Mirror-wave Structures in the Solar Wind: Grad-Shafranov Reconstruction, MHD, and Hall MHD Simulations with Double-polytropic Energy Closures

Mirror-mode waves with anticorrelated density and magnetic field are widely observed in the solar wind and planetary magnetospheres. In this study we analyze the characteristics of three mirror-wave events observed by the Magnetospheric Multiscale Mission in the Earth's magnetosheath based on the Grad-Shafranov (GS) reconstruction model with temperature anisotropy. The GS scheme solves steady, two-dimensional MHD equations with field-aligned flow from the plasma and magnetic field measurements taken by a single spacecraft traversing across a coherent field structure. The reconstructed 2D plasma and field maps are obtained in the de Hoffmann-Teller frame and on the plane perpendicular to the invariant axis. The energy closures are a set of empirical energy laws with two polytropic exponents inferred from the observed mirror events which are in the ranges of It is shown that the mirror waves are nonpropagating with linear magnetic field polarization and possess anticorrelated density, temperatures, and magnetic field with the widths of 10-40 ion inertial lengths. The double-polytropic MHD and Hall MHD simulations of mirror instability show consistent results with the GS reconstructions in terms of field-line geometry, phase relations and the sizes of mirror waves, etc.