A two-stage cascade device is proposed for generating heavy completely stripped atoms. The first stage of an ECR source of 10-GHz type is to produce ions in high charge states. In the second, electrons emitted by an electron gun and a plasma of residual gas are heated under synchrotron gyromagnetic autoresonance (SGA) regime. Such a created SGA plasma under certain conditions might be negatively charged. Ions transported from the first stage into SGA plasma are trapped by an electrostatic pit where they experience further stripping under collisions with energetic electrons. Parameters of the second stage are defined. Computer simulation of ionizing processes shows that for obtaining 1×107 completely stripped argon atoms one should inject 9×109 ions in the state Z=+15 during 36 ms into the second stage where the 10-GHz microwave field accelerates the electrons up to an energy of 200 keV. The residual gas pressure is taken to equal 1×10 -8 Torr.