Ion-pressure equations derived from measurements in space

Cluster measurements at the bow shock, the magnetosheath, and the magnetospheric boundary layer are used to derive ion-pressure equations for hot anisotropic plasmas. It is demonstrated that both perpendicular and parallel ion pressures are well approximated by polybaric expressions proportional to (NBkappa)-B-gamma, where N is the plasma density, B is the magnetic field, gamma is in the range 0.5 to 2, and kappa is between -2 and 0. The parameters derived from observations are distinctively different from those predicted by double-adiabatic theory and are shown to hold for pressure variations over 4 orders of magnitude and for a range of plasma beta (ratio of kinetic/magnetic pressures) between 10(-4) and 10. The results are relevant for simulations and theories of astrophysical, solar, interplanetary, and magnetospheric processes based on MHD equations.