  The gradient of fusion-born alpha particles that arises in a fusion reactor
can be exploited to amplify waves, which cool the alpha particles while
diffusively extracting them from the reactor. The corresponding extraction of
the resonant alpha particle charge has been suggested as a mechanism to drive
rotation. By deriving a coupled linear-quasilinear theory of alpha channeling,
we show that, for a time-growing wave with a purely poloidal wavevector, a
current in the nonresonant ions cancels the resonant alpha particle current,
preventing the rotation drive but fueling the fusion reaction.
