  The nonresonant cosmic ray instability, predicted by Bell (2004), is thought
to play an important role in the acceleration and confinement of cosmic rays
(CR) close to supernova remnants. Despite its importance, the exact mechanism
responsible for the saturation of the instability has not been determined, and
there is no first-principle prediction for the amplitude of the saturated
magnetic field. Using a survey of self-consistent hybrid simulations (with
kinetic ions and fluid electrons), we study the non-linear evolution of the
Bell instability as a function of the parameters of the CR population. We find
that saturation is achieved when the magnetic pressure in the amplified field
is comparable to the initial CR momentum flux.

High Energy Astrophysical Phenomena