The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities

TL;DR

This study demonstrates through numerical calculations that nonlinear Landau damping does not significantly suppress the oblique plasma instability, confirming it as the main cooling mechanism for ultrarelativistic pair beams in intergalactic space.

Contribution

The paper provides detailed numerical analysis showing that nonlinear Landau damping is insufficient to suppress the oblique instability, reaffirming its dominance in beam cooling.

Findings

Effective damping rate is 8×10⁻⁴ of the linear growth rate.

Wave energy grows to approximate equipartition with the beam.

Oblique instability remains the primary cooling mechanism.

Abstract

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.