This report describes a concept of an EIC cooling system, based on a proven induction linac technology with a dc electron beam. The system would operate in a full energy range of proton beams (100 - 270 GeV) and would provide 50-100 A electron beams, circulating in a cooler ring for 5 ms. Every 5 ms a new electron pulse would be injected into the cooler ring to provide continuous cooling at collisions. Operations with a 10-ms cycle is possible but it will reduce the cooling rates by ~30$%$. The system is capable of delivering the required performance in the entire EIC energy range with emittance cooling times of less than 1-2 hours.
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