  In various media the elementary components can emit traveling waves such as
electromagnetic, gravitational or acoustic types. If these elementary emitters
are synchronized, the resulting emission is coherent. Moreover, the faster the
emitters approach an observer, the more intense and directional their apparent
emission is, with associated frequency increase. Multi-stream flows
ubiquitously occur in media (such as with shock waves and jets in astrophysical
and laboratory plasmas) and produce fast moving density singularities, where
high concentration and synchronism can bring constructive interference.
However, a singularity emitting such characteristic coherent radiation has not
been demonstrated yet. We show this general phenomenon in laser-driven
relativistic plasma, which is an ideal medium for realizing these effects in
the laboratory under controllable conditions. Our experiments and simulations
reveal bright coherent soft x-ray radiation from nanoscale electron density
singularities in multi-stream plasma. They constitute a new compact x-ray
source of ultrashort duration, demanded in numerous applications. In general,
singularities can be bright sources of other types of traveling waves. Thus our
findings open new opportunities in different fields of science. For example,
gravitational wave generation, as proposed in ultrahigh-energy accelerators,
can be significantly enhanced by intentionally induced density singularities in
the particle bunches. Further, we anticipate that multi-stream flows in cosmic
media can produce intense bursts of coherent electromagnetic and/or
gravitational waves, especially at longer wavelengths which facilitate
constructive interference. We can then expect to observe more directional short
wavelength bursts from cosmic emitters approaching at relativistic speeds.
Thus, we present a new framework for interpreting a broad range of experimental
results.
