Kinetic simulations of the current-driven instability in cosmic ray modified relativistic shocks

We study the current-driven instability predicted by Bell (2004) using particle-in-cell simulations. We use one-dimensional simulations to test the dispersion relation and the nonlinear properties of the instability for the case of a relativistic shock front under idealized conditions. We find that if the cosmic rays (CR) are energetic enough to not get deflected by the generated magnetic field, the instability can grow exponentially until the Alfvén velocity of the plasma becomes comparable to the speed of light. We also use one- and two-dimensional simulations to study the effect of the back reaction of the instability on CR. We find that the deflection and filamentation of CR and background plasma play an important role in the saturation of the instability. The current-driven instability is a viable mechanism for the amplification of magnetic fields in both non-relativistic and relativistic shock environments.