Collision parameters needed to measure polarisation-dependent nonlinear pair creation

Pair creation by a $\gamma$ ray in a high-intensity electromagnetic field (the nonlinear Breit-Wheeler process) is sensitive to the $\gamma$-ray polarisation. Here we study the stability required in order to measure this polarisation dependence in a head-on collision between a high-power linearly polarised laser and a relativistic electron beam, where the $\gamma$-rays produced via nonlinear Compton scattering are highly polarised. We find that the laser strength parameter $a_0$ has to be known to within a few per cent, and that the alignment of the laser and electron beam cannot fluctuate by more than half the spot size, in order to attribute the reduction in positron yield to polarisation effects. These collision parameters are difficult to achieve, but may be realised in future precision experiments that focus on beam stability.