Modeling of Saturn's magnetosphere during Voyager 1 and Voyager 2 encounters

We model Saturn's magnetosphere during the Voyager 1 encounter on days 317 and 318 in 1980 and the Voyager 2 encounter on days 237 and 238 in 1981, respectively. The rotating magnetosphere of Saturn is modeled by two-dimensional axisymmetric equilibrium solutions of the Grad-Shafranov type equation, which includes effects of the plasma pressure gradient force and the centrifugal force due to plasma toroidal rotation, by prescribing the radial profiles of plasma density and temperature in the equatorial plane. By varying the equatorial plasma profiles the equilibrium solutions are obtained with reasonably good fit to the observed plasma and magnetic field data along the orbits of the Voyager 1 encounter with the Saturn's magnetosphere on days 317 and 318 in 1980 and the Voyager 2 encounter on days 237 and 238 in 1981. The numerical equilibrium solutions provide detailed information of the global distribution of plasma environment and magnetic field structure of the Saturn's inner magnetosphere (for L < 24), and the results show that the plasma environment and the magnetic field configuration of the Saturn's magnetosphere are very different between these two spacecraft encounters with the Saturn. In particular, the meridian distributions of heavy ion density, azimuthal current density, and heavy ion beta have thin disk-like shapes centered at the equator for the Voyager 1 case, but have fat torus shapes for the Voyager 2 case. The difference results from the difference in the equatorial plasma pressure profile which decreases with R for R > 5R(S) for the Voyager 1 case, but is quite flat between R similar or equal to 5 and 17R(S) for the Voyager 2 case.