On 2D electron cloud dynamics in high-current plasma lens for ion beam focusing.

In this paper we are dealing with the appear the stable existence and dynamics of 2-D electron vortical structures in crossed electric and magnetic fields. The collective interactions in which the electron motion is nonlinear and ion motion is linear, is concerned. By using of the kinetic equation and the catastrophe theory approach we deduce an origin of the vortical structures. The nonlinear differential equation for the electric potential in a hydrodynamical approximation is obtained. It describes a drift motion of the electrons in oscillating electic fields of the high-current plasma lens(PL), arising due to presence the principal unremoval radical gradient of the axical component of the magnetic field. It was shown that the considered equations have contained the solutions in the form of the single vortical structures. The stability of the structures are given.