Ion beam emittance on the collective accelerator exit

The conditions of ion production in the electron ring are considered. It is shown that two extreme cases depending on ratio of neutral atoms time of flight across the ring to ionization time are possible: the uniform production of ions in the ring cross section and the production on the ring surface. The dependence of ion magnetic moment on its production point is shown. The change of ion average magnetic moment and its dispersion in the process of step-by-step ionization is found. The minimum possible value of two-size transverse projection of ion beam phase volume is estimated. Distribution functions of ions in the electron ring on transverse and longitudinal velocities are found. Transverse projection configuration of the phase volume in Cartesian coordinates are given after the separation of beam electron and ion components and after ions going out of the magnetic field. The comparison of these projections with the transverse acceptance of the heavy ions synchrotron (HIS) is made. It is shown that the removal of ion azimuthal velocity is required for the beam effective injection into the HIS