“…A regular smooth solution across the whole acceleration region from v i < c s to the region with v i > c s by imposing the regularity condition at the sonic point 25,26 . As an example, in case of the ion acceleration in the Hall thrusters, the regular solution is obtained by imposing an analytical condition on the ion flux, electron current and ionization source, eventually, defining the operational diagram for the Hall thruster discharge 27,28 .…”