Understanding the Breakdown of the Bell Instability in the Limit of High Cosmic Ray Current Density

A critical component to explaining the observation of cosmic ray acceleration at supernova remnants is the non-resonant Bell's instability, where the relative drift between the thermal ions and the cosmic rays lead to the amplification of magnetic fields necessary to accelerate particles with diffusive shock acceleration. In order to extend our understanding of particle acceleration in other astrophysical systems, and to inform limitations on the amount of heating possible from the Bell instability in supernova remnants, in this work we investigate the instabilities present in the high cosmic ray current density limit, where the assumptions underlying the Bell instability break down. Despite the increase in the free energy in the particles, in this limit significantly less magnetic field amplification is observed. We discuss the saturation of the instabilities in this regime, how they scale with respect to the sources of free energy in the system, and, critically, their relevance for the injection of electrons into the process of diffusive shock acceleration.