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We demonstrate control of the thermal hysteresis in superconducting constrictions by adding a resistive shunt. In order to prevent thermal relaxation oscillations, the shunt resistor is placed in close vicinity of the constriction, making the inductive current-switching time smaller than the thermal equilibration time. We investigate the current-voltage characteristics of the same constriction with and without the shunt-resistor. The widening of the hysteresis-free temperature range is explained on the basis of a simple model.

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