  We explore the electrostatic bending response of a chain of charged particles
confined on a finite helical filament. We analyze how the energy difference
$\Delta E$ between the bent and the unbent helical chain scales with the length
of the helical segment and the radius of curvature and identify features that
are not captured by the standard notion of the bending rigidity, normally used
as a measure of bending tendency in the linear response regime. Using instead
$\Delta E$ to characterize the bending response of the helical chain we
identify two regimes with qualitatively different bending behaviors for the
ground state configuration: the regime of small and the regime of large
radius-to-pitch ratio, respectively. Within the former regime, $\Delta E$
changes smoothly with the variation of the system parameters. Of particular
interest are its oscillations with the number of charged particles encountered
for commensurate fillings which yield length-dependent oscillations in the
preferred bending direction of the helical chain. We show that the origin of
these oscillations is the non-uniformity of the charge distribution caused by
the long-range character of the Coulomb interactions and the finite length of
the helix. In the second regime of large values of the radius-to-pitch ratio,
sudden changes in the ground state structure of the charges occur as the system
parameters vary, leading to complex and discontinuous variations in the ground
state bending response $\Delta E$.
