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Nonthermal relativistic plasmas are ubiquitous in astrophysical systems likepulsar wind nebulae and active galactic nuclei, as inferred from their emissionspectra. The underlying nonthermal particle acceleration (NTPA) processes havetraditionally been modeled with a Fokker-Planck (FP) diffusion-advectionequation in momentum space. In this paper, we directly test the FP framework inab-initio kinetic simulations of driven magnetized turbulence in relativisticpair plasma. By statistically analyzing the motion of tracked particles, wedemonstrate the diffusive nature of NTPA and measure the FP energy diffusion($D$) and advection ($A$) coefficients as functions of particle energy $\gammam_e c^2$. We find that $D(\gamma)$ scales as $\gamma^2$ in the high-energynonthermal tail, in line with 2nd-order Fermi acceleration theory, but has amuch weaker scaling at lower energies. We also find that $A$ is not negligibleand reduces NTPA by tending to pull particles towards the peak of the particleenergy distribution. This study provides strong support for the FP picture ofturbulent NTPA, thereby enhancing our understanding of space and astrophysicalplasmas.

First-principles demonstration of diffusive-advective particle acceleration in kinetic simulations of relativistic plasma turbulence