Diffusive radiation in Langmuir turbulence produced by jet shocks

Anisotropic distributions of charged particles including two-stream distributions give rise to generation of either stochastic electric fields (in the form of Langmuir waves, Buneman instability) or random quasi-static magnetic fields (Weibel and filamentation instabilities) or both. These two-stream instabilities are known to play a key role in collisionless shock formation, shock-shock interactions, and shock-induced electromagnetic emission. This paper applies the general non-perturbative stochastic theory of radiation to study electromagnetic emission produced by relativistic particles, which random walk in the stochastic electric fields of the Langmuir waves. This analysis takes into account the cumulative effect of uncorrelated Langmuir waves on the radiating particle trajectory giving rise to angular diffusion of the particle, which eventually modifies the corresponding radiation spectra. We demonstrate that the radiative process considered is probably relevant for emission produced in various kinds of astrophysical jets, in particular, prompt gamma-ray burst spectra, including X-ray excesses and prompt optical flashes.