  We analyze the equilibrium configuration for a modulated beam with sharp
boundaries exposed to the fields self-generated by the interaction with a
plasma. Through a semi-analytical approach we show the presence of multiple
equilibrium configurations and we determine the one more suitable for wakefield
excitation. Once pointed out the absence of confinement for the front of the
beam and the consequently divergence driven by the emittance, we study the
evolution of the equilibrium configuration while propagating in the plasma,
discarding all the others time-dependencies. We show the onset of a rigid
backward drift of the equilibrium configuration and we provide an explanation
in the increasing length of the first bunch.
