The particle dynamics in the electron cooling system based on the modified betatron

The electron cooling system with circulating electron beam is considered for the cooling of ions of energy of few GeV. The prototype of the electron cooling system based on modified betatron for cooling of antiprotons in the Recycler ring (Fermilab) is under development in the JINR. The peculiarities of the modified betatron are its section structure, the longitudinal guiding magnetic field and the quadrupole spiral field used to form a closed orbit. The longitudinal magnetic field provides the electron magnetisation and long lifetime of the circulating electrons as the strong coupling between the horizontal and vertical degrees of freedom and leads to additional resonances.