  We study the effect of a tangled sub-fG level intergalactic magnetic field
(IGMF) on the electrostatic instability of a blazar-induced pair beam.
Sufficiently strong IGMF may significantly deflect the TeV pair beams, which
would reduce the flux of secondary cascade emission below the observational
limits. A similar flux reduction may result from the electrostatic beam-plasma
instability, which operates the best in the absence of IGMF. Considering IGMF
with correlation lengths smaller than a kpc, we find that weak magnetic fields
increase the transverse momentum of the pair beam particles, which dramatically
reduces the linear growth rate of the electrostatic instability and hence the
energy-loss rate of the pair beam. We show that the beam-plasma instability is
eliminated as an effective energy-loss agent at a field strength three orders
of magnitude below that needed to suppress the secondary cascade emission by
magnetic deflection. For intermediate-strength IGMF, we do not know a viable
process to explain the observed absence of GeV-scale cascade emission.
