Over the past decades, there has been growing observational and theoretical evidence that cosmic-ray-induced instabilities play an important role in both acceleration and transport of cosmic rays (CRs). For instance, the efficient acceleration of charged particles at supernova remnant shocks requires rapidly growing instabilities, so much so that none of the proposed processes seem sufficient to warrant acceleration to PeV energies. In this work, we investigate whether an acoustic instability triggered by the presence of a CR pressure gradient can lead to significant self-confinement of charged particles in the vicinity of shocks. We validate the expected growth rates and obtain the scale and energy of magnetic field perturbations induced by such system using magnetohydrodynamical (MHD) simulations. Our results suggest a strong suppression of the diffusion coefficient for particles with Larmor radius around a thousandth of the precursor scale length.
Capanema et al. (Tue,) studied this question.