  Time-dependent cascades of electron-positron pairs are thought to be the main
source of plasma in pulsar magnetospheres and a primary ingredient to explain
the nature of pulsar radio emission, a longstanding open problem in high-energy
astrophysics. During these cascades - positive feedback loops of gamma-ray
photon emission, via curvature radiation by TeV electrons and positrons, and
pair production -, the plasma self-consistently develops inductive waves that
couple to electromagnetic modes capable of escaping the pulsar dense plasma. In
this work, we present an analytical description of pair cascades relevant in
pulsars, including their onset, exponential growth and saturation stages. We
study this problem in the case of a background linear electric field, relevant
in pulsar polar caps, and using an heuristic model of the pair production
process. The analytical results are confirmed with particle-in-cell simulations
performed with OSIRIS including heuristic pair production.
