Three-dimensional, one-fluid, ideal MHD model of magnetosheath flow with anisotropic pressure

We present a three-dimensional, one-fluid, steady state magnetohydrodynamic (MHD) model of magnetosheath flow near the subsolar line with unequal plasma pressures perpendicular (P⊥) and parallel (P‖) to the magnetic field (P⊥ \u3e P‖). Aside from an assumption on the total pressure normal to the magnetopause, our analytical-numerical method is completely general and is an extension of our isotropic, “magnetic string” MHD model, which we describe in detail here. The MHD equations are closed by a relation between P⊥ and P‖ as in the Bounded Anisotropy Model [Denton et al. 1994] corresponding to the threshold of the electromagnetic proton cyclotron wave instability. We take an IMF oriented perpendicular to the solar wind velocity. As boundary conditions, we have Rankine-Hugoniot relations at the bow shock and a no-flow condition at the magnetopause. We obtain steady state profiles of the magnetic field and plasma parameters for upstream sonic and Alfvén Mach numbers equal to 10, and compare them with the isotropic case (P‖ = P⊥). Anisotropy slightly thickens the magnetosheath. In the anisotropic model, the density, the parallel and perpendicular temperatures, plasma pressures, and betas all decrease toward the magnetopause. Isotropic profiles lie between those of quantities perpendicular and parallel to the field. Anisotropy has considerable effect on the density profile, which lies below that in the isotropic limit throughout the magnetosheath. Density depletion results from stretching of magnetic field lines, which is caused by field-aligned plasma flow. Approaching the magnetopause, the tangential component of velocity parallel to the magnetic field decreases, while the tangential component perpendicular to the magnetic field increases. These are features characterizing a stagnation line flow at the magnetopause. The acceleration along the magnetic field is produced by the gradient of P‖ and the mirror force, which depends on anisotropy. They both make substantial contributions and are responsible for the changes we see from isotropy. The acceleration perpendicular to magnetic field is also larger than in the case of isotropy and is caused by the gradient of total pressure, the magnetic strength, and the mirror force. In addition, acceleration in both directions is affected by the decreasing density