Particle dynamics in the cosmic-ray driven turbulence at shock waves

Collisionless shocks that form in astrophysical plasmas accelerate particles primarily via diffusive shock acceleration. In this process, charged particles cross the shock front multiple times, scattering off electromagnetic fluctuations on both sides of the discontinuity. These fluctuations can be generated by non-thermal particles, known as cosmic rays, through streaming plasma instabilities. During the nonlinear development of the instability, broad-range turbulence emerges, potentially affecting the dynamics of particles with gyroradii much smaller than those of cosmic rays. We analyze the trajectories of both computational and test particles in fully kinetic simulations of the non-resonant Bell instability. This includes investigating the dominant drifts, examining the scattering efficiency, and computing diffusion coefficients for particles with energies ranging from thermal to suprathermal. We compare the behavior of test and computational particles and study their dependence on the integrators of the particle equations of motion and the electromagnetic field interpolation schemes. This allows us to determine the significance of particle feedback on the turbulence evolution and the applicability of a simplified test particle description. Finally, we discuss the implications of our results for particle heating and injection at collisionless shocks.