The future linear collider will collide dense $e^+e^-$ bunches at high energies up to 1 TeV, generating very intense electromagnetic fields at the interaction point (IP). These fields are strong enough to lead to nonlinear effects which affect all IP
processes and which are described by strong field physics theory. In order to test this theory, we propose an experiment that will focus an intense laser on the LC electron beam post-IP. Similar experiments at SLAC E144 have investigated nonlinear Compton scattering, Breit-Wheeler pair production using an electron beam of 46.6 GeV. The higher beam energies available at the future LC would allow more precise studies of these phenomena. Mass-shift and spin-dependent effects could also be investigated.
Future lepton colliders will be precision machines whose physics program includes close study of the Higgs sector and searches for new physics via polarised beams. The luminosity requirements of such machines entail very intense lepton bunches at the
interaction point with associated strong electromagnetic fields. These strong fields not only lead to obvious phenomena such as beamstrahlung, but also potentially affect every particle physics process via virtual exchange with the bunch fields. For precision studies, strong field effects have to be understood to the sub-percent level. Strong external field effects can be taken into account exactly via the Furry Picture or, in certain limits, via the Quasi-classical Operator method . Significant theoretical development is in progress and here we outline the current state of play.
