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Magnetized plasmas with shearing flows are found in many natural contexts, such as around Earth’s magnetopause. In collisionless plasmas where physical quantities vary on a scale of the order of or larger than ion scales, the hybrid Vlasov-Maxwell description (kinetic ions coupled to a neutralizing electron fluid via electromagnetic fields) represents a suitable approach. When crossing the magnetopause, the ion temperature, density, and direction of magnetic field vary. We derive a form for an exact stationary solution of the hybrid Vlasov-Maxwell equations that represent a magnetized plasma with a quasi-planar shearing flow, variable density and ion temperature, and variable magnetic field direction. A stationary ion distribution function is expressed as a suitable combination of particle constants of motion and evaluated numerically in such a way to obtain configurations with variable density and temperature and two quasi-planar oppositely directed velocity shear layers. Properties of particular configurations are derived from Magnetospheric Multiscale measures during crossings of Earth’s magnetopause. In the first case a quasi-uniformly directed, nearly perpendicular magnetic field is present, while in the second case, going from the magnetosheath to the magnetosphere, the magnetic field makes a wide rotation from one side to the other of the shearing flow plane. In both cases, the ion distribution function departs from a Maxwellian in the shear layers, displaying temperature anisotropy and agyrotropy, with a nonsymmetric behavior in the two shear layers. The configurations considered here can be used as models for Earth’s magnetopause in simulations of the Kelvin-Helmholtz instability.
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