Relativistic surfatron process for Landau resonant electrons in radiation belts

Recent theoretical studies of the nonlinear wave-particle interactions for relativistic particles have shown that Landau resonant orbits could be efficiently accelerated along the mean background magnetic field for propagation angles $\theta$ in close proximity to a critical propagation $\theta_\textrm{c}$ associated with a Hopf--Hopf bifurcation condition. In this report, we extend previous studies to reach greater modeling capacities for the study of electrons in radiation belts by including longitudinal wave effects and inhomogeneous magnetic fields. We find that even though both effects can limit the surfatron acceleration of electrons in radiation belts, gains in energy of the order of 100 keV, taking place on the order of ten milliseconds, are sufficiently strong for the mechanism to be relevant to radiation belt dynamics.