  We study different types of microswimmers moving in channels with varying
cross section and thereby interacting hydrodynamically with the channel walls.
Starting from the Smoluchowski equation for a dilute suspension, for which
interactions among swimmers can be neglected, we derive analytic expressions
for the lateral probability distribution between plane channel walls. For
weakly corrugated channels we extend the Fick--Jacobs approach to microswimmers
and thereby derive an effective equation for the probability distribution along
the channel axis. Two regimes arise dominated either by entropic forces due to
the geometrical confinement or by the active motion. In particular, our results
show that the accumulation of microswimmers at channel walls is sensitive to
both, the underlying swimming mechanism and the geometry of the channels.
Finally, for asymmetric channel corrugation our model predicts a rectification
of microswimmers along the channel, the strength and direction of which
strongly depends on the swimmer type.
