Electron vortexes in high-current plasma lens

High-current plasma lens (PL) collective processes due to unremovable radial gradients of the magnetic field in the ion beam focusing direction have been reported in [1]. There the theoretical analysis of the linear growth stage of a small-scaled instability was presented. Now we consider PL hydrodynamic instability in nonlinear approximation. It is shown, on the example of high-current FL, that drift motion of electrons in variable electric fields caused by the principally unremovable radial gradient of the magnetic field axial component is transformed into the set of single vortex structures. The nonlinear differential equation of the electric potential describing such structures is received and its solutions are found for different configurations of external magnetic fields. It is shown that such kind of vortex can be stable. Computer models for such kind of vortex has been created. Creation of vortexes limits maximum values of space electrostatic fields in plasmaoptics. In the low current regime of the PL with strong ion beam space charge overcompensation the equation obtained describes nonlinear motion of the electron fluid caused by diocotron instability.