  Alpha channeling uses waves to extract hot ash from a fusion plasma, while
transferring energy from the ash to the wave. Intriguingly, it has been
proposed that the extraction of this charged ash could create a radial electric
field, efficiently driving ExB rotation. However, existing theories ignore the
response of the nonresonant particles, which play a critical role in enforcing
momentum conservation in quasilinear theory. Because cross-field charge
transport and momentum conservation are fundamentally linked, this
non-consistency throws the whole effect into question. Here, we review recent
developments that have largely resolved this question of rotation drive by
alpha channeling. We build a simple, general, self-consistent quasilinear
theory for electrostatic waves, applicable to classic examples such as the
bump-on-tail instability. As an immediate consequence, we show how waves can
drive currents in the absence of momentum injection even in a collisionless
plasma. To apply this theory to the problem of ash extraction and rotation
drive, we develop the first linear theory able to capture the alpha channeling
process. The resulting momentum-conserving linear-quasilinear theory reveals a
fundamental difference between the reaction of nonresonant particles to plane
waves that grow in time, versus steady-state waves that have nonuniform spatial
structure, allowing rotation drive in the latter case while precluding it in
the former. This difference can be understood through two conservation laws,
which demonstrate the local and global momentum conservation of the theory.
Finally, we show how the oscillation-center theories often obscure the
time-dependent nonresonant recoil, but ultimately lead to similar results.
