Kinetic turbulence in relativistic plasma: from thermal bath to non-thermal continuum

We present results from particle-in-cell simulations of driven turbulence in magnetized, collisionless, and relativistic pair plasma. We find that fluctuations are consistent with the classical $k_{\perp }^{-5\mathrm{/}3}$ magnetic energy spectrum at fluid scales and a steeper $k_{\perp }^{-4}$ spectrum at sub-Larmor scales, where $k_{\perp }$ is the wavevector perpendicular to the mean field. We demonstrate the development of a non-thermal, power-law particle energy distribution, $f(E)\sim E^{-\alpha }$, with index $\alpha$ that decreases with increasing magnetization and increases with increasing system size (relative to the characteristic Larmor radius). Our simulations indicate that turbulence can be a viable source of energetic particles in high-energy astrophysical systems, such as pulsar wind nebulae, if scalings asymptotically become insensitive to the system size.