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 non-thermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter $σ\gg 1$) 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 $α$ in the power-law particle energy distribution function, $f(γ)dγ\propto γ^{-α}dγ$, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponent $α$ is in good agreement with the numerical results.

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