Ultra-high brilliance multi-MeV $gamma$-ray beam from non-linear Thomson scattering

We report on the generation of a narrow divergence ($thetaapprox 2.5$ mrad), multi-MeV ($E_text{MAX} = 18$ MeV) and ultra-high brilliance ($approx 2times10^{19}$ photons s$^{-1}$ mm$^{-2}$ mrad $^{-2}$ 0.1% BW) $gamma$-ray beam from the scattering of an ultra-relativistic laser-wakefield accelerated electron beam in the field of a relativistically intense laser (dimensionless amplitude $a_0approx2$). The spectrum of the generated $gamma$-ray beam is measured, with MeV resolution, seamlessly from 6 MeV to 18 MeV, giving clear evidence of the onset of non-linear Thomson scattering. The photon source has the highest brilliance in the multi-MeV regime ever reported in the literature.