  The dependence of wakefield amplitude and phase on beam and plasma parameters
is studied in the parameter area of interest for self-modulating proton
beam-driven plasma wakefield acceleration. The wakefield sensitivity to small
parameter variations reveals the expected level of shot-to-shot jitter of
experimental results. Of all the parameters, the plasma density stands out, as
the wakefield phase is extremely sensitive to this parameter. The study of
large variations determines the effects that limit the achievable accelerating
field in different parts of the parameter space: nonlinear elongation of the
wakefield period, insufficient charge of the drive beam, emittance-driven beam
divergence, and motion of plasma ions.
