A limited closure relation for anisotropic plasmas from the Earth's magnetosheath

The ions of the terrestrial magnetosheath are typically observed to have bi-Maxwellian velocity distributions with Tperpendicular>Tparallel, where perpendicular and parallel denote directions perpendicular and parallel to the background magnetic field. Observations of the highly compressed magnetosheath have demonstrated an inverse correlation between the proton temperature anisotropy and the proton parallel β. Hybrid computer simulations have shown that wave--particle scattering by the proton cyclotron anisotropy instability can yield similar correlations between these two parameters. Although these correlations are due to nonlinear plasma processes, they correspond to a threshold of this instability that can be determined from linear Vlasov theory. This proton anisotropy/β correlation represents a limited closure relation for anisotropic magnetohydrodynamic plasma models