Strong radiation damping effects in a gamma-ray source generated by the interaction of a high intensity laser with a wakefield accelerated electron beam

We present numerical calculations of the angularly resolved radiation spectrum from a relativistic electron beam interacting with an ultrashort laser pulse. These calculations include the effect of semi-classical radiation reaction forces including a Gaunt factor for synchrotron radiation. For a laser of $5\times10^{21}$ Wcm$^{-2}$ intensity interacting with a 200 MeV electron beam with an emittance similar to that in laser wakefield acceleration experiments, radiation reaction does not produce a significant change in the angular and energy distribution of \emph{photons}. However the effects of radiation reaction are clear when observing the \emph{electron beam} properties. The result is that near-term experiments using such a counter-propagating beam-laser geometry should be able to measure the effects of quantum effects in radiation reaction. The calculations also show that the brilliance of this source is very high, with a peak spectral brilliance exceeding $10^{29}$ photons$\,$s$^{-1}$mm$^{-2}$mrad$^{-2}(0.1$\% bandwidth$)^{-1}$ with approximately 2\% efficiency and with a peak energy of 10 MeV.