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The nonlinear evolution of collisionless plasmas is typically a multi-scaleprocess where the energy is injected at large, fluid scales and dissipated atsmall, kinetic scales. Accurately modelling the global evolution requires totake into account the main micro-scale physical processes of interest. This iswhy comparison of different plasma models is today an imperative task aiming atunderstanding cross-scale processes in plasmas. We report here the firstcomparative study of the evolution of a magnetized shear flow, through avariety of different plasma models by using magnetohydrodynamic, Hall-MHD,two-fluid, hybrid kinetic and full kinetic codes. Kinetic relaxation effectsare discussed to emphasize the need for kinetic equilibriums to study thedynamics of collisionless plasmas in non trivial configurations. Discrepanciesbetween models are studied both in the linear and in the nonlinear regime ofthe magnetized Kelvin-Helmholtz instability, to highlight the effects of smallscale processes on the nonlinear evolution of collisionless plasmas. Weillustrate how the evolution of a magnetized shear flow depends on the relativeorientation of the fluid vorticity with respect to the magnetic field directionduring the linear evolution when kinetic effects are taken into account. Evenif we found that small scale processes differ between the different models, weshow that the feedback from small, kinetic scales to large, fluid scales isnegligable in the nonlinear regime. This study show that the kinetic modelingvalidates the use of a fluid approach at large scales, which encourages thedevelopment and use of fluid codes to study the nonlinear evolution ofmagnetized fluid flows, even in the colisionless regime.

Nonlinear evolution of the magnetized Kelvin-Helmholtz instability: from fluid to kinetic modeling