Revisit of Nonlinear Landau Damping for Electrostatic Instability Driven by Blazar-induced Pair Beams

Abstract

We revisit the effect of non-linear Landau (NL) damping on the electrostatic instability of blazarinduced 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 non-linear Landau damping, once it operates efficiently, transports essentially the entire wave energy to small wavenumbers where wave driving is weak or absent. The relaxation time also strongly depends on the IGM 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 non-linearly 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 non-linear processes, such as the modulation instability, could provide additional damping of the non-resonant 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.

Revisit of non-linear Landau damping for electrostatic instability driven by blazar-induced pair beams

“…For a full discussion of the results we refer to [25]. In the following summarize the main findings.…”

“…The primary goal of this paper is to investigate the effect of non-linear Landau damping considering the realistic behavior of the electrostatic growth rate at large wave numbers for blazar-induced pair beams. For a more detailed description of this research we refer to our main paper [25].…”

The growth of the longitudinal beam–plasma instability in the presence of an inhomogeneous background

“…A plausible explanation of such a mystery is that virulent kinetic plasma instabilities in the IGM, induced by the pair beams, reduce the pair-beam energy on time scales much shorter than that of the inverse Compton cascade. The validity of such a scenario strongly depends on the nonlinear saturation of these instabilities (Miniati & Elyiv 2013;Chang et al 2014;Sironi & Giannios 2014;Chang et al 2016;Kempf, Kilian & Spanier 2016;Shalaby et al 2017a;Vafin et al 2018Vafin et al , 2019.…”

PIC simulation methods for cosmic radiation and plasma instabilities

“…Using analytical methods Vafin et al [316] found that the energy loss by driving the electrostatic instability is likely dominant, suppressing the GeV-band cascade emission. Modeling the spectral evolution of the waves under nonlinear Landau damping instead suggests that there is no constant saturation level in the resonant band in k space, which might invalidate the analytical extrapolation [317].…”