First-principles Demonstration of Diffusive-advective Particle Acceleration in Kinetic Simulations of Relativistic Plasma Turbulence

Nonthermal relativistic plasmas are ubiquitous in astrophysical systems like pulsar wind nebulae and active galactic nuclei, as inferred from their emission spectra. The underlying nonthermal particle acceleration (NTPA) processes have traditionally been modeled with a Fokker–Planck (FP) diffusion-advection equation in momentum space. In this Letter, we directly test the FP framework in ab initio kinetic simulations of driven magnetized turbulence in relativistic pair plasma. By statistically analyzing the motion of tracked particles, we demonstrate the diffusive nature of NTPA and measure the FP energy diffusion (D) and advection (A) coefficients as functions of particle energy $\gamma {m}_{e}{c}^{2}$. We find that $D(\gamma )$ scales as ${\gamma }^{2}$ in the high-energy nonthermal tail, in line with second-order Fermi acceleration theory, but has a much weaker scaling at lower energies. We also find that A is not negligible and reduces NTPA by tending to pull particles toward the peak of the particle energy distribution. This study provides strong support for the FP picture of turbulent NTPA, thereby enhancing our understanding of space and astrophysical plasmas.