  Recent advances in numerical algorithms and computational power have enabled
first-principles simulations of pulsar magnetospheres using Particle-in-Cell
(PIC) techniques. These ab-initio simulations seem to indicate that pair
creation through photon-photon collision at the light cylinder is required to
sustain the pulsar engine. However, for many rotation-powered pulsars pair
creation operates effectively only near the stellar surface where magnetic
field is high. How these "weak pulsars" fill their magnetospheres without
efficient photon-photon pair conversion in the outer magnetosphere is still an
open question. In this paper, we present a range of self-consistent solutions
to the pulsar magnetosphere that do not require pair production near the light
cylinder. When pair production is very efficient near the star, the pulsar
magnetosphere converges to previously-reported solutions. However, in the
intermediate regime where pair supply is barely enough to sustain the
magnetospheric current, we observe a time-dependent solution with quasi-period
about half of the rotation period. This new quasi-periodic solution may explain
the observed pulsar death line without invoking multipolar components near the
star, and can potentially explain the core vs. conal emission patterns observed
in pulsar radio signals.
