Excitation of the nonresonant streaming instability around sources of ultrahigh-energy cosmic rays

¹ Gran Sasso Science Institute (GSSI) Viale Francesco Crispi 7 67100 L’Aquila, Italy
² INFN-Laboratori Nazionali del Gran Sasso (LNGS) Via G. Acitelli 22 67100 Assergi (AQ), Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 20 June 2025
Accepted: 4 January 2026

Abstract

Aims. The interpretation of the ultrahigh-energy cosmic-ray (UHECR) spectrum and composition suggests a suppression of the flux below ≈1 EeV, as observed by the Pierre Auger Observatory and Telescope Array. A natural explanation for this phenomenon involves magnetic confinement effects. We investigate the possibility that UHECRs self-generate the magnetic turbulence necessary for this confinement via current-driven plasma instabilities.

Methods. Specifically, we show that the electric current produced by escaping UHECRs can excite a nonresonant streaming instability in the surrounding plasma. This instability reduces the diffusion coefficient in the source environment and effectively traps particles with energies E ≲ 1 EeV ℒ₄₄^3/4 R_Mpc^−3/2λ₃₀ for times that exceed the age of the Universe. Here, ℒ₄₄ is the source luminosity in units of 10⁴⁴ erg/s, R_Mpc is the radial size in Mpc, and λ₃₀ is the intergalactic magnetic field coherence length in units of 30 Mpc. We discuss the conditions in detail (the source luminosity, the initial magnetic field, and the environment in which this complex phenomenon occurs) that need to be fulfilled in order for self-confinement to take place near a source of UHECRs, and we also discuss the caveats that affect our conclusions. We emphasize that these conclusions were derived within a simplified model framework; their wider applicability requires that the assumptions hold in realistic source environments.

Results. By modeling a population of UHECR sources with a luminosity function typical of extragalactic gamma-ray sources, we connected the spectrum of escaping particles to the luminosity distribution. Furthermore, we calculated the contribution of these confined particles to cosmogenic neutrino production and found consistency with current observational constraints. Our results suggest that self-induced turbulence might play an important role in shaping the UHECR spectrum. In particular, it might account for the flux suppression near their sources. This offers a promising framework for interpreting current observations.