**1. Introduction**

The realization that outer space is becoming an integral part of our earthly existence becomes commonplace. Hundreds of all kinds of spacecraft (maneuverable and marching), plow the vastness of the vast space. The moving force of such spacecraft has become the electric propulsions different kinds. Traditionally, Hall thrusters (plasma accelerators with closed Hall current and metal or dielectric walls [1–4] attract a special attention of the electric propulsion community. Remarkably high efficiency, simplicity, and potential durability make the Hall thruster one of the primary candidates for miniaturization and application in small communications satellites and using for primary propulsion in deep-space scientific missions. Hall thrusters inherit coaxial geometry for which the material of the annular chamber walls significantly affects the plasma discharge properties and erosion of the dielectric walls. In order to avoid erosion developers, try to create modified wall less accelerator constructions [5, 6]. But these attempts while are not completed, quite complicated and sound many skepticisms.

One of the promising ways to avoid erosion issues is the separation of the magnetic and electrical circuits of the accelerator, which is easier to do in the cylindrical geometry. This principle was carried out and tested in the original Hall type erosion-less accelerator on a laboratory stand at the Institute of Physics NAS of Ukraine [7–10]. The novelty of the proposed idea is the use of a virtual parallel surface of the anode to the cathode due to the principle of equipotentialization of magnetic field lines. Which allows to avoid sputtering of the cathode surface. It was shown the potential drop forms at the axis of system that can use for ion beam formation and accelerating.

We describe the Hall-type accelerator with closed Hall current and open (that is unbounded by metal or dielectric) walls that was proposed and considered both theoretically and experimentally. A two-dimensional hybrid model in cylindrical coordinates is constructed in the framework of which the possibility of creation a positive space charge at the system axes is shown. It is shown that the ions flow from the hump of electrical potential can lead to the creation of a powerful ion flow, which moves along the symmetry axis in both sides from the center. The formation of the actual traction beam should occur due to the acceleration of ions by the accumulated positive bulk charge. Thus, such type of accelerator could sound interest in manipulating high-current flow of charge particle as well as can be attractive for many different high-tech applications and for potential elaborations of low cost, compact and durability electric thrusters.

This article is the brief review of the current status an ongoing experimental and theoretical research and simulations results of such kind accelerator based on the axial-symmetric cylindrical electrostatic plasma lens configuration and the fundamental plasma-optical principles of magnetic electron isolation and equipotentialization magnetic field lines.
