Self-consistent plasma wake field interaction in quantum beam transport

A review of a recent theoretical investigation of the quantum transverse beam motion that has been developed in terms of a coupled system of nonlinear spinorial equations is carried out. This is done assuming that a relativistic electron/positron beam is traveling through a plasma along an external magnetic field in overdense condition. Three different nonliner regimes of this analysis are considered: the strictly local regime, where the beam spot size is much greater than the plasma wavelength (then, the spinorial system is reduced to a 2D cubic nonlinear Schrodinger equation in the form of Gross-Pitaevskii equation); the moderately nonlocal regime where the beam spot size is comparable to the plasma wavelength; and, finally, the strongly nonlocal regime where the beam spot size is much smaller than the plasma wavelength. In all the cases the existence of quantum beam vortices and ring solitons is demonstrated both analytically and numerically.