  Synchrotron radiation sources are immensely useful tools for scientific
researches and many practical applications. Currently, the state-of-the-art
synchrotrons rely on conventional accelerators, where electrons are accelerated
in a straight line and radiate in bending magnets or other insertion devices.
However, these facilities are usually large and costly. Here, we propose a
compact all-optical synchrotron-like radiation source based on laser-plasma
acceleration either in a straight or in a curved plasma channel. With the laser
pulse off-axially injected in a straight channel, the centroid oscillation of
the pulse causes a wiggler motion of the whole accelerating structure including
the trapped electrons, leading to strong synchrotron-like radiations with
tunable spectra. It is further shown that a ring-shaped synchrotron is possible
in a curved plasma channel. Due to the intense acceleration and bending fields
inside plasmas, the central part of the sources can be made within palm size.
With its potential of high flexibility and tunability, such compact light
sources once realized would find applications in wide areas and make up the
shortage of large synchrotron radiation facilities.
