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

A Kinetic Study of the Saturation of the Bell Instability