Parametric excitation of plasma oscillations in Josephson Junctions

A theory is presented for parametric excitation of plasma oscillations in a Josephson junction biased in the zero voltage mode. A threshold curve for the onset of the parametric excitation is deduced via the stability properties of a Mathieu differential equation obtained by a self-consistent linearization procedure. The important parameters turn out to be the plasma frequency and the circuit losses. The results of the calculation are compared with the experiments performed on a Josephson junction analog and good agreement is obtained. It is suggested that the effect should be observable in tunnel junctions, but perhaps less likely in point contacts.