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Theoretical model of the fast fault current limiter based on an air core transformer, the secondary winding of which is loaded with high-Tc superconductor (HTSC) sample, has been analyzed. The fault current limiter was designed to protect a strong magnetic field pulse generation system. Transformer parameters and HTSC sample resistance in the normal state have been chosen to provide the fault current limitation efficiency. The current limiting dynamics was investigated by solving nonlinear system of equations. A detailed explanation of the results is presented. It is shown that application of the fault current limiter allows us to increase the initial reservoir capacitor voltage of the protected system up to 2.6 times.