A simplified model describing the PWFA (plasma wakefield acceleration) transverse instability in the form of a wake function parameterized only with an effective cavity aperture radius $a$ is benchmarked against PIC-simulations. This wake function implies a $1/a^4$ scaling of the transverse wakefields, which indicates transverse intra-beam wakefields typically several orders of magnitude higher than in conventional acceleration structures. Furthermore, the wakefield formalism is utilized to perform a parameter study for a SI{1.5}{teraelectronvolt} plasma wakefield accelerator, where the constraint on drive beam to main beam efficiency imposed by transverse wakefields is taken into account. Eventually, a parameter set with promising properties in terms of energy spread, stability and luminosity per power was found.
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