Highly polarised gamma photons from electron-laser collisions

We detail a method to produce a GeV-photon source with polarisation purity exceeding $96\%$ and $89\%$ for linear and circular polarisation respectively and with a brilliance of the order of $10^{21}\,\textrm{photons}/(\textrm{s}~\textrm{mm}^2~\textrm{mrad}^2~0.1\%~\textrm{BW})$. Using currently available multi-GeV electron bunches and laser pulses of moderately relativistic intensities, we show how the weakly nonlinear regime can produce photons polarised mainly parallel to the laser field. We demonstrate the robustness of this scheme by considering electron bunches of various emissivities colliding with linearly and circularly-polarised laser pulses at a range of angles.