Numerical calculation of the height of velocity-matching step of flux-flow type Josephson oscillator

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Abstract
The height of the velocity‐matching step (VM step) of a flux‐flow type Josephson oscillator is studied systematically by numerical simulations. It is defined by the phase velocity of the propagating fluxons equaling that of the electromagnetic wave in the junction structure. The height of VM step (γm) is an important parameter for the practical application of such a device. The results presented on γm are important data in order to save computer time in the simulation of electromagnetic properties, such as the output voltage, at the velocity‐matching condition. The detailed simulations were performed using the perturbed sine‐Gordon equation (PSGE) with a uniformly distributed bias current γ. The PSGE was solved numerically by using an implicit finite‐difference scheme. The distributions of electromagnetic fields in an overlap, long Josephson junction in the flux‐flow state are mapped. The parameters influencing γm are discussed. We show that γm increases almost linearly with an external magnetic field βe or with the quasiparticle damping α, while it is less dependent on surface loss β. γm increases slowly with junction length above a minimum length, and it levels out at long lengths. We also present an approximate expression for γm which fits numerical results well.