  Electron-positron pair cascades developed in the extreme electromagnetic
fields of neutron star polar caps are considered a key source of magnetospheric
plasma in these objects. We use a simplified model that maps the Quantum
Electrodynamics processes governing the pair cascades to analytically and
numerically model the development of the pair cascade, and show that
large-amplitude oscillations of the electric field are inductively driven by
the resulting plasma. A plasma instability arises in these oscillations, and
particles accelerated in growing electric field perturbations can drive
secondary pair bursts that damp the large-amplitude oscillations. An analytical
model is proposed to describe this interplay between the pair production and
kinetic collective plasma processes. All analytical results are shown to be in
excellent agreement with particle-in-cell simulations.
