Geometry-driven transport and heating of trapped particles in magnetospheric plasmas

This paper develops a geometry-based framework for trapped-particle dynamics in planetary magnetospheres by casting the guiding-center Hamiltonian in Frenet-Serret coordinates, so that field-line curvature and torsion drive particle drifts and adiabatic invariants. Envelope equations then capture ensemble phase-space widths, oscillations and equilibrium scaling under geometric focusing. A minimal Lorentzian diffusion term reproduces resonant, wave-driven drift-shell broadening. Numerical tests on ideal dipole fields confirm the predicted scalings for curvature effects, drift-shell width, envelope oscillation frequencies and broadening rates. This approach bridges microscopic Hamiltonian dynamics and macroscopic transport, and can be extended to realistic field geometries and in situ wave measurements for radiation-belt modeling.