Particle dynamics in a storage ring with a longitudinal magnetic field

The use of an electron cooling system with a circulating electron beam for the Fermilab Recycler permits to avoid the problems of a traditional electron cooling system and to cool down antiprotons at an energy of 8 GeV. In this system the Recycler ring is equipped with an additional electron ring, which is periodically filled with new cold electrons. The electron beam circulates in a longitudinal (quasitoroidal) magnetic field and long-term stability of the beam is provided by additional spiral coils, which form a quadrupole electrostatic field. Such a ring (called a modified betatron) has been designed in JINR and now is under construction. This ring also was proposed to be used as low-energy positron storage ring (5–20 keV) for positronium generation. The electron cooling of positrons is an essential property of this system. The positronium is generated by recombination of positrons and electrons in the electron cooling section of the ring. The problems of storage of particles with a low momentum spread (Δp/p⩽10−3) in a ring with a longitudinal magnetic field having a racetrack configuration is discussed.