conclusions. The considered configurations can be used as models for the Earth's magnetopause in simulations of the Kelvin-Helmholtz instability.