  Laser plasma accelerators capable of generating >10 GeV electron beams may
require plasma mirrors to remove undepleted laser energy at the end of each
accelerator stage. Near the plasma mirror surface, the electron bunch can
interact with the reflected light, resulting in inverse Compton scattering. For
realistic conditions, we show that a significant fraction of electrons emit one
or more photons, increasing the energy spread of the electron bunch. We provide
an analytical expression for calculating this effect, and use it to estimate
the minimum drift space required before the plasma mirror to meet given energy
spread specifications. Mitigation strategies, necessary to achieve sub-percent
energy spread in multi-GeV laser wakefield electron sources, are proposed and
explored.
