  Using full-scale 3D particle-in-cell simulations we show that the radiation
reaction dominated regime can be reached in an all optical configuration
through the collision of a $\sim$1 GeV laser wakefield accelerated (LWFA)
electron bunch with a counter propagating laser pulse. In this configuration
radiation reaction significantly reduces the energy of the particle bunch, thus
providing clear experimental signatures for the process with currently
available lasers. We also show that the transition between classical and
quantum radiation reaction could be investigated in the same configuration with
laser intensities of $10^{24}\mathrm{W/cm^2}$.
