Dependence of the maximal superconducting current on the resonance frequency in a shunted Josephson junction

We have analyzed the phase dynamics and current-voltage characteristics of a Josephson junction shunted by an LC circuit. When the Josephson frequency omega (J) becomes equal to the natural frequency omega(rc) of the formed resonance circuit, the I-V curve acquires additional branches. We have studied the features of the rc branch and the superconducting circuit for different values of the resonance frequency. It is shown that the maximal superconducting current through the Josephson junction on the rc-branch depends on the resonance frequency and is determined by the closeness of the end point of the rc branch to the critical current. We have determined the dependence of the maximal superconducting current on the resonance frequency for different values of the dissipation parameters. The limiting value of the maximal superconducting current is independent (to within 1%) of the parameters of the system.