  Beam-driven plasma wakefield accelerators typically use the external
injection scheme to ensure controllable beam quality at injection. However, the
externally injected witness bunch may exhibit a non-Gaussian transverse density
distribution. Using particle-in-cell simulations, we show that the common beam
quality factors, such as the normalized RMS emittance and beam radius, do not
strongly depend on the initial transverse shapes of the witness beam.
Nonetheless, a beam with a highly-peaked transverse spatial profile can achieve
a higher fraction of the total beam charge in the core. The same effect can be
seen when the witness beam's transverse momentum profile has a peaked
non-Gaussian distribution. In addition, we find that an initially
non-axisymmetric beam becomes symmetric due to the interaction with the plasma
wakefield, and so it does not cause a detrimental effect for the beam
acceleration.
