In multimessenger high-energy astrophysics, interpreting observed spectra often hinges on understanding the underlying competition between energy gains and radiative losses within the accelerator. To progress along these lines, we report here on numerical particle-in-cell simulations of particle acceleration in relativistic, magnetized turbulent pair plasmas including synchrotron radiative losses. We investigate a regime of weak synchrotron cooling, where the maximal energy predicted by balancing the acceleration and radiation rates resides in the suprathermal tail, i.e., above the thermal bulk and below the confinement energy associated with the outer scale of the turbulence. Our key finding is that the particle energy spectrum, along with the radiated synchrotron spectral power, does not terminate at this maximal energy (or corresponding frequency), but extends significantly beyond with a steepened spectrum, up to the synchrotron burn-off limit where particles cool within a gyrotime. For our adopted parameters (turbulence magnetization parameter $\sigma \approx 1$ and amplitude $\delta B/B_0\simeq 1$), the particle distribution function follows $\mathrm{d}n/\mathrm{d}\gamma \propto {\gamma }^{-s}$ with $s\simeq 3$ below the predicted maximal energy, then steepens to $s\simeq 4$ above. The particle energy distribution and the radiated synchrotron spectra display strong variability near the cutoff energy down to timescales well below the largest eddy turn-around time. We substantiate our results by demonstrating that the acceleration rate itself displays a broken power-law-like distribution, whose mean value defines the diffusion coefficient and whose maximal value is the gyrofrequency. We perform a detailed analysis of the acceleration mechanism for the highest-energy particles and demonstrate that they are accelerated to this extreme limit by a generalized Fermi process in ideal electric fields. This process is driven by a gradient of the four-velocity field $u_E$ of the magnetic field lines of relativistic amplitude, $\delta u_E\gtrsim c$, ordered on a scale comparable to, or larger than, the particle gyroradius at the synchrotron burn-off limit. We contend that this is a generic feature of relativistic, large-amplitude turbulence. Finally, we apply our results to the case of the Crab nebula, which exhibits a hierarchy of characteristic Lorentz factors similar to that studied here. We conclude that stochastic acceleration in this environment is a promising mechanism for explaining the highest-energy part of the synchrotron spectral energy distribution and its variability.

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• Cosmic ray acceleration
• Magnetohydrodynamic turbulence
• Particle acceleration in plasmas