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Thermal Wave Model is used to study the strong self-consistent Plasma WakeField interaction (transverse effects) between a strongly magnetized plasma anda relativistic electron/positron beam travelling along the external magneticfield, in the long beam limit, in terms of a nonlocal NLS equation and thevirial equation. In the linear regime, vortices predicted in terms ofLaguerre-Gauss beams characterized by non-zero orbital angular momentum (vortexcharge). In the nonlinear regime, criteria for collapse and stable oscillationsis established and the thin plasma lens mechanism is investigated, for beamsize much greater than the plasma wavelength. The beam squeezing and theself-pinching equilibrium is predicted, for beam size much smaller than theplasma wavelength, taking the aberrationless solution of the nonlocal NonlinearSchroeding equation.

Self consistent thermal wave model description of the transverse dynamics for relativistic charged particle beams in magnetoactive plasmas