  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}{\tera\electronvolt} 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.
