Quantumlike description of the nonlinear and collective effects on   relativistic electron beams in strongly magnetized plasmas
  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. 
Fatema Tanjia, Sergio De Nicola, Renato Fedele, P. K. Shukla, and   Dusan Jovanovic
physics.plasm-ph physics.acc-ph