Direct Numerical Demonstration of Diffusive Nonthermal Particle Acceleration in Particle-in-Cell Simulations of Kinetic Turbulence in Relativistic Pair Plasmas

Nonthermal particle acceleration (NTPA) is ubiquitous in high-energy astrophysics, as evidenced by cosmic rays and the emission spectra of pulsar wind nebulae and active galactic nuclei. Most analytical models of NTPA posit diffusive Fermi acceleration described by a Fokker-Planck (FP) advection-diffusion equation in momentum space. We test the applicability of the FP framework directly in kinetic particle-in-cell simulations of driven magnetized turbulence in relativistic pair plasma. By statistically analyzing the motion of almost a million tracked particles, we confirm the diffusive nature of turbulent NTPA and measure the FP energy diffusion (D) and advection (A) coefficients as functions of particle energy γm_ec². We find that D(γ) is proportional to γ² in the high-energy nonthermal tail, in line with 2nd-order Fermi acceleration theory, but has a much shallower scaling of about γ^2/3 at lower energies, while A tends to pull particles towards the peak of the distribution. We also explore the effects of magnetization. Our results provide strong support for the FP picture of turbulent NTPA, thereby enhancing our understanding of space, solar, and astrophysical plasmas.