Energy diffusion and advection coefficients in kinetic simulations of relativistic plasma turbulence*

Turbulent magnetised plasmas, which are ubiquitous in high-energy astrophysical systems, feature extended broadband nonthermal emission spectra implying nonthermal particle energy distributions. The underlying turbulent nonthermal particle acceleration processes have traditionally been modeled with a Fokker-Planck momentum-space diffusion-advection equation. We analyse the energy histories of large numbers of particles in kinetic simulations of driven pair plasma turbulence with varying initial magnetisation and system size. For each simulation, we test the energy-diffusion assumption of the Fokker-Planck particle acceleration framework, and then measure the energy diffusion and advection coefficients D and A as a function of particle energy ε. In the nonthermal energy range, we find the diffusion coefficient scaling is consistent with ε²σ^3/2 where σ is the instantaneous magnetisation. We also measure the evolution of the power-law index of the particle energy distribution and find that it is well-described by an exponential in time. We then construct a model connecting the Fokker-Planck coefficients and the observed power-law evolution, predicting that A ∽ ε log(ε/ε*), which is consistent with the measurements. These results enhance our understanding of turbulent nonthermal particle acceleration.