Fast radio bursts are mysterious transient sources likely located at cosmological distances. The derived brightness temperatures exceed by many orders of magnitude the self-absorption limit of incoherent synchrotron radiation, implying the operation of a coherent emission process. We propose a radiation mechanism for fast radio bursts where the emission arises from collisionless Bremsstrahlung in strong plasma turbulence excited by relativistic electron beams. We discuss possible astrophysical scenarios in which this process might operate. The emitting region is a turbulent plasma hit by a relativistic jet, where Langmuir plasma waves produce a concentration of intense electrostatic soliton-like regions (cavitons). The resulting radiation is coherent and, under some physical conditions, can be polarised and have a power-law distribution in energy. We obtain radio luminosities in agreement with the inferred values for fast radio bursts. The timescale of the radio flare in some cases can be extremely fast, of the order of $10^{-3}$ s. The mechanism we present here can explain the main features of fast radio bursts and is plausible in different astrophysical sources, such as gamma-ray bursts and some Active Galactic Nuclei.

6 pages, 1 figure. Accepted for publication in Phys. Rev. D