We present a model-independent way to characterise properties of the magnetic-field turbulence in the emitting regions of Gamma-Ray Burst afterglows. Our only assumption is that afterglows’ synchrotron radiation is efficient. It turns out that the gyroradius of plasma particles must be smaller (with a good margin) than the correlation length of the magnetic-field fluctuations. Such turbulence is essentially non-linear and therefore must be produced by some kind of magnetohydrodynamical instability, likely acting on top of kinetic Weibel instability. We also find that the emitting particles are loosely confined to local magnetic-field structures and diffusion allows them to sample the entire distribution of local magnetisation values. This means that one-zone approach to modelling the afterglow spectra is still valid despite the non-linear nature of the magnetic turbulence. However, the non-linear turbulence may (and likely will) change the synchrotron spectrum of individual electrons.

The recent theory of propagation and generation of waves in a pulsar’s magnetosphere is discussed. In particular we consider models of pulsar radio emission due to plasma instabilities. Wave–particle interactions can lead to quasilinear diffusion increasing a particle’s pitch-angle. The recent model of γ-ray emission from synchrotron radiation as a result of quasilinear diffusion is discussed.