  The rapid development of high brilliance X-ray radiation sources is
revolutionizing physics, chemistry, and biology research through their novel
applications. Another breakthrough is anticipated with the construction of
next-generation laser facilities which will operate at intensities beyond
$10^{23}$ $\mathrm{W/cm^2}$, leading to higher yield, shorter wavelength
radiation sources. We use numerical simulations to demonstrate that a source of
collimated multi-MeV photons with conversion efficiency comparable to the one
expected for these facilities is achievable at an order of magnitude lower in
intensity, within reach of the existing facilities. In the optimal setup, the
laser pulse irradiates a bulk solid-density target, heating the target
electrons and inducing relativistic transparency. As the pulse then propagates,
it generates a beam of energetic electrons which in turn drives a strong
azimuthal magnetic field. This field significantly enhances the radiation
reaction for the electrons, yielding tens of TW of directed MeV photons for a
PW-class laser.
