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Particle accelerator complex NICA (Nuclotron-based Ion Collider fAcility) comprises superconducting Booster and Nuclotron synchrotrons which magnets operating at pulse mode in opposite phase with period of about 4 seconds. Summary stored energy of Booster and Nuclotron magnets will vary from 1 to 2.6 MJ during the period. NICA power supply system can be significantly improved by Superconducting Magnetic Energy Storage (SMES) application that will help to move the energy back and force between Booster and Nuclotron. The useful energy at this SMES must be about 1.6 MJ so the maximum total SMES energy should be 3-5 MJ. SMES with this energy should have several Tesla magnetic fields to keep a reasonable size. SMES operating current can be not less than Booster and Nuclotron magnets current so it might be 10-12 kA. It is better to make such a SMES magnet from an HTS (high temperature superconductor) cable for the stability at 6-7 T and 4 s pulse mode. The SMES magnet is planned to be wound as a short solenoid (Brooks coil) of cables optimized for several coaxial sections. HTS cables with helical structure similar to well-known CORC (conductors on round core) cables are under the development at JINR. The HTS cabling technology is based on the same principle as Nuclotron type cable manufacturing technology. HTS tapes, cables and magnets experimental study and testing methods are being developed on the base of an existing test facility at LHEP. First HTS cable short sample with 6 HTS tapes was prepared and tested at 77 K in self-field. Its critical current is about 800 A that will allow achieve required operating currents of SMES magnet with a reasonable amount of HTS tapes in cables. Developments of high field high current fast cycling HTS magnets for accelerators are also being planned at JINR.

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