  It is possible using current high intensity laser facilities to reach the
quantum radiation reaction regime for energetic electrons. An experiment using
a wakefield accelerator to drive GeV electrons into a counterpropagating laser
pulse would demonstrate the increase in the yield of high energy photons caused
by the stochastic nature of quantum synchrotron emission: we show that a beam
of $10^9$ 1 GeV electrons colliding with a 30 fs laser pulse of intensity
$10^{22}~\text{Wcm}^{-2}$ will emit 6300 photons with energy greater than 700
MeV, $60\times$ the number predicted by classical theory.
