Formation by ions the plasma channel at propagation of the finite sequence of relativistic electron bunches (REB) in underdense plasmas

2.5-dimensional particle simulation results on the wake-field excitation by the programmed finite sequence of REB in underdense plasmas are presented. The REB/background plasma configuration is described by a full set of 2D3V relativistic Vlasov equations for each plasma species and Maxwell equations for self-consistent electromagnetic field. The computer simulation showed that the transversal dimension of the bunch, propagating in plasma, to vary over a wide range at our conditions when transversal and longitudinal bunch sizes are smaller than the skin-depth. In these cases significant nonlinearities in both plasma and beam behavior have been observed. The ions form the plasma channel due to their transversal motion in self-consistent fields. This phenomenon plays a considerable role in the REB propagation in plasmas