A simplified model describing the PWFA (plasma wakefield acceleration) transverse instability in the form of a wake function is benchmarked against PIC-simulations. The wakefield formalism is then combined with short PIC-simulations to perform a parameter study for a 1.5 TeV PWFA electron accelerator taking the effects of beam loading, energy spread and transverse instabilities into account to derive a parameter set with reasonable energy spread, stability and efficiency.

This parameter set then forms the basis for subsequent multi-TeV PWFA e+e- and gamma-gamma collider parameter studies, where we assess the performance of such colliders in terms of luminosity and secondary background particles. Beam parameters at the interaction point were optimised in order to mitigate luminosity spread caused by beamstrahlung while maximising total luminosity.