Cassini/MIMI measurements of energetic ion moments and the polytropic index in Saturn's magnetosphere.

The k-distribution function provides a microscopic description of statistical information on the energetic charged particle distributions and is an invaluable aid towards the determination of macroscopic parameters (energetic ion moments) that are fundamentally important for studying the source, loss, transport and acceleration of energetic plasma inside the magnetosphere. We use κ-distribution fits to combined CHEMS (3 to 236 keV/e), LEMMS (0.024 < E < 18 MeV), and INCA (5.2 to >220 keV) H⁺ and O⁺ energetic ion spectra covering measurements made during 2004-2016 to calculate the >20 keV energetic ion moments inside Saturn's magnetosphere. We focus on partial density (n), integral intensity (I_n), partial pressure (P), integral energy intensity (I_E); as well as the characteristic energy (E_C=I_E/I_n), temperature and κ-index of these ions as a function of local time (00:00 to 24:00 hrs) and L-shell (5-20 R_S). The Roelof and Skinner [2000] model, ie., a semi-empirical parametric model that uses a combination of Gaussian and exponential decay functions, together with a two harmonic expansion that allows us to modulate the ion distributions in both L-shell and local time, is then utilized to retrieve the equatorial H⁺ and O⁺ density, pressure, and temperature, allowing also the determination of the polytropic index (Γ; ratio between the specific heat at constant pressure and constant volume) for both H⁺ and O⁺. We find that (a) The 9<L<20 region corresponds to a local equatorial acceleration region, where sub-adiabatic transport of H⁺ (Γ 1.25) and quasi-isothermal behavior of O⁺ (Γ 0.95) dominate the ion energetics; (b) Energetic ions are heavily depleted in the inner magnetospheric regions, and their behavior appears to be quasi-isothermal (Γ <1); (c) The (quasi-) periodic energetic ion injections in the outer parts of Saturn's magnetosphere (especially beyond 17-18 Rs) produce durable signatures in the energetic ion moments; (d) The plasma sheet does not seem to have a "ground thermodynamic state", but the extended neutral gas distribution at Saturn provides an effective cooling mechanism that does not allow the plasma sheet to behave adiabatically.