  Run-and-tumble dynamics is a wide-spread mechanism of swimming bacteria. The
accumulation of run-and-tumble microswimmers near impermeable surfaces is
studied theoretically and numerically in the low-density limit in two and three
spatial dimensions. Both uni-modal and exponential distributions of the run
lengths are considered. Constant run lengths lead to {peaks and depletions
regions} in the density distribution of particles near the surface, in contrast
to {exponentially-distributed run lengths}. Finally, we present a universal
accumulation law for large channel widths, which applies not only to
run-and-tumble swimmers, but also to many other kinds of self-propelled
particles.
