Effective sine-Gordon model for the static properties of narrow window junctions

We show that the maximum tunneling current for a long thin window Josephson junction in the presence of an external magnetic field is given to a good approximation by the solution of an effective sine-Gordon model with approp riate rescalings. This model is obtained via a reduction of the two-dimensi onal system to a one-dimensional integro-differential equation (nonlocal si ne-Gordon). The passive region introduces an effective Josephson characteri stic length. Using numerical simulations we show that for a narrow junction the cases of inline and overlap current feed are well described by the eff ective model. We discuss the influence of the width of the junction and fin d that the model gives a good approximation for the behavior of large area windows in the inline geometry, while it deviates for the overlap. (C) 1999 American Institute of Physics. [S0021-8979(99)02122-7].