  Pulsar radio emission may be generated in pair discharges which fill the
pulsar magnetosphere with plasma as an accelerating electric field is screened
by freshly created pairs. In this Letter we develop a simplified analytic
theory for the screening of the electric field in these pair discharges and use
it to estimate total radio luminosity and spectrum. The discharge has three
stages. First, the electric field is screened for the first time and starts to
oscillate. Next, a nonlinear phase occurs. In this phase, the amplitude of the
electric field experiences strong damping because the field dramatically
changes the momenta of newly created pairs. This strong damping ceases, and the
system enters a final linear phase, when the electric field can no longer
dramatically change pair momenta. Applied to pulsars, this theory may explain
several aspects of radio emission, including the observed luminosity,
$L_{\rm{rad}} \sim 10^{28} \rm{erg} \, \rm{s}^{-1}$, and the observed spectrum,
$S_\omega \sim \omega^{-1.4 \pm 1.0} $.
