  The non-resonant (Bell) streaming instability driven by energetic particles
is crucial for producing amplified magnetic fields that are key to the
acceleration of cosmic rays (CRs) in supernova remnants, around Galactic and
extra-galactic CR sources, and for the CR transport. We present a covariant
theory for the saturation of the Bell instability, substantiated by
self-consistent kinetic simulations, that can be applied to arbitrary CR
distributions and discuss its implications in several heliospheric and
astrophysical contexts.
