We apply collisionless particle-in-cell simulations of relativistic pair plasmas to explore whether driven turbulence is a viable high-energy astrophysical particle accelerator .
We characterize nonthermal particle distributions for varying system sizes up to L / 2 \pi \rho _ { e 0 } = 163 , where L / 2 \pi is the driving scale and \rho _ { e 0 } is the initial characteristic Larmor radius .
We show that turbulent particle acceleration produces power-law energy distributions that , when compared at a fixed number of large-scale dynamical times , slowly steepen with increasing system size .
We demonstrate , however , that convergence is obtained by comparing the distributions at different times that increase with system size ( approximately logarithmically ) .
We suggest that the system-size dependence arises from the time required for particles to reach the highest accessible energies via Fermi acceleration .
The converged power-law index of the energy distribution , \alpha \approx 3.0 for magnetization \sigma = 3 / 8 , makes turbulence a possible explanation for nonthermal spectra observed in systems such as the Crab nebula .