  We present the first self-consistent global simulations of pulsar
magnetospheres with operating $e^\pm$ discharge. We focus on the simple
configuration of an aligned or anti-aligned rotator. The star is spun up from
zero (vacuum) state to a high angular velocity, and we follow the coupled
evolution of its external electromagnetic field and plasma particles using the
"particle-in-cell" method. A plasma magnetosphere begins to form through the
extraction of particles from the star; these particles are accelerated by the
rotation-induced electric field, producing curvature radiation and igniting
$e^\pm$ discharge. We follow the system evolution for several revolution
periods, longer than required to reach a quasi-steady state. Our numerical
experiment puts to test previous ideas for the plasma flow and gaps in the
pulsar magnetosphere. We first consider rotators capable of producing pairs out
to the light cylinder through photon-photon collisions. We find that their
magnetospheres are similar to the previously obtained force-free solutions with
a current sheet and the Y-point near the light cylinder. The magnetosphere
continually ejects $e^\pm$ pairs and ions. Pair creation is sustained by a
strong electric field along the current sheet. We observe powerful curvature
and synchrotron emission from the current sheet, consistent with Fermi
observations of gamma-ray pulsars. We then study pulsars that can only create
pairs in the strong-field region near the neutron star, well inside the light
cylinder. We find that both aligned and anti-aligned rotators relax to the
"dead" state with suppressed pair creation and electric currents, regardless of
the discharge voltage.

High Energy Astrophysical Phenomena