The main goal of the Tera Watt A Cumulator project (Institute for Theoretical and Experimental Physics, Moscow) is accumulation in the storage ring of an intense ion beam, its longitudinal compression and the use of the extracted beam for plasma experiments. However, beam parameters at the target are decreased because of extreme transverse heating and growth of the beam momentum spread due to intrabeam scattering. These effects can be suppressed by application of the electron cooling system (ECS). Design study of ECS has been performed in the Joint Institute for Nuclear Research. The design project and characteristics of the system are described, as well as analysis of the accumulation kinetics in the presence of the cooling system. Design work has shown that because of the small length of the straight section (2.35 m), the effective length of the cooling system is small (about 55–60 cm). Nevertheless, for long accumulation times (>100 s), the system allows us to significantly improve the beam parameters at the target (specific energy, specific power, and so on) and to suppress the beam losses by an order of magnitude.