New Vortices in Axisymmetric Beams in Inhomogeneous Magnetic Field

We analyzed localized vortices in non-neutral inhomogeneous by density and velocity electron beams propagating in vacuum along the inhomogeneous external magnetic field. These vortices distinguish from vortices, which used in [1,2,3] because of inhomogeneous external magnetic field. Also new types of vortex are obtained by new solution method of nonlinear equations [3]. That method distinguish from standard Larichev-Reznik or Reznik method, which used in [1]. It has been found new expression for electric field potential of vortex in a wave frame. The expression is axisymmetric in a wave frame. New vortices are new solitons in the inhomogeneous external magnetic field.