The AC current instability mechanisms are investigated in high-Tc superconductor and superconducting tape at conduction-cooled conditions when the electric field and applied current may essentially exceed the critical values of a superconductor. It is shown that there exist the characteristic times defining the corresponding time windows that are the basis of the existence of the stable AC regimes despite the high values of the induced electric field and the temperature of a superconductor. It is proved that these values are higher than the corresponding values of the electric field and the temperature before the thermal runaway. These states may be defined as stable overloaded regimes. Therefore, high-Tc superconducting magnets are possible to operate stably at AC overloaded regimes and the conduction-cooled conditions, which will be characterized by very high AC losses.
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