  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.
