Actual Stationary State for Plasma Lens

The electrostatic plasma lens (PL) provides an attractive and unique tool for manipulating and controlling the high-current heavy ion beams. The concept of the PL is based on using the magnetically insulated electrons and equipotentialization of magnetic field lines. Today, the applications of PL are, however limited. The reason is that estimating the behavior of electrons for complicated magnetic fields runs into severe difficulties. We show that there are specific conditions that admit steady-state of a longitudinal motion, and consider the question of its stability. These results are needed to develop an optimized PL with minimal spherical aberration, in part by optimizing the magnetic field configuration in the low-magnetic-field range.