  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.
