Spatial intermittency of particle distribution in relativistic plasma turbulence

Relativistic magnetically dominated turbulence is an efficient engine for particle acceleration in a collisionless plasma. Ultrarelativistic particles accelerated by interactions with turbulent fluctuations form non-thermal power-law distribution functions in the momentum (or energy) space, $f(\gamma )d\gamma \propto {\gamma }^{-\alpha }d\gamma$, where $\gamma$ is the Lorenz factor. We argue that in addition to exhibiting non-Gaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particle-in-cell numerical simulations and phenomenological modeling, we propose that the bulk plasma density has log-normal statistics, while the density of the accelerated particles, $n$, has a power-law distribution function, $P(n)dn\propto n^{-\beta }dn$. We argue that the scaling exponents are related as $\beta \approx \alpha +1$, which is broadly consistent with numerical simulations. Non-space-filling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence.