The toroidal low-energy particle accumulator is intended for confining and electronic cooling of a circulating positron beam and generating antihydrogen and positronium in flight. Its special features are a longitudinal magnetic field, a spiral particle winding, and a sectional structure of the optical components, which serve to form a closed orbit. The longitudinal magnetic field simultaneously magnetizes the positron beam and as a consequence, ensures a long lifetime for the circulating beam. However, such afield results in strong coupling of the horizontal and vertical degrees of freedom and the appearance of additional resonances. The particle dynamics is simulated using the specially developed BETATRON computer code, based on the BOLIDE program package (for producing interfaces for computational and simulation programs). In the present work, the results of the simulation of particle dynamics and a calculation of the structure functions for a positron storage ring are presented.
