  Plasma wake-field acceleration experiments are performed at the SPARC LAB
test facility by using a gas-filled capillary plasma source composed of a
dielectric capillary. The electron can reach GeV energy in a few centimeters,
with an accelerating gradient orders of magnitude larger than provided by
conventional techniques. In this acceleration scheme, wake fields produced by
passing electron beams through dielectric structures can determine a strong
beam instability that represents an important hurdle towards the capability to
focus high-current electron beams in the transverse plane. For these reasons,
the estimation of the transverse wakefield amplitudes assumes a fundamental
role in the implementation of the plasma wake-field acceleration. In this work,
it presented a study to investigate which parameters affect the wake-field
formation inside a cylindrical dielectric structure, both the capillary
dimensions and the beam parameters, and it is introduced a quantitative
evaluation of the longitudinal and transverse electric fields.
