  We explore a model system consisting of a particle confined to move along a
toroidal helix while being exposed to a static potential as well as a driving
force due to a harmonically oscillating electric field. It is shown that in the
limit of a vanishing helix radius the governing equations of motion coincide
with those of the well-known Kapitza pendulum - a classical pendulum with
oscillating pivot - implying that the driven toroidal helix represents a
corresponding generalization. It is shown that the two dominant static fixed
points present in the Kapitza pendulum are also present for a finite helix
radius. The dependence of the stability of these two fixed points on the helix
radius, the driving amplitude, and the static potential are analyzed both
analytically and numerically. Additionally, the most prominent deviations of
the driven helix from Kapitzas pendulum with respect to the resulting phase
space are investigated and analyzed in some detail. These effects include an
unusual transition to chaos and an effective directed transport due to the
simultaneous presence of multiple chaotic phase space regions.
