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We revisit the effect of nonlinear Landau (NL) damping on the electrostatic instability of blazar-induced pair beams, using a realistic pair-beam distribution. We employ a simplified 2D model in k-space to study the evolution of the electric-field spectrum and to calculate the relaxation time of the beam. We demonstrate that the 2D model is an adequate representation of the 3D physics. We find that nonlinear Landau damping, once it operates efficiently, transports essentially the entire wave energy to small wave numbers where wave driving is weak or absent. The relaxation time also strongly depends on the intergalactic medium temperature, T-IGM, and for T-IGM << 10 eV, and in the absence of any other damping mechanism, the relaxation time of the pair beam is longer than the inverse Compton (IC) scattering time. The weak late-time beam energy losses arise from the accumulation of wave energy at small k, that nonlinearly drains the wave energy at the resonant k of the pair-beam instability. Any other dissipation process operating at small k would reduce that wave-energy drain and hence lead to stronger pair-beam energy losses. As an example, collisions reduce the relaxation time by an order of magnitude, although their rate is very small. Other nonlinear processes, such as the modulation instability, could provide additional damping of the nonresonant waves and dramatically reduce the relaxation time of the pair beam. An accurate description of the spectral evolution of the electrostatic waves is crucial for calculating the relaxation time of the pair beam.
The flat spectrum radio quasar 3C 279 is known to exhibit pronounced variability in the high-energy (100MeV < E < 100 GeV) gamma-ray band, which is continuously monitored with Fermi-LAT. During two periods of high activity in April 2014 and June 2015 target-of-opportunity observations were undertaken with the High Energy Stereoscopic System (H.E.S.S.) in the very-high-energy (VHE, E > 100 GeV) gamma-ray domain. While the observation in 2014 provides an upper limit, the observation in 2015 results in a signal with 8 : 7 sigma significance above an energy threshold of 66 GeV. No VHE variability was detected during the 2015 observations. The VHE photon spectrum is soft and described by a power-law index of 4.2 +/- 0.3. The H.E.S.S. data along with a detailed and contemporaneous multiwavelength data set provide constraints on the physical parameters of the emission region. The minimum distance of the emission region from the central black hole was estimated using two plausible geometries of the broad-line region and three potential intrinsic spectra. The emission region is confidently placed at r greater than or similar to 1 : 7 X 1017 cm from the black hole, that is beyond the assumed distance of the broad-line region. Time-dependent leptonic and lepto-hadronic one-zone models were used to describe the evolution of the 2015 flare. Neither model can fully reproduce the observations, despite testing various parameter sets. Furthermore, the H.E.S.S. data were used to derive constraints on Lorentz invariance violation given the large redshift of 3C 279.