  Observational studies of the Earth's radiation belts indicate that Alfv\'enic
fluctuations in the frequency range of 2-25 mHz accelerate magnetically trapped
electrons to relativistic energies. For decades, statistical models of the
Earth's radiation belts have quantified the impact of Alfv\'enic waves in terms
of quasi-linear diffusive models. However, quasi-linear models are inadequate
to quantify Alfv\'enic radial transport occurring on timescales comparable to
the azimuthal drift period of $0.1- 10$ MeV electrons. With recent advances in
observational methodologies offering spatial and temporal coverage of the
Earth's radiation belts on fast timescales, a theoretical framework that
distinguishes between fast and diffusive radial transport can also be tested
for the first time with in situ measurements. In this report, we present a
drift kinetic description of radial transport for planetary radiation belts. We
characterize linear processes that are too fast to be modelled by quasi-linear
models and determine the conditions under which nonlinearities become
dynamically significant. In the linear regime, wave-particle interactions are
categorized in terms of resonant and non-resonant responses. We demonstrate
that the phenomenon of zebra stripes is non-resonant and can originate from the
injection of particles in the inner radiation belts. We derive a radial
diffusion coefficient for a field model that satisfies Faraday's law and that
contains two terms: one scaling as $L^{10}$ independent of the azimuthal number
$m$, and a second one scaling as $m^2 L^6$. In the nonlinear regime, we show
that azimuthally symmetric waves with properties consistent with in situ
measurements can energize 10-100 keV electrons in less than a drift period.
This coherent process provides new evidence that acceleration by Alfv\'enic
waves in radiation belts cannot be fully contained within diffusive models.
