The Linear Instability of Dilute Ultrarelativistic $e^{\pm}$ Pair Beams

TL;DR

This paper investigates the linear plasma instabilities affecting ultrarelativistic electron-positron beams from TeV sources, revealing their instability and energy dissipation mechanisms in intergalactic space.

Contribution

It provides a detailed calculation of the linear growth rates of beam plasma and oblique instabilities, clarifying their regimes and applicability for ultrarelativistic pair beams.

Findings

Ultrarelativistic $e^{ m ext{±}}$ beams are linearly unstable to plasma instabilities.

The study delineates the conditions for reactive and kinetic regimes.

Both beam plasma and oblique modes grow at maximum rates across a range of parameters.

Abstract

The annihilation of TeV photons from extragalactic TeV sources and the extragalactic background light produces ultrarelativistic $e^{\pm}$ beams, which are subject to powerful plasma instabilities that sap their kinetic energy. Here we study the linear phase of the plasma instabilities that these pair beams drive. To this end, we calculate the linear growth rate of the beam plasma and oblique instability in the electrostatic approximation in both the reactive and kinetic regimes, assuming a Maxwell-J{\"u}ttner distribution for the pair beam. We reproduce the well-known reactive and kinetic growth rates for both the beam plasma and oblique mode. We demonstrate for the oblique instability that there is a broad spectrum of unstable modes that grow at the maximum rate for a wide range of beam temperatures and wave vector orientations relative to the beam. We also delineate the conditions for applicability for the reactive and kinetic regimes and find that the beam plasma mode transitions to the reactive regime at a lower Lorentz factor than the oblique mode due to a combination of their different scalings and the anisotropy of the velocity dispersions. Applying these results to the ultrarelativistic $e^{\pm}$ beams from TeV blazars, we confirm that these beams are unstable to both, the kinetic oblique mode and the reactive beam-plasma mode. These results are important in understanding how powerful plasma instabilities may sap the energy of the ultrarelativistic $e^{\pm}$ beams as they propagate through intergalactic space.