  (Abridged) An issue of considerable interest in the theory of jet formation
by the Blandford-Znajek mechanism, is how plasma is being continuously supplied
to the magnetosphere to maintain it in a force-free state. Injection of
electron-positron pairs via annihilation of MeV photons, emitted from a hot
accretion flow, has been shown to be a viable possibility, but requires a high
enough accretion rate. At lower accretion rates, and in the absence of any
other form of plasma supply, the magnetosphere becomes charge starved, forming
intermittent spark gaps that can induce intense pair cascades via interactions
with soft disk radiation, enabling outflow formation. It is often speculated
that enough plasma can penetrate the inner magnetosphere from the accretion
flow through some rearrangement of magnetic field lines (e.g., interchange
instability). However, the question arises whether such episodes of plasma
intrusion can prevent the formation of spark gaps. To address this question we
conducted a suite of numerical experiments, by means of radiative, 2D
axisymmetric general relativistic particle-in-cell simulations, in which plasma
is injected into specified regions at a prescribed rate. We find that when pair
production is switched off, nearly complete screening is achieved when the
plasma is injected within the outer light cylinder at a high enough rate.
Injection beyond the outer light cylinder results in either, the formation of
large vacuum gaps, or coherent, large-amplitude oscillations of the
magnetosphere, depending on the injection rate. Within the allowed dynamic
range of our simulations, we see no evidence for the system to approach a
steady state as the injection rate is increased. Switching on pair production
results in nearly complete screening of the entire magnetosphere in all cases,
with some fraction of the maximum Blandford-Znajek power emitted as TeV
gamma-rays.
