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Abstract The nonresonant streaming instability (Bell instability) plays a pivotal role in the acceleration and confinement of cosmic rays (CRs), yet the exact mechanism responsible for its saturation and the magnitude of the final amplified magnetic field have not been assessed from first principles. Using a survey of hybrid simulations (with kinetic ions and fluid electrons), we study the evolution of the Bell instability as a function of the parameters of the CR population. We find that at saturation, the magnetic pressure in the amplified field is comparable with the initial CR anisotropic pressure, rather than with the CR energy flux, as previously argued. These results provide a predictive prescription for the total magnetic field amplification expected in the many astrophysical environments where the Bell instability is important. 

Cosmic rays leave their sources mainly along the local magnetic field present in the region around the source and in doing so they excite both resonant and non-resonant modes through streaming instabilities. The excitation of these modes leads to enhanced particle scattering and in turn to a large pressure gradient that causes the formation of expanding bubbles of gas and self-generated magnetic fields. By means of hybrid particle-in-cell simulations, we demonstrate that, by exciting this instability, cosmic rays excavate a cavity around their source where the diffusivity is strongly suppressed. This phenomenon is general and is expected to occur around any sufficiently powerful cosmic ray source in the Galaxy. Our results are consistent with recent γ-ray observations where emission from the region around supernova remnants and stellar clusters have been used to infer that the diffusion coefficient around these sources is ∼10−100 times smaller than the typical Galactic one.