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applied flux approximately arcsin bridge cali circulating current critical cur critical phase angle cryostat current density current vs reduced curve data taken Deaver determined devices differential amplifier diode earlier field fluctuation tail flux jump flux-flow model fluxoid grains granular Gubser heater current hysteretic ideal Josephson junction lead cylinder linear region liquid helium magnetic magnitude maximum critical current measure microwave data microwave frequencies NbN cylinder NbN weak links nitric acid non-hysteretic regime output voltage parameter phase difference Phys pick-up coil plots quantized quantum mechanical R.L. Steiner ratio reduced temperature residual field S.A. Wolf sample area sample NN45 screening current signal sinusoidal current-phase relation slope solenoid SQUID output stainless steel tubes static current-phase relation superconducting ring temperature for sample temperature independent thermal equilibrium tion total flux traces transition temperature University of Virginia vacuum vector potential versus temperature x-axis y-axis calibration zero