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We apply collisionless particle-in-cell simulations of relativistic pairplasmas to explore whether driven turbulence is a viable high-energyastrophysical particle accelerator. We characterize nonthermal particledistributions for varying system sizes up to $L/2\pi\rho_{e0} = 163$, where$L/2\pi$ is the driving scale and $\rho_{e0}$ is the initial characteristicLarmor radius. We show that turbulent particle acceleration produces power-lawenergy distributions that, when compared at a fixed number of large-scaledynamical times, slowly steepen with increasing system size. We demonstrate,however, that convergence is obtained by comparing the distributions atdifferent times that increase with system size (approximately logarithmically).We suggest that the system-size dependence arises from the time required forparticles to reach the highest accessible energies via Fermi acceleration. Theconverged power-law index of the energy distribution, $\alpha \approx 3.0$ formagnetization $\sigma = 3/8$, makes turbulence a possible explanation fornonthermal spectra observed in systems such as the Crab nebula.

System-size convergence of nonthermal particle acceleration in relativistic plasma turbulence