Beam-driven plasma wakefield acceleration (PWFA) is considered one of the most promising novel acceleration technologies capable of drastically shrinking the footprints of high-energy particle colliders. However, there are several challenges that need to be addressed before PWFA can be deployed for high-energy, high-efficiency, high beam brightness particle colliders. Transverse instabilities due to interactions between particle beams and accelerating structures are known to restrict the maximum beam charge in conventional linear colliders such as CLIC (Compact Linear Collider), and are considered one of the most important challenges for PWFA accelerators.
Using a simplified model (benchmarked against particle-in-cell simulations) to describe the PWFA transverse instability in the form of a wake function drastically simplifies computationally expensive particle-in-cell simulations, and allows for a parameter scan for a 1.5 TeV PWFA electron accelerator. The results reveal a parameter set with reasonable stability, energy spread and efficiency, which is used to perform beam-beam studies of multi-TeV PWFA electron-positron and photon linear colliders. The beam-beam studies demonstrate that such colliders may offer significant luminosity improvements over CLIC, which also allows these colliders to reach luminosity goals at lower beam power. However, the examined parameters for both collider types also produce more unwanted background particles.