Two dimensional Reconstruction of a Time dependent Mirror Structure from Double polytropic MHD Simulation

A new reconstruction method incorporated with pressure anisotropy parameter, α(B), has recently been developed for magnetohydrostatic equilibria and successfully applied to recovering a two dimensional (2 D) magnetic field map of mirror structures observed in the Earth's magnetosheath. Here, α(B)=μ₀(p_∥-p_⊥)/B² is assumed to be a function of magnetic field strength, B, alone. The fundamental reconstruction theory assumes that the magnetic field and plasma configurations are time independent and 2 D, which may not be fulfilled in the real applications to satellite observations. When the 2 D structure is time dependent, the intrinsic field line invariant F_z=(1-α)B_z is violated so that the quantity F_z is not constant for the same field line. This paper aims to examine the performance of the α(B) reconstruction of a time dependent mirror structure, using data from a 2 D, double polytropic Magnetohydrodynamics (MHD) simulation. With a single branched fitting function for the field line invariant, results show that the geometry of time dependent mirror structure can be reasonably reconstructed, including the distribution maps of gyrotropic pressures p_∥ and p_⊥. As expected, the assumption of α(B) is well satisfied for the mirror structure. Additionally, another two reconstruction methods are also tested, namely, the Grad Shafranov reconstruction and the α(A) reconstruction. The former is considered isotropic pressure, while the latter assumes that α is function of vector potential A alone. As expected, these two reconstruction methods fail to recover the geometry of the mirror structure. We suggest that use of a single branched fitting function is more appropriate for reconstruction of a time dependent, wave like structure, regardless of which magnetohydrostatic reconstruction method is applied.