Modeling the Saturation of the Bell Instability Using Hybrid Simulations
The nonresonant cosmic ray instability, predicted by Bell (2004), is thought to play an important role in the acceleration and confinement of cosmic rays (CRs) 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 kinetic hybrid simulations (with kinetic ions and fluid electrons), we study the saturation of the non-resonant streaming instability as a function of the parameters of both the thermal background plasma and the CR population. The strength of the saturated magnetic field has important implications for both CR acceleration in supernova remnants and CR diffusion in the Galaxy.
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10178657
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ICRC2019
5. We have performed two-dimensional hybrid simulations of non-relativistic collisionless shocks in the presence of pre-existing energetic particles (‘seeds’); such a study applies, for instance, to the re-acceleration of galactic cosmic rays (CRs) in supernova remnant (SNR) shocks and solar wind energetic particles in heliospheric shocks. Energetic particles can be effectively reflected and accelerated regardless of shock inclination via a process that we call diffusive shock re-acceleration. We find that re-accelerated seeds can drive the streaming instability in the shock upstream and produce effective magnetic field amplification. This can eventually trigger the injection of thermal protons even at oblique shocks that ordinarily cannot inject thermal particles. We characterize the current in reflected seeds, finding that it tends to a universal value $J\simeq en_{\text{CR}}v_{\text{sh}}$ , where $en_{\text{CR}}$ is the seed charge density and $v_{\text{sh}}$ is the shock velocity. When applying our results to SNRs, we find that the re-acceleration of galactic CRs can excite the Bell instability to nonlinear levels in less than ${\sim}10~\text{yr}$ , thereby providing a minimum level of magnetic field amplification for any SNR shock. Finally, we discuss the relevance of diffusive shock re-acceleration also for other environments, such as heliospheric shocks, galactic superbubbles and clusters of galaxies.