  The production of electron-positron pairs in a vacuum neutron star
magnetosphere is investigated for both low (compared to the Schwinger one) and
high magnetic fields. The case of a strong longitudinal electric field where
the produced electrons and positrons acquire a stationary Lorentz factor in a
short time is considered. The source of electron-positron pairs has been
calculated with allowance made for the pair production by curvature and
synchrotron photons. Synchrotron photons are shown to make a major contribution
to the total pair production rate in a weak magnetic field. At the same time,
the contribution from bremsstrahlung photons may be neglected. The existence of
a time delay due to the finiteness of the electron and positron acceleration
time leads to a great reduction in the electron-positron plasma generation rate
compared to the case of a zero time delay. The effective local source of
electron-positron pairs has been constructed. It can be used in the
hydrodynamic equations that describe the development of a cascade after the
absorption of a photon from the cosmic gamma-ray background in a neutron star
magnetosphere.
