  Recent progress in laser-driven plasma acceleration now enables the
acceleration of electrons to several gigaelectronvolts. Taking advantage of
these novel accelerators, ultra-short, compact and spatially coherent X-ray
sources called betatron radiation have been developed and applied to
high-resolution imaging. However, the scope of the betatron sources is limited
by a low energy efficiency and a photon energy in the 10's of kiloelectronvolt
range, which for example prohibits the use of these sources for probing dense
matter. Here, based on three-dimensional particle-in-cell simulations, we
propose an original hybrid scheme that combines a low-density laser-driven
plasma accelerator with a high-density beam-driven plasma radiator, and thereby
considerably increases the photon energy and the radiated energy of the
betatron source. The energy efficiency is also greatly improved, with about 1%
of the laser energy transferred to the radiation, and the gamma-ray photon
energy exceeds the megaelectronvolt range when using a 15 J laser pulse. This
high-brilliance hybrid betatron source opens the way to a wide range of
applications requiring MeV photons, such as the production of medical isotopes
with photo-nuclear reactions, radiography of dense objects in the defense or
industrial domains and imaging in nuclear physics.
