Exact Shearing Flow Magnetized Hybrid Kinetic Equilibria with Inhomogeneous Temperature

Abstract

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.