  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.
