New solutions for target delivery systems are essential for advanced inertial fusion energy (IFE) laser facilities. Original target delivery concept based on magnetic levitation (MAGLEV) technology has been proposed at the Lebedev Physical Institute (LPI). The operational principle is the quantum levitation of Type-II, high-temperature superconductors (HTSC) in gradient magnetic fields. In doing so, a cryogenic target is placed inside a levitating HTSC-sabot, which is accelerated above a permanent magnet guideway system. In this paper, we continue our researches on building a cyclotron accelerator with a limited magnetic track for noncontact target delivery. The target sabot models were made from second-generation high-temperature superconductor (2G-HTSC) tapes with a J-PI-04-20Ag-20 Cu structure and high vortex pinning to ensure levitation stability of the acceleration process. Careful execution of demo experiments (T similar to 80 K) clarify that the HTSC-sabot runs stably above the circular track during its acceleration. The calculation and experimental results are in a good agreement at T similar to 80 K, which allows estimating the running performance of the cyclotron accelerator at operating temperature T similar to 17 K. The estimations have shown that for magnetic fields B similar to 2 T with induction gradients partial derivative B-2/partial derivative x similar to 2 x 10(2) T-2/m, the cyclotron accelerator with a radius of similar to 4 m can overcome the target injection velocity V-inj= 200 m/s at a = 1000g, which is the lower limit for future IFE power plant. For existing laser facilities the velocities 20-100 m/s can be easily reached for a more comfortable acceleration range a = 10-250g. In addition, the article discusses promising research at the LPI in the field of cyclotron acceleration, both from the point of view of selecting new HTSC materials and improving the design of HTSC-sabots. The obtained results provide the design reference for building the higher-performance cyclotron accelerators for IFE.