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The dissipation of turbulent magnetic fields is an appealing scenario toexplain the origin of non-thermal particles in high-energy astrophysicalsources. However, it has been suggested that the particle distribution mayeffectively thermalise when the radiative (synchrotron and/or Inverse Compton)losses are severe. Inspired by recent PIC simulations of relativisticturbulence, which show that electrons are impulsively heated in intermittentcurrent sheets by a strong electric field aligned with the local magneticfield, we instead argue that in plasmas where the particle number density isdominated by the pairs (electron-positron and electron-positron-ion plasmas):(i) as an effect of fast cooling and of different injection times, the electronenergy distribution is ${\rm d}n_e/{\rm d}\gamma\propto\gamma^{-2}$ for$\gamma\lesssim\gamma_{\rm heat}$ (the Lorentz factor $\gamma_{\rm heat}$ beingclose to the equipartition value), while the distribution steepens at higherenergies; (ii) since the time scales for the turbulent fields to decay and forthe photons to escape are of the same order, the magnetic and the radiationenergy densities in the dissipation region are comparable; (iii) if the massenergy of the plasma is dominated by the ion component, the pairs with aLorentz factor smaller than a critical one (of the order of theproton-to-electron mass ratio) become isotropic, while the pitch angle remainssmall otherwise. The outlined scenario is consistent with the typicalconditions required to reproduce the Spectral Energy Distribution of blazars,and allows one to estimate the magnetisation of the emission site. Finally, weshow that turbulence within the Crab Nebula may power the observed gamma-rayflares if the pulsar wind is nearly charge-separated at high latitudes.

Magnetic energy dissipation and origin of non-thermal spectra in radiatively efficient relativistic sources