The impact of nonlinear Landau damping on cosmic ray streaming and the role of external turbulence

Abstract

Cosmic rays (CRs) streaming faster than the Alfvén speed generate Alfvén waves that scatter them. The saturated wave amplitude is regulated by a damping mechanism. This damping controls the CR scattering rate and drift velocity, and thus the rate at which CRs transfer momentum and energy to the ambient plasma, which sets the strength of CR feedback. In the ionized interstellar medium, nonlinear Landau damping (NLLD) is commonly invoked as the dominant damping mechanism for Alfvén waves. We test this assumption with fluid-PIC simulations in which thermal ions and electrons are modeled as fluids with optional Landau closures, allowing us to compare otherwise identical runs with and without NLLD. When waves are self-generated by monoenergetic CRs, runs with and without Landau closures are indistinguishable: NLLD is inefficient and the CRs isotropize in the wave frame. Once high-amplitude Alfvén waves mimicking external turbulence are seeded, NLLD curbs wave growth and equalizes forward- and backward-propagating waves. We show that the saturated drift velocity, which falls below the Alfvén speed, can be accurately predicted from the wave spectra alone. If the CR distribution is undersampled, a numerical instability corrupts the largest resonant scales: unphysical, unresolved pitch-angle gradients resonantly generate backward-propagating waves, driving an inverse cascade that should be absent from purely streaming-driven waves. While power-law CR distributions may permit stronger NLLD, our results indicate that NLLD is unlikely to be an intrinsic saturation mechanism of the streaming instability; instead, its effectiveness hinges on the interplay of streaming-generated modes with those of external origin.