  In a collisionless plasma, the energy distribution function of plasma
particles can be strongly affected by turbulence. In particular, it can develop
a non-thermal power-law tail at high energies. We argue that turbulence with
initially relativistically strong magnetic perturbations (magnetization
parameter $\sigma \gg 1$) quickly evolves into a state with ultra-relativistic
plasma temperature but mildly relativistic turbulent fluctuations. We present a
phenomenological and numerical study suggesting that in this case, the exponent
$\alpha$ in the power-law particle energy distribution function,
$f(\gamma)d\gamma\propto \gamma^{-\alpha}d\gamma$, depends on magnetic
compressibility of turbulence. Our analytic prediction for the scaling exponent
$\alpha$ is in good agreement with the numerical results.
