The dynamics of transients in an overdamped Josephson junction biased by trains of short current pulses with controllable parameters

The paper discusses the development of the method for studying the dynamics of an overdamped Josephson junction biased by a periodic current with controlled parameters, suggested earlier by the authors. The results obtained allow several known experimental observations to be explained. Analytic expressions for the rate of transient process damping and energy expenditures necessary for switching a Josephson junction from one quantum state to another are derived. Problems of interactions between the bias current and supercurrent and the influence of cos?-type terms on the rates of transient process damping and energy conversion are discussed. The results for junction biasing by short (uni-or bipolar) δ function-shaped pulses are obtained in the form of exact analytic expressions. Diagrams illustrating the dependence of the Shapiro step width on the shape of biasing pulses are given.