Mapping the transitions of Proton Adiabaticity in Jupiter's Inner Radiation Belt: A comprehensive approach

The dynamics of energetic charged particles in Jupiter's inner magnetosphere are governed by the conservation of adiabatic invariants, yet the transition to non-adiabatic motion has not been systematically quantified across particle energy, M-shell, and pitch angle. Prior work relies on an empirical gyro-radius threshold (rL<1000~km) tested at only two M-shells, leaving the intermediate, partially adiabatic regime uncharacterized. We develop a fully relativistic, three-dimensional test-particle model (Boris pusher) coupled to the JRM33 and Con2020 magnetic field models to investigate ultra-relativistic proton dynamics in Jupiter's inner radiation belt.A simulation design experiment encompassing 135 simulations (five energies,1--100~GeV; nine M-shells, 3--7~RJ; three pitch angles, alpha₀=30^∘,60^∘,89^∘) was performed, yielding three formally defined regimes: fully adiabatic, partially adiabatic, and fully non-adiabatic. The Boris pusher is found to be more reliable for long-term invariant studies compared to the Runge-Kutta scheme. A field-geometric curvature parameter, κ=(Rc/rL)1/2, to be effective in adiabaticity break down criteria which is validated via simulations. It is found that the adiabatic--partial boundary shifts to lower energy with increasing M-shell and pitch angle; at M=6.0\,RJ, even 1~GeV protons exceed the gyro-radius threshold, and the partially adiabatic regime is most prominent at $M=3.0$--4.5\,RJ for 1--10~GeV. The transitional zone for 10--20~GeV protons overlaps substantially with the interchange-event range reported from independent electron pitch-angle observations, suggesting a shared association with reduced magnetic confinement in this region. These results provide a validated, framework, with direct relevance to the radiation hazard environment for future Jovian spacecraft missions.