Model of a long Josephson tunnel junction including surface losses and self-pumping effect

We have numerically investigated the dynamics of a long linear Josephson tunnel junction with overlap geometry (Flux-Flow Oscillator, FFO). The study is performed in the frame of a modified sine-Gordon model, which includes surface losses, self-pumping effect, and in an empirical way the superconducting gap. The electromagnetic coupling to the environment is modeled by a simple resistor-capacitor load (RC-load) placed at both ends of the FFO. In our model the damping parameter depends both on the spatial coordinate and on the amplitude of the AC voltage. In order to find the DC current-voltage curves the damping parameter has to be calculated self-consistently by successive approximations and time integration of the perturbed sine-Gordon equation. The modified model gives better qualitative agreement with experimental results than the conventional perturbed sine-Gordon model