A New Cosmic-Ray-driven Instability

Cosmic-ray-driven (CR-driven) instabilities play a decisive role during particle acceleration at shocks and CR propagation in galaxies and galaxy clusters. These instabilities amplify magnetic fields and modulate CR transport so that the intrinsically collisionless CR population is tightly coupled to the thermal plasma and provides dynamical feedback. Here, we show that CRs with a finite pitch angle drive electromagnetic waves (along the background magnetic field) unstable on intermediate scales between the gyroradii of CR ions and electrons as long as CRs are drifting with a velocity less than half of the Alfvén speed of electrons. By solving the linear dispersion relation, we show that this new instability typically grows faster by more than an order of magnitude in comparison to the commonly discussed resonant instability at the ion gyroscale. We find the growth rate for this intermediate-scale instability and identify the growing modes as background ion-cyclotron modes in the frame that is comoving with the CRs. We confirm the theoretical growth rate with a particle-in-cell simulation and study the nonlinear saturation of this instability. We identify three important astrophysical applications of this intermediate-scale instability, which is expected to (1) modulate CR transport and strengthen CR feedback in galaxies and galaxy clusters, (2) enable electron injection into the diffusive shock acceleration process, and (3) decelerate CR escape from the sites of particle acceleration, which would generate gamma-ray halos surrounding CR sources such as supernova remnants.