  Large arrays of aligned carbon nanotubes (CNTs), open at one end, could be
used as target material for the directional detection of weakly interacting
dark matter particles (WIMPs). As a result of a WIMP elastic scattering on a
CNT, a carbon ion might be injected in the body of the array and propagate
through multiple collisions within the lattice. The ion may eventually emerge
from the surface with open end CNTs, provided that its longitudinal momentum is
large enough to compensate energy losses and its transverse momentum approaches
the channeling conditions in a single CNT. Therefore, the angle formed between
the WIMP wind apparent orientation and the direction of parallel carbon
nanotube axes must be properly chosen. We focus on very low ion recoil kinetic
energies, related to low mass WIMPs (~ 10 GeV) where most of the existing
experiments have low sensitivity. Relying on some exact results on
two-dimensional lattices of circular obstacles, we study the low energy ion
motion in the transverse plane with respect to CNT directions. New constraints
are obtained on how to devise the CNT arrays to maximize the detection
efficiency.
