The Jovian paraboloid magnetospheric model is applied for the investigation of the planet's auroral emission and plasma disk structure in the middle magnetosphere. Jupiter's auroral emission demonstrates the electrodynamic coupling between the ionosphere and magnetosphere. For comparison of different regions in the ionospheric level and in the magnetosphere, the paraboloid model of the global magnetospheric magnetic field is used. This model provides mapping along highly-conducting magnetic field lines. The paraboloid magnetic field model is also applied for consideration of the stability of the background plasma disk in the rotating Jupiter magnetosphere with respect to the flute perturbations. Model radial distribution of the magnetic field and experimental data on the plasma angular velocity in the middle Jovian magnetosphere are used. A dispersion relation of the plasma perturbations in the case of a perfectly conducting ionosphere is obtained. Analyzing starting conditions of a flute instability in the disk, the "threshold" radial profile of the plasma density is determined. An application of the results obtained to the known data on the Jovian plasma disk is discussed.