The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma
  Instabilities
  Very-high energy gamma-rays from extragalactic sources pair-produce off of
the extragalactic background light, yielding an electron-positron pair beam.
This pair beam is unstable to various plasma instabilities, especially the
"oblique" instability, which can be the dominant cooling mechanism for the
beam. However, recently, it has been claimed that nonlinear Landau damping
renders it physically irrelevant by reducing the effective damping rate to a
low level. Here, we show with numerical calculations that the effective damping
rate is $8\times 10^{-4}$ of the growth rate of the linear instability, which
is sufficient for the "oblique" instability to be the dominant cooling
mechanism of these pair beams. In particular, we show that previous estimates
of this rate ignored the exponential cutoff in the scattering amplitude at
large wavenumber and assumed that the damping of scattered waves entirely
depends on collisions, ignoring collisionless processes. We find that the total
wave energy eventually grows to approximate equipartition with the beam by
increasingly depositing energy into long wavelength modes. As we have not
included the effect of nonlinear wave-wave interactions on these long
wavelength modes, this scenario represents the "worst-case" scenario for the
oblique instability. As it continues to drain energy from the beam at a faster
rate than other processes, we conclude that the "oblique" instability is
sufficiently strong to make it the physically dominant cooling mechanism for
high-energy pair beams in the intergalactic medium.
