Electron vortexes in high-current plasma lens

High-current plasma lens (PL) instability of two-dimensional oscillations caused by unremovable radial gradients of the magnetic field and fast ion beams are considered. It is supposed that electron motion is nonlinear and ion motion is linear. The nonlinear differential equation of the electric potential in a hydrodynamical approximation is obtained and its solutions are found for different configurations of external magnetic fields. It is shown that these solutions may be represented in the form of stable vortex structures. Computer models for such kinds of vortices have been created. Creation of vortexes limits maximum values of space electrostatic fields in plasma optics. 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