  We investigate self-consistent particle acceleration near a pulsar polar cap
(PC) by the electrostatic field due to the effect of inertial frame dragging.
Test particles gain energy from the electric field parallel to the open
magnetic field lines and lose energy by both curvature radiation (CR) and
resonant and non-resonant inverse Compton scattering (ICS) with soft thermal
X-rays from the neutron star (NS) surface. Gamma-rays radiated by electrons
accelerated from the stellar surface produce pairs in the strong magnetic
field, which screen the electric field beyond a pair formation front (PFF).
Some of the created positrons can be accelerated back toward the surface and
produce gamma-rays and pairs that create another PFF above the surface. We find
that ICS photons control PFF formation near the surface, but due to the
different angles at which the electron and positron scatter the soft photons,
positron initiated cascades develop above the surface and screen the
accelerating electric field. Stable acceleration from the NS surface is
therefore not possible in the presence of dominant ICS energy losses. However,
we find that stable acceleration zones may occur at some distance above the
surface, where CR dominates the electron and positron energy losses, and there
is up-down symmetry between the electron and positron PFFs. We examine the
dependence of CR-controlled acceleration zone voltage, width and height above
the surface on parameters of the pulsar and its soft X-ray emission. For most
pulsars, we find that acceleration will start at a height of 0.5 - 1 stellar
radii above the NS surface.
