  As new laser facilities are developed with intensities on the scale of 10^22
- 10^24 W cm^-2 , it becomes ever more important to understand the effect of
strong field quantum electrodynamics processes, such as quantum radiation
reaction, which will play a dominant role in laser-plasma interactions at these
intensities. Recent all-optical experiments, where GeV electrons from a laser
wakefield accelerator encountered a counter-propagating laser pulse with a_0 >
10, have produced evidence of radiation reaction, but have not conclusively
identified quantum effects nor their most suitable theoretical description.
Here we show the number of collisions and the conditions required to accomplish
this, based on a simulation campaign of radiation reaction experiments under
realistic conditions. We conclude that while the critical energy of the photon
spectrum distinguishes classical and quantum-corrected models, a better means
of distinguishing the stochastic and deterministic quantum models is the change
in the electron energy spread. This is robust against shot-to-shot fluctuations
and the necessary laser intensity and electron beam energies are already
available. For example, we show that so long as the electron energy spread is
below 25%, collisions at a_0 = 10 with electron energies of 500 MeV could
differentiate between different quantum models in under 30 shots, even with
shot to shot variations at the 50% level.
