  The accumulation of electrons and positrons in the vacuum magnetosphere of a
neutron star with a surface magnetic field of B~10^12 G is considered. It is
shown that particles created in the magnetosphere or falling into the
magnetosphere from outside undergo ultra-relativistic oscillations with a
frequency of 10-100 MHz. These oscillations decay due to energy losses to
curvature radiation and bremsstrahlung, with their frequencies reaching 1-10
GHz. Simultaneously, the particles undergo regular motion along the force-free
surface along closed trajectories. This leads to the gradual accumulation of
particles at the force-free surface and the formation of a fully
charge-separated plasma layer with a density of the order of the
Goldreich-Julian density. The presence of a constant source of
electron-positron pairs in the magnetosphere due to the absorption of energetic
cosmic gamma-rays leads to the growth of this layer, bringing about a rapid
filling of the pulsar magnetosphere with electron-positron plasma if the
pair-creation multiplication coefficient is sufficiently high.
