Plasma transport in rapidly rotating magnetospheres: General equations

We derive the general form of the equations governing the time evolution of a multicomponent plasma embedded in a rotating magnetosphere. Our set of equations includes evolution equations for the mass, radial momentum, and angular momentum of magnetic flux tubes; evolution equations for the equatorial density and perpendicular and parallel thermal pressures of each plasma component; and an electric current continuity equation involving a coupling with the ionosphere. In a second step we approximate the magnetic field strength and potential energy by means of a second-order series expansion along field lines. This parabolic approximation enables us to write the density and pressure equations in a very simple form and to gain a clear physical understanding of the compression and acceleration mechanisms at hand. Finally, for the purpose of closing the system of equations, we make the assumption that each plasma component is either cool and dominated by the centrifugal force, or hot and dominated by pressure forces. In subsequent papers we will use our formalism to study the large-scale convection and describe the radial transport of mass and angular momentum in the Jovian and Kronian magnetospheres.