  Upcoming tokamak experiments fueled with deuterium and tritium are expected
to have large alpha particle populations. Such experiments motivate new
attention to the theory of alpha particle confinement and transport. A key
topic is the interaction of alphas with perturbations to the tokamak fields,
including those from ripple and magnetohydrodynamic modes like Alfv\'{e}n
eigenmodes. These perturbations can transport alphas, leading to changed
localization of alpha heating, loss of alpha power, and damage to device walls.
Alpha interaction with these perturbations is often studied with single
particle theory. In contrast, we derive a drift kinetic theory to calculate the
alpha heat flux resulting from arbitrary perturbation frequency and periodicity
(provided these can be studied drift kinetically). Novel features of the theory
include the retention of a large effective collision frequency resulting from
the resonant alpha collisional boundary layer, correlated interactions over
many poloidal transits, and finite orbit effects. Heat fluxes are considered
for the example cases of ripple and the toroidal Alfv\'{e}n eigenmode (TAE).
The ripple heat flux is small. The TAE heat flux is significant and scales with
the square of the perturbation amplitude, allowing the derivation of
constraints on mode amplitude for avoidance of significant alpha depletion. A
simple saturation condition suggests that TAEs in one upcoming experiment will
not cause significant alpha transport via the mechanisms in this theory.
However, saturation above the level suggested by the simple condition, but
within numerical and experimental experience, which could be accompanied by the
onset of stochasticity, could cause significant transport.
