Impedance of small superconductors in a relaxation-oscillation mode

A study of the impedance of small superconductors operating in the relaxation-oscillation mode using numerical simulation of the relaxation oscillation and its interaction with an external signal is reported. The simulation is based on the equation for the superconducting current component which applies to the time interval between the two operations of the superconductor; the impedance is determined as the ratio of the particular harmonic of the voltage across the superconductor to the external current in the stationary state when the effect of the arbitrarily selected initial conditions can be ignored. The impedance for a small superconductor in the relaxation model showed singularities due to synchronization of the oscillations, including the region of the subharmonic steps of the voltage-current characteristics; therefore, this model reflects the actual nature of the oscillation better than the resistive model for which the singularities are found only in the region of harmonic steps.