Charging of Superconducting Layers and Novel Type of Hysteresis in   Coupled Josephson Junctions
  A manifestation of a novel type of hysteresis related to the parametric resonance in the system of coupled Josephson junctions is demonstrated. Opposite to McCumber and Steward hysteresis, we find that the width of this hysteresis is inversely proportional to the McCumber parameter and depends also on coupling between junctions and the boundary conditions. An investigation of time dependence of the electric charge in superconducting layers allow us to explain the origin of this hysteresis by different charge dynamics for increasing and decreasing bias current processes. The effect of wavelength of the longitudinal plasma waves created at the resonance on the charging of superconducting layers is demonstrated. We found a strong effect of the dissipation in the system on the amplitude of the charge oscillations at the resonance. 
Yu. M. Shukrinov and Ma. A. Gaafar
cond-mat.supr-con