Importance of the Resonant Cosmic-Ray Streaming Instability Upstream of Collisionless Shocks
Abstract
Cosmic rays (CRs) escaping collisionless shocks form a dilute, relativistic population whose current amplifies the upstream magnetic field, a process widely attributed to the non-resonant (Bell) instability. Solving the dispersion relation for both cold and finite-spread CR distributions, we show that for the maximum-energy escaping population, the resonant mode can outgrow the non-resonant mode. At slower shocks, this dominance persists for broader CR distributions, and sufficient pitch-angle broadening can even stabilize the non-resonant mode while leaving the resonant mode unstable. Relativistic hybrid particle-in-cell simulations confirm the cold-beam linear theory predictions and, in the nonlinear regime, saturate at δB/B0 ∼ 1 with significant pitch-angle redistribution. Neglecting the resonant instability thus underestimates magnetic field growth at the very scale needed to confine the highest-energy escaping CRs.
Related
- A comparison of particle and fluid approaches for modeling the streaming instability in global patch simulations
- Streaming instabilities in weakly ionized protoplanetary discs: The ambipolar streaming instability
- Collisionless whistler heat-flux instability in ultra-high-β plasmas
- Saturation Level of the Streaming Instability
- Closing the Gap: A Test of the Streaming Instability Using Simulations and Observations of the Cold-Classical Kuiper Belt Size Distribution
BibTeX
@misc{ostler2026importance,
title = {{Importance of the Resonant Cosmic-Ray Streaming Instability Upstream of Collisionless Shocks}},
author = {Bricker Ostler and Benedikt Schroer and Damiano Caprioli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22480},
eprint = {2609.22480},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22480},
}
RIS
TY - UNPB
TI - Importance of the Resonant Cosmic-Ray Streaming Instability Upstream of Collisionless Shocks
AU - Bricker Ostler
AU - Benedikt Schroer
AU - Damiano Caprioli
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22480
UR - https://arxiv.org/abs/2609.22480
AB - Cosmic rays (CRs) escaping collisionless shocks form a dilute, relativistic population whose current amplifies the upstream magnetic field, a process widely attributed to the non-resonant (Bell) instability. Solving the dispersion relation for both cold and finite-spread CR distributions, we show that for the maximum-energy escaping population, the resonant mode can outgrow the non-resonant mode. At slower shocks, this dominance persists for broader CR distributions, and sufficient pitch-angle broadening can even stabilize the non-resonant mode while leaving the resonant mode unstable. Relativistic hybrid particle-in-cell simulations confirm the cold-beam linear theory predictions and, in the nonlinear regime, saturate at δB/B_0 ∼ 1 with significant pitch-angle redistribution. Neglecting the resonant instability thus underestimates magnetic field growth at the very scale needed to confine the highest-energy escaping CRs.
ER -