In high-energy astrophysical sources, the plasma is often magnetically-dominated, i.e. the magnetic energy per particle exceeds the rest mass. Since there is a huge separation of scales between the size of the source and the Larmor radius of the particles that emit the observed radiation, the dissipation of the magnetic energy is likely mediated by a turbulent cascade.
The advent of large-scale Particle-In-Cell simulations makes it possible to study turbulent energy dissipation in magnetically-dominated plasmas from first principles. I will show that turbulence is able to accelerate non-thermal particles, even when the radiative losses are severe. The accelerated particles are strongly anisotropic, and move nearly in the same direction of the local magnetic field. As an effect of the anisotropy, the synchrotron emission is severely suppressed with respect to the standard case of isotropic particles. I will discuss the implications of the particle anisotropy for the modelling of high-energy astrophysical sources.