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 plas ma pressures perpendicular (P-perpendicular to) and parallel (P-parallel to ) to the magnetic field (P-perpendicular to > P-parallel to) 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 isotropi c, "magnetic string" MHD model, which we describe in detail here. The MHD e quations are closed by a relation between P-perpendicular to and P-parallel to 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 bounda ry 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 Alfven Mach nu mbers equal to 10, and compare them with the isotropic case (P-parallel to = P-perpendicular to). Anisotropy slightly thickens the magnetosheath. In t he anisotropic model, the density, the parallel and perpendicular temperatu res, plasma pressures, and betas all decrease toward the magnetopause. Isot ropic profiles lie between those of quantities perpendicular and parallel t o the field. Anisotropy has considerable effect on the density profile, whi ch lies below that in the isotropic limit throughout the magnetosheath. Den sity depletion results from stretching of magnetic field lines, which is ca used by field-aligned plasma flow. Approaching the magnetopause, the tangen tial component of velocity parallel to the magnetic field decreases, while the tangential component perpendicular to the magnetic field increases. The se are features characterizing a stagnation line flow at the magnetopause. The acceleration along the magnetic field is produced by the gradient of P- parallel to and the mirror force, which depends on anisotropy. They both ma ke substantial contributions and are responsible for the changes we see;fro m isotropy. The acceleration perpendicular to magnetic field is also larger than in the case of isotropy and is caused by the gradient of total pressu re, the magnetic strength, and the mirror force. In addition, acceleration in both directions is affected by the decreasing density.