Outward transport of plasma in the inner and middle magnetospheres of gas giants results from an interplay between mass loading from the inner dominant mass sources (volcanic moons), flux tube interchange in the centrifugally unstable magnetospheric plasma disk, turbulent heating of the plasma, and coupling between the equatorial plasma and the planetary upper atmosphere through magnetic field-aligned current loops and/or Alfven waves. We present a new analytical formalism describing large scale transport in gas giant systems, combining two historical approaches: radial diffusion of mass and energy through flux tube interchange, and angular momentum transport through corotation enforcement. Under the hypotheses of axisymmetry, steady-state, and multi-fluid plasma, we provide transport equations for total contents of flux tubes. They feature new transport parameters accounting for the latitudinal extent of the disk, and self-consistently include field-aligned potential drops in the magnetosphere-ionosphere coupling. Our general formalism has a wealth of applications, two of which are presented, corresponding to the cases of the two gas giants: the effect of interhemispheric asymmetries in the resistive and magnetic properties between the northern and southern ionospheres on the transport of angular momentum at Jupiter, and the influence of the plasma disk thickness on transport at Saturn. We apply our formalism to derive ionospheric parameters and reproduce the Juno and Cassini data. Further work will allow for more complete numerical solutions of our equations, with the aim of capturing the broad complexity of fast rotating magnetospheric systems which can be found inside and outside the Solar System. Jupiter and Saturn, the two gas giant systems of the Solar System, are characterized by strong magnetic fields, fast rotation, and the presence of embedded (cryo)volcanic moons feeding their systems with gas and dust. Once produced, the gas is ionized and "picked-up" by the rotating magnetic field, resulting in a global plasma outflow from the inner to the outer regions forming an elongated disk along the centrifugal equator. This outward transport of plasma involves complex interactions between neutral gas, plasma, magnetic field, and the planet's upper atmosphere. In this work, we present a new unified formalism combining the description of angular momentum, mass, and energy transport in gas giant magnetospheres. This formalism is valid in their inner and middle magnetospheric regions where the system is approximately axisymmetrical. Assuming a steady-state flow, we self-consistently account for the impact of particle acceleration along field lines and the latitudinal distribution of the plasma disk on the global dynamics of the system. We provide simple numerical applications at Jupiter and Saturn which illustrate the influences of coupling of the plasma disk to the upper atmosphere of the planet and of the thickness of the disk, using the cases of Jupiter and Saturn. We develop a new self-consistent model of transport for the mass, angular momentum, and energy contents in gas giant magnetospheres We explore the two end-members of disk thickness cases, using Jupiter and Saturn as examples of thin and extended disks We explicitly describe the effects of inter-hemispheric asymmetries of neutral winds and ionospheric conductances on the rotation curve
