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The hybrid Vlasov-Maxwell system of equations is suitable to describe amagnetized plasma at scales of the order of or larger than proton kineticscales. An exact stationary solution is presented by revisiting previousresults with a uniform-density shear flow, directed either parallel orperpendicular to a uniform magnetic field, and by adapting the solution to thehybrid Vlasov-Maxwell model. A quantitative characterization of the equilibriumdistribution function is provided by studying both analytically and numericallythe temperature anisotropy and gyrotropy and the heat flux. In both cases, inthe shear region, the velocity distribution significantly departs from localthermodynamical equilibrium. A comparison between the time behavior of theusual "fluid-like" equilibrium shifted Maxwellian and the exact stationarysolutions is carried out by means of numerical simulations of the hybridVlasov-Maxwell equations. These hybrid equilibria can be employed as anunperturbed states for numerous problems which involve sheared flows, such asthe wave propagation in inhomogeneous background and the onset of theKelvin-Helmholtz instability.

Exact hybrid-Vlasov equilibria for sheared plasmas with in-plane and out-of-plane magnetic field