Turbulence and Particle Acceleration in a Relativistic Plasma

In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a nonthermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter σ ≫ 1) quickly evolves into a state with ultrarelativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponent α in the power-law particle-energy distribution function, f(γ)dγ ∝ γ−αdγ, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponent α is in good agreement with the numerical results.