  A numerical analysis of the self-interaction induced by a relativistic
electron/positron beam in the presence of an intense external longitudinal
magnetic field in plasmas is carried out. Within the context of the Plasma Wake
Field theory in the overdense regime, the transverse beam-plasma dynamics is
described by a quantumlike Zakharov system of equations in the long beam limit
provided by the Thermal Wave Model. In the limiting case of beam spot size much
larger than the plasma wavelength, the Zakharov system is reduced to a 2D
Gross-Pitaevskii-type equation, where the trap potential well is due to the
external magnetic field. Vortices, "beam halos" and nonlinear coherent states
(2D solitons) are predicted.
