Large-amplitude, pair-creating oscillations in pulsar and black hole magnetospheres

A time-dependent model for pair creation in a pulsar magnetosphere is developed in which the parallel electric field oscillates with large amplitude. Electrons and positrons are accelerated periodically, and the amplitude of the oscillations is assumed to be large enough to cause creation of upgoing and downgoing pairs at different phases of the oscillation. With a charge-starved initial condition, we find that the oscillations result in bursts of pair creation in which the pair density rises exponentially with time. The pair density saturates at N+/- similar or equal to E-0(2)/(8 pi m(e)c(2)Gamma(thr)), where E-0 is the parallel electric field in the charge-starved initial state and Gamma(thr) is the Lorentz factor for effective pair creation. The frequency of oscillations following the pair creation burst is given roughly by omega(osc) = eE(0)/(8m(e)c Gamma(thr)). A positive feedback keeps the system stable, such that the average pair creation rate balances the loss rate due to pairs escaping the magnetosphere.